Random errors in interferometry with the least-squares method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Qi

2011-01-20

This investigation analyzes random errors in interferometric surface profilers using the least-squares method when random noises are present. Two types of random noise are considered here: intensity noise and position noise. Two formulas have been derived for estimating the standard deviations of the surface height measurements: one is for estimating the standard deviation when only intensity noise is present, and the other is for estimating the standard deviation when only position noise is present. Measurements on simulated noisy interferometric data have been performed, and standard deviations of the simulated measurements have been compared with those theoretically derived. The relationships havemore » also been discussed between random error and the wavelength of the light source and between random error and the amplitude of the interference fringe.« less

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Error Analyses of the North Alabama Lightning Mapping Array (LMA)

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Solokiewicz, R. J.; Blakeslee, R. J.; Goodman, S. J.; Christian, H. J.; Hall, J. M.; Bailey, J. C.; Krider, E. P.; Bateman, M. G.; Boccippio, D. J.

2003-01-01

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA-MSFC and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results, except that the chi-squared theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

A Comparison of Normal and Elliptical Estimation Methods in Structural Equation Models.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Cheevatanarak, Suchittra

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

A Canonical Ensemble Correlation Prediction Model for Seasonal Precipitation Anomaly

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Guilong

2001-01-01

This report describes an optimal ensemble forecasting model for seasonal precipitation and its error estimation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. This new CCA model includes the following features: (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States precipitation field. The predictor is the sea surface temperature.

An Investigation of the Standard Errors of Expected A Posteriori Ability Estimates.

ERIC Educational Resources Information Center

De Ayala, R. J.; And Others

Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the…

Modeling Multiplicative Error Variance: An Example Predicting Tree Diameter from Stump Dimensions in Baldcypress

Treesearch

Bernard R. Parresol

1993-01-01

In the context of forest modeling, it is often reasonable to assume a multiplicative heteroscedastic error structure to the data. Under such circumstances ordinary least squares no longer provides minimum variance estimates of the model parameters. Through study of the error structure, a suitable error variance model can be specified and its parameters estimated. This...

Systematic Error Modeling and Bias Estimation

PubMed Central

Zhang, Feihu; Knoll, Alois

2016-01-01

This paper analyzes the statistic properties of the systematic error in terms of range and bearing during the transformation process. Furthermore, we rely on a weighted nonlinear least square method to calculate the biases based on the proposed models. The results show the high performance of the proposed approach for error modeling and bias estimation. PMID:27213386

Optimal estimation of large structure model errors. [in Space Shuttle controller design

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1979-01-01

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

RLS Channel Estimation with Adaptive Forgetting Factor for DS-CDMA Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Kojima, Yohei; Tomeba, Hiromichi; Takeda, Kazuaki; Adachi, Fumiyuki

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can increase the downlink bit error rate (BER) performance of DS-CDMA beyond that possible with conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. Recently, we proposed a pilot-assisted channel estimation (CE) based on the MMSE criterion. Using MMSE-CE, the channel estimation accuracy is almost insensitive to the pilot chip sequence, and a good BER performance is achieved. In this paper, we propose a channel estimation scheme using one-tap recursive least square (RLS) algorithm, where the forgetting factor is adapted to the changing channel condition by the least mean square (LMS)algorithm, for DS-CDMA with FDE. We evaluate the BER performance using RLS-CE with adaptive forgetting factor in a frequency-selective fast Rayleigh fading channel by computer simulation.

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

NASA Astrophysics Data System (ADS)

Behnabian, Behzad; Mashhadi Hossainali, Masoud; Malekzadeh, Ahad

2018-02-01

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.

Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

NASA Astrophysics Data System (ADS)

Zhang, Ling; Cai, Yunlong; Li, Chunguang; de Lamare, Rodrigo C.

2017-12-01

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

The Influence of Dimensionality on Estimation in the Partial Credit Model.

ERIC Educational Resources Information Center

De Ayala, R. J.

1995-01-01

The effect of multidimensionality on partial credit model parameter estimation was studied with noncompensatory and compensatory data. Analysis results, consisting of root mean square error bias, Pearson product-moment corrections, standardized root mean squared differences, standardized differences between means, and descriptive statistics…

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

Difference-based ridge-type estimator of parameters in restricted partial linear model with correlated errors.

PubMed

Wu, Jibo

2016-01-01

In this article, a generalized difference-based ridge estimator is proposed for the vector parameter in a partial linear model when the errors are dependent. It is supposed that some additional linear constraints may hold to the whole parameter space. Its mean-squared error matrix is compared with the generalized restricted difference-based estimator. Finally, the performance of the new estimator is explained by a simulation study and a numerical example.

Bias correction by use of errors-in-variables regression models in studies with K-X-ray fluorescence bone lead measurements.

PubMed

Lamadrid-Figueroa, Héctor; Téllez-Rojo, Martha M; Angeles, Gustavo; Hernández-Ávila, Mauricio; Hu, Howard

2011-01-01

In-vivo measurement of bone lead by means of K-X-ray fluorescence (KXRF) is the preferred biological marker of chronic exposure to lead. Unfortunately, considerable measurement error associated with KXRF estimations can introduce bias in estimates of the effect of bone lead when this variable is included as the exposure in a regression model. Estimates of uncertainty reported by the KXRF instrument reflect the variance of the measurement error and, although they can be used to correct the measurement error bias, they are seldom used in epidemiological statistical analyzes. Errors-in-variables regression (EIV) allows for correction of bias caused by measurement error in predictor variables, based on the knowledge of the reliability of such variables. The authors propose a way to obtain reliability coefficients for bone lead measurements from uncertainty data reported by the KXRF instrument and compare, by the use of Monte Carlo simulations, results obtained using EIV regression models vs. those obtained by the standard procedures. Results of the simulations show that Ordinary Least Square (OLS) regression models provide severely biased estimates of effect, and that EIV provides nearly unbiased estimates. Although EIV effect estimates are more imprecise, their mean squared error is much smaller than that of OLS estimates. In conclusion, EIV is a better alternative than OLS to estimate the effect of bone lead when measured by KXRF. Copyright © 2010 Elsevier Inc. All rights reserved.

Comparing Parameter Estimation Techniques for an Electrical Power Transformer Oil Temperature Prediction Model

NASA Technical Reports Server (NTRS)

Morris, A. Terry

1999-01-01

This paper examines various sources of error in MIT's improved top oil temperature rise over ambient temperature model and estimation process. The sources of error are the current parameter estimation technique, quantization noise, and post-processing of the transformer data. Results from this paper will show that an output error parameter estimation technique should be selected to replace the current least squares estimation technique. The output error technique obtained accurate predictions of transformer behavior, revealed the best error covariance, obtained consistent parameter estimates, and provided for valid and sensible parameters. This paper will also show that the output error technique should be used to minimize errors attributed to post-processing (decimation) of the transformer data. Models used in this paper are validated using data from a large transformer in service.

Hazard Function Estimation with Cause-of-Death Data Missing at Random.

PubMed

Wang, Qihua; Dinse, Gregg E; Liu, Chunling

2012-04-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.

Eta Squared, Partial Eta Squared, and Misreporting of Effect Size in Communication Research.

ERIC Educational Resources Information Center

Levine, Timothy R.; Hullett, Craig R.

2002-01-01

Alerts communication researchers to potential errors stemming from the use of SPSS (Statistical Package for the Social Sciences) to obtain estimates of eta squared in analysis of variance (ANOVA). Strives to clarify issues concerning the development and appropriate use of eta squared and partial eta squared in ANOVA. Discusses the reporting of…

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Comparison of structural and least-squares lines for estimating geologic relations

USGS Publications Warehouse

Williams, G.P.; Troutman, B.M.

1990-01-01

Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.

Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration

NASA Astrophysics Data System (ADS)

Zhou, Y.; Zhang, X.; Xiao, W.

2018-04-01

As the geomagnetic sensor is susceptible to interference, a pre-processing total least square iteration method is proposed for calibration compensation. Firstly, the error model of the geomagnetic sensor is analyzed and the correction model is proposed, then the characteristics of the model are analyzed and converted into nine parameters. The geomagnetic data is processed by Hilbert transform (HHT) to improve the signal-to-noise ratio, and the nine parameters are calculated by using the combination of Newton iteration method and the least squares estimation method. The sifter algorithm is used to filter the initial value of the iteration to ensure that the initial error is as small as possible. The experimental results show that this method does not need additional equipment and devices, can continuously update the calibration parameters, and better than the two-step estimation method, it can compensate geomagnetic sensor error well.

Multistage estimation of received carrier signal parameters under very high dynamic conditions of the receiver

NASA Technical Reports Server (NTRS)

Kumar, Rajendra (Inventor)

1991-01-01

A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.

Multistage estimation of received carrier signal parameters under very high dynamic conditions of the receiver

NASA Technical Reports Server (NTRS)

Kumar, Rajendra (Inventor)

1990-01-01

A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.

A channel estimation scheme for MIMO-OFDM systems

NASA Astrophysics Data System (ADS)

He, Chunlong; Tian, Chu; Li, Xingquan; Zhang, Ce; Zhang, Shiqi; Liu, Chaowen

2017-08-01

In view of the contradiction of the time-domain least squares (LS) channel estimation performance and the practical realization complexity, a reduced complexity channel estimation method for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) based on pilot is obtained. This approach can transform the complexity of MIMO-OFDM channel estimation problem into a simple single input single output-orthogonal frequency division multiplexing (SISO-OFDM) channel estimation problem and therefore there is no need for large matrix pseudo-inverse, which greatly reduces the complexity of algorithms. Simulation results show that the bit error rate (BER) performance of the obtained method with time orthogonal training sequences and linear minimum mean square error (LMMSE) criteria is better than that of time-domain LS estimator and nearly optimal performance.

Empirical State Error Covariance Matrix for Batch Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joe

2015-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

A weighted least squares estimation of the polynomial regression model on paddy production in the area of Kedah and Perlis

NASA Astrophysics Data System (ADS)

Musa, Rosliza; Ali, Zalila; Baharum, Adam; Nor, Norlida Mohd

2017-08-01

The linear regression model assumes that all random error components are identically and independently distributed with constant variance. Hence, each data point provides equally precise information about the deterministic part of the total variation. In other words, the standard deviations of the error terms are constant over all values of the predictor variables. When the assumption of constant variance is violated, the ordinary least squares estimator of regression coefficient lost its property of minimum variance in the class of linear and unbiased estimators. Weighted least squares estimation are often used to maximize the efficiency of parameter estimation. A procedure that treats all of the data equally would give less precisely measured points more influence than they should have and would give highly precise points too little influence. Optimizing the weighted fitting criterion to find the parameter estimates allows the weights to determine the contribution of each observation to the final parameter estimates. This study used polynomial model with weighted least squares estimation to investigate paddy production of different paddy lots based on paddy cultivation characteristics and environmental characteristics in the area of Kedah and Perlis. The results indicated that factors affecting paddy production are mixture fertilizer application cycle, average temperature, the squared effect of average rainfall, the squared effect of pest and disease, the interaction between acreage with amount of mixture fertilizer, the interaction between paddy variety and NPK fertilizer application cycle and the interaction between pest and disease and NPK fertilizer application cycle.

Hazard Function Estimation with Cause-of-Death Data Missing at Random

PubMed Central

Wang, Qihua; Dinse, Gregg E.; Liu, Chunling

2010-01-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data. PMID:22267874

The Estimation of Gestational Age at Birth in Database Studies.

PubMed

Eberg, Maria; Platt, Robert W; Filion, Kristian B

2017-11-01

Studies on the safety of prenatal medication use require valid estimation of the pregnancy duration. However, gestational age is often incompletely recorded in administrative and clinical databases. Our objective was to compare different approaches to estimating the pregnancy duration. Using data from the Clinical Practice Research Datalink and Hospital Episode Statistics, we examined the following four approaches to estimating missing gestational age: (1) generalized estimating equations for longitudinal data; (2) multiple imputation; (3) estimation based on fetal birth weight and sex; and (4) conventional approaches that assigned a fixed value (39 weeks for all or 39 weeks for full term and 35 weeks for preterm). The gestational age recorded in Hospital Episode Statistics was considered the gold standard. We conducted a simulation study comparing the described approaches in terms of estimated bias and mean square error. A total of 25,929 infants from 22,774 mothers were included in our "gold standard" cohort. The smallest average absolute bias was observed for the generalized estimating equation that included birth weight, while the largest absolute bias occurred when assigning 39-week gestation to all those with missing values. The smallest mean square errors were detected with generalized estimating equations while multiple imputation had the highest mean square errors. The use of generalized estimating equations resulted in the most accurate estimation of missing gestational age when birth weight information was available. In the absence of birth weight, assignment of fixed gestational age based on term/preterm status may be the optimal approach.

Multilevel Modeling and Ordinary Least Squares Regression: How Comparable Are They?

ERIC Educational Resources Information Center

Huang, Francis L.

2018-01-01

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques…

Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.

PubMed

Wang, Xin; Li, Yan; Wei, Haoyun; Chen, Xia

2017-06-01

Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors (RSS) from the three quantitative analyses were compared. In methane gas analysis, SWLS yielded the lowest SEP and RSS among the three methods. In methane/toluene mixture gas analysis, a modification of the SWLS has been presented to tackle the bias error from other components. The SWLS without modification presents the lowest SEP in all cases but not bias and RSS. The modification of SWLS reduced the bias, which showed a lower RSS than CLS, especially for small components.

Modified fast frequency acquisition via adaptive least squares algorithm

NASA Technical Reports Server (NTRS)

Kumar, Rajendra (Inventor)

1992-01-01

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error.

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard; Felus, Yaron A.

2008-06-01

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

NASA Technical Reports Server (NTRS)

Erkmen, Baris I.; Moision, Bruce E.

2010-01-01

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Optimally weighted least-squares steganalysis

NASA Astrophysics Data System (ADS)

Ker, Andrew D.

2007-02-01

Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first derivation of estimation error, for a certain method of steganalysis (the Least-Squares variant of Sample Pairs Analysis) of LSB replacement steganography in digital images. In this paper we make use of our theoretical results to find an improved estimator and detector. We also extend the theoretical analysis to another (more accurate) steganalysis estimator (Triples Analysis) and hence derive an improved version of that estimator too. Experimental results show that the new steganalyzers have improved accuracy, particularly in the difficult case of never-compressed covers.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

PubMed

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Optimized tuner selection for engine performance estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L. (Inventor); Garg, Sanjay (Inventor)

2013-01-01

A methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. Theoretical Kalman filter estimation error bias and variance values are derived at steady-state operating conditions, and the tuner selection routine is applied to minimize these values. The new methodology yields an improvement in on-line engine performance estimation accuracy.

Attenuation of the Squared Canonical Correlation Coefficient under Varying Estimates of Score Reliability

ERIC Educational Resources Information Center

Wilson, Celia M.

2010-01-01

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability.…

Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies

PubMed Central

Palmer, Tom M; Holmes, Michael V; Keating, Brendan J; Sheehan, Nuala A

2017-01-01

Abstract Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors. PMID:29106476

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

An Interactive Computer Package for Use with Simulation Models Which Performs Multidimensional Sensitivity Analysis by Employing the Techniques of Response Surface Methodology.

DTIC Science & Technology

1984-12-01

total sum of squares at the center points minus the correction factor for the mean at the center points ( SSpe =Y’Y-nlY), where n1 is the number of...SSlac=SSres- SSpe ). The sum of squares due to pure error estimates 0" and the sum of squares due to lack-of-fit estimates 0’" plus a bias term if...Response Surface Methodology Source d.f. SS MS Regression n b’X1 Y b’XVY/n Residual rn-n Y’Y-b’X’ *Y (Y’Y-b’X’Y)/(n-n) Pure Error ni-i Y’Y-nl1Y SSpe / (ni

On the robustness of a Bayes estimate. [in reliability theory

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Methods for estimating the magnitude and frequency of peak streamflows at ungaged sites in and near the Oklahoma Panhandle

USGS Publications Warehouse

Smith, S. Jerrod; Lewis, Jason M.; Graves, Grant M.

2015-09-28

Generalized-least-squares multiple-linear regression analysis was used to formulate regression relations between peak-streamflow frequency statistics and basin characteristics. Contributing drainage area was the only basin characteristic determined to be statistically significant for all percentage of annual exceedance probabilities and was the only basin characteristic used in regional regression equations for estimating peak-streamflow frequency statistics on unregulated streams in and near the Oklahoma Panhandle. The regression model pseudo-coefficient of determination, converted to percent, for the Oklahoma Panhandle regional regression equations ranged from about 38 to 63 percent. The standard errors of prediction and the standard model errors for the Oklahoma Panhandle regional regression equations ranged from about 84 to 148 percent and from about 76 to 138 percent, respectively. These errors were comparable to those reported for regional peak-streamflow frequency regression equations for the High Plains areas of Texas and Colorado. The root mean square errors for the Oklahoma Panhandle regional regression equations (ranging from 3,170 to 92,000 cubic feet per second) were less than the root mean square errors for the Oklahoma statewide regression equations (ranging from 18,900 to 412,000 cubic feet per second); therefore, the Oklahoma Panhandle regional regression equations produce more accurate peak-streamflow statistic estimates for the irrigated period of record in the Oklahoma Panhandle than do the Oklahoma statewide regression equations. The regression equations developed in this report are applicable to streams that are not substantially affected by regulation, impoundment, or surface-water withdrawals. These regression equations are intended for use for stream sites with contributing drainage areas less than or equal to about 2,060 square miles, the maximum value for the independent variable used in the regression analysis.

Retrieval of the aerosol optical thickness from UV global irradiance measurements

NASA Astrophysics Data System (ADS)

Costa, M. J.; Salgueiro, V.; Bortoli, D.; Obregón, M. A.; Antón, M.; Silva, A. M.

2015-12-01

The UV irradiance is measured at Évora since several years, where a CIMEL sunphotometer integrated in AERONET is also installed. In the present work, measurements of UVA (315 - 400 nm) irradiances taken with Kipp&Zonen radiometers, as well as satellite data of ozone total column values, are used in combination with radiative transfer calculations, to estimate the aerosol optical thickness (AOT) in the UV. The retrieved UV AOT in Évora is compared with AERONET AOT (at 340 and 380 nm) and a fairly good agreement is found with a root mean square error of 0.05 (normalized root mean square error of 8.3%) and a mean absolute error of 0.04 (mean percentage error of 2.9%). The methodology is then used to estimate the UV AOT in Sines, an industrialized site on the Atlantic western coast, where the UV irradiance is monitored since 2013 but no aerosol information is available.

August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

USGS Publications Warehouse

Lombard, Pamela J.; Tasker, Gary D.; Nielsen, Martha G.

2003-01-01

Methods for estimating August median streamflow were developed for ungaged, unregulated streams in the eastern part of Aroostook County, Maine, with drainage areas from 0.38 to 43 square miles and mean basin elevations from 437 to 1,024 feet. Few long-term, continuous-record streamflow-gaging stations with small drainage areas were available from which to develop the equations; therefore, 24 partial-record gaging stations were established in this investigation. A mathematical technique for estimating a standard low-flow statistic, August median streamflow, at partial-record stations was applied by relating base-flow measurements at these stations to concurrent daily flows at nearby long-term, continuous-record streamflow- gaging stations (index stations). Generalized least-squares regression analysis (GLS) was used to relate estimates of August median streamflow at gaging stations to basin characteristics at these same stations to develop equations that can be applied to estimate August median streamflow on ungaged streams. GLS accounts for varying periods of record at the gaging stations and the cross correlation of concurrent streamflows among gaging stations. Twenty-three partial-record stations and one continuous-record station were used for the final regression equations. The basin characteristics of drainage area and mean basin elevation are used in the calculated regression equation for ungaged streams to estimate August median flow. The equation has an average standard error of prediction from -38 to 62 percent. A one-variable equation uses only drainage area to estimate August median streamflow when less accuracy is acceptable. This equation has an average standard error of prediction from -40 to 67 percent. Model error is larger than sampling error for both equations, indicating that additional basin characteristics could be important to improved estimates of low-flow statistics. Weighted estimates of August median streamflow, which can be used when making estimates at partial-record or continuous-record gaging stations, range from 0.03 to 11.7 cubic feet per second or from 0.1 to 0.4 cubic feet per second per square mile. Estimates of August median streamflow on ungaged streams in the eastern part of Aroostook County, within the range of acceptable explanatory variables, range from 0.03 to 30 cubic feet per second or 0.1 to 0.7 cubic feet per second per square mile. Estimates of August median streamflow per square mile of drainage area generally increase as mean elevation and drainage area increase.

Channel estimation in few mode fiber mode division multiplexing transmission system

NASA Astrophysics Data System (ADS)

Hei, Yongqiang; Li, Li; Li, Wentao; Li, Xiaohui; Shi, Guangming

2018-03-01

It is abundantly clear that obtaining the channel state information (CSI) is of great importance for the equalization and detection in coherence receivers. However, to the best of the authors' knowledge, in most of the existing literatures, CSI is assumed to be perfectly known at the receiver. So far, few literature discusses the effects of imperfect CSI on MDM system performance caused by channel estimation. Motivated by that, in this paper, the channel estimation in few mode fiber (FMF) mode division multiplexing (MDM) system is investigated, in which two classical channel estimation methods, i.e., least square (LS) method and minimum mean square error (MMSE) method, are discussed with the assumption of the spatially white noise lumped at the receiver side of MDM system. Both the capacity and BER performance of MDM system affected by mode-dependent gain or loss (MDL) with different channel estimation errors have been studied. Simulation results show that the capacity and BER performance can be further deteriorated in MDM system by the channel estimation, and an 1e-3 variance of channel estimation error is acceptable in MDM system with 0-6 dB MDL values.

Effects of shape, size, and chromaticity of stimuli on estimated size in normally sighted, severely myopic, and visually impaired students.

PubMed

Huang, Kuo-Chen; Wang, Hsiu-Feng; Chen, Chun-Ching

2010-06-01

Effects of shape, size, and chromaticity of stimuli on participants' errors when estimating the size of simultaneously presented standard and comparison stimuli were examined. 48 Taiwanese college students ages 20 to 24 years old (M = 22.3, SD = 1.3) participated. Analysis showed that the error for estimated size was significantly greater for those in the low-vision group than for those in the normal-vision and severe-myopia groups. The errors were significantly greater with green and blue stimuli than with red stimuli. Circular stimuli produced smaller mean errors than did square stimuli. The actual size of the standard stimulus significantly affected the error for estimated size. Errors for estimations using smaller sizes were significantly higher than when the sizes were larger. Implications of the results for graphics-based interface design, particularly when taking account of visually impaired users, are discussed.

Error estimation of deformable image registration of pulmonary CT scans using convolutional neural networks.

PubMed

Eppenhof, Koen A J; Pluim, Josien P W

2018-04-01

Error estimation in nonlinear medical image registration is a nontrivial problem that is important for validation of registration methods. We propose a supervised method for estimation of registration errors in nonlinear registration of three-dimensional (3-D) images. The method is based on a 3-D convolutional neural network that learns to estimate registration errors from a pair of image patches. By applying the network to patches centered around every voxel, we construct registration error maps. The network is trained using a set of representative images that have been synthetically transformed to construct a set of image pairs with known deformations. The method is evaluated on deformable registrations of inhale-exhale pairs of thoracic CT scans. Using ground truth target registration errors on manually annotated landmarks, we evaluate the method's ability to estimate local registration errors. Estimation of full domain error maps is evaluated using a gold standard approach. The two evaluation approaches show that we can train the network to robustly estimate registration errors in a predetermined range, with subvoxel accuracy. We achieved a root-mean-square deviation of 0.51 mm from gold standard registration errors and of 0.66 mm from ground truth landmark registration errors.

High-Accuracy Decoupling Estimation of the Systematic Coordinate Errors of an INS and Intensified High Dynamic Star Tracker Based on the Constrained Least Squares Method

PubMed Central

Jiang, Jie; Yu, Wenbo; Zhang, Guangjun

2017-01-01

Navigation accuracy is one of the key performance indicators of an inertial navigation system (INS). Requirements for an accuracy assessment of an INS in a real work environment are exceedingly urgent because of enormous differences between real work and laboratory test environments. An attitude accuracy assessment of an INS based on the intensified high dynamic star tracker (IHDST) is particularly suitable for a real complex dynamic environment. However, the coupled systematic coordinate errors of an INS and the IHDST severely decrease the attitude assessment accuracy of an INS. Given that, a high-accuracy decoupling estimation method of the above systematic coordinate errors based on the constrained least squares (CLS) method is proposed in this paper. The reference frame of the IHDST is firstly converted to be consistent with that of the INS because their reference frames are completely different. Thereafter, the decoupling estimation model of the systematic coordinate errors is established and the CLS-based optimization method is utilized to estimate errors accurately. After compensating for error, the attitude accuracy of an INS can be assessed based on IHDST accurately. Both simulated experiments and real flight experiments of aircraft are conducted, and the experimental results demonstrate that the proposed method is effective and shows excellent performance for the attitude accuracy assessment of an INS in a real work environment. PMID:28991179

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 2. Applications

USGS Publications Warehouse

Cooley, Richard L.

1983-01-01

This paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability. Consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions. First, if the parameters are properly scaled, linearized expressions for the mean square error (MSE) in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear. Second, by using prior information, the MSE in properly scaled parameters can be reduced greatly over the MSE of ordinary least squares estimates of parameters. Third, plots of estimated MSE and the estimated standard deviation of MSE versus an auxiliary parameter (the ridge parameter) specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates. Fourth, proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information. Results of a case study of Truckee Meadows, Reno-Sparks area, Washoe County, Nevada, conform closely to the results of the hypothetical problem. In the Truckee Meadows case, incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares. However, the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares.

Estimating Relative Positions of Outer-Space Structures

NASA Technical Reports Server (NTRS)

Balian, Harry; Breckenridge, William; Brugarolas, Paul

2009-01-01

A computer program estimates the relative position and orientation of two structures from measurements, made by use of electronic cameras and laser range finders on one structure, of distances and angular positions of fiducial objects on the other structure. The program was written specifically for use in determining errors in the alignment of large structures deployed in outer space from a space shuttle. The program is based partly on equations for transformations among the various coordinate systems involved in the measurements and on equations that account for errors in the transformation operators. It computes a least-squares estimate of the relative position and orientation. Sequential least-squares estimates, acquired at a measurement rate of 4 Hz, are averaged by passing them through a fourth-order Butterworth filter. The program is executed in a computer aboard the space shuttle, and its position and orientation estimates are displayed to astronauts on a graphical user interface.

Functional Mixed Effects Model for Small Area Estimation.

PubMed

Maiti, Tapabrata; Sinha, Samiran; Zhong, Ping-Shou

2016-09-01

Functional data analysis has become an important area of research due to its ability of handling high dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models, and in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area level data, and fit a varying coefficient linear mixed effect model where the varying coefficients are semi-parametrically modeled via B-splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors, and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.

The Use of Neural Networks in Identifying Error Sources in Satellite-Derived Tropical SST Estimates

PubMed Central

Lee, Yung-Hsiang; Ho, Chung-Ru; Su, Feng-Chun; Kuo, Nan-Jung; Cheng, Yu-Hsin

2011-01-01

An neural network model of data mining is used to identify error sources in satellite-derived tropical sea surface temperature (SST) estimates from thermal infrared sensors onboard the Geostationary Operational Environmental Satellite (GOES). By using the Back Propagation Network (BPN) algorithm, it is found that air temperature, relative humidity, and wind speed variation are the major factors causing the errors of GOES SST products in the tropical Pacific. The accuracy of SST estimates is also improved by the model. The root mean square error (RMSE) for the daily SST estimate is reduced from 0.58 K to 0.38 K and mean absolute percentage error (MAPE) is 1.03%. For the hourly mean SST estimate, its RMSE is also reduced from 0.66 K to 0.44 K and the MAPE is 1.3%. PMID:22164030

An analysis of input errors in precipitation-runoff models using regression with errors in the independent variables

USGS Publications Warehouse

Troutman, Brent M.

1982-01-01

Errors in runoff prediction caused by input data errors are analyzed by treating precipitation-runoff models as regression (conditional expectation) models. Independent variables of the regression consist of precipitation and other input measurements; the dependent variable is runoff. In models using erroneous input data, prediction errors are inflated and estimates of expected storm runoff for given observed input variables are biased. This bias in expected runoff estimation results in biased parameter estimates if these parameter estimates are obtained by a least squares fit of predicted to observed runoff values. The problems of error inflation and bias are examined in detail for a simple linear regression of runoff on rainfall and for a nonlinear U.S. Geological Survey precipitation-runoff model. Some implications for flood frequency analysis are considered. A case study using a set of data from Turtle Creek near Dallas, Texas illustrates the problems of model input errors.

Chemical library subset selection algorithms: a unified derivation using spatial statistics.

PubMed

Hamprecht, Fred A; Thiel, Walter; van Gunsteren, Wilfred F

2002-01-01

If similar compounds have similar activity, rational subset selection becomes superior to random selection in screening for pharmacological lead discovery programs. Traditional approaches to this experimental design problem fall into two classes: (i) a linear or quadratic response function is assumed (ii) some space filling criterion is optimized. The assumptions underlying the first approach are clear but not always defendable; the second approach yields more intuitive designs but lacks a clear theoretical foundation. We model activity in a bioassay as realization of a stochastic process and use the best linear unbiased estimator to construct spatial sampling designs that optimize the integrated mean square prediction error, the maximum mean square prediction error, or the entropy. We argue that our approach constitutes a unifying framework encompassing most proposed techniques as limiting cases and sheds light on their underlying assumptions. In particular, vector quantization is obtained, in dimensions up to eight, in the limiting case of very smooth response surfaces for the integrated mean square error criterion. Closest packing is obtained for very rough surfaces under the integrated mean square error and entropy criteria. We suggest to use either the integrated mean square prediction error or the entropy as optimization criteria rather than approximations thereof and propose a scheme for direct iterative minimization of the integrated mean square prediction error. Finally, we discuss how the quality of chemical descriptors manifests itself and clarify the assumptions underlying the selection of diverse or representative subsets.

Per-pixel bias-variance decomposition of continuous errors in data-driven geospatial modeling: A case study in environmental remote sensing

NASA Astrophysics Data System (ADS)

Gao, Jing; Burt, James E.

2017-12-01

This study investigates the usefulness of a per-pixel bias-variance error decomposition (BVD) for understanding and improving spatially-explicit data-driven models of continuous variables in environmental remote sensing (ERS). BVD is a model evaluation method originated from machine learning and have not been examined for ERS applications. Demonstrated with a showcase regression tree model mapping land imperviousness (0-100%) using Landsat images, our results showed that BVD can reveal sources of estimation errors, map how these sources vary across space, reveal the effects of various model characteristics on estimation accuracy, and enable in-depth comparison of different error metrics. Specifically, BVD bias maps can help analysts identify and delineate model spatial non-stationarity; BVD variance maps can indicate potential effects of ensemble methods (e.g. bagging), and inform efficient training sample allocation - training samples should capture the full complexity of the modeled process, and more samples should be allocated to regions with more complex underlying processes rather than regions covering larger areas. Through examining the relationships between model characteristics and their effects on estimation accuracy revealed by BVD for both absolute and squared errors (i.e. error is the absolute or the squared value of the difference between observation and estimate), we found that the two error metrics embody different diagnostic emphases, can lead to different conclusions about the same model, and may suggest different solutions for performance improvement. We emphasize BVD's strength in revealing the connection between model characteristics and estimation accuracy, as understanding this relationship empowers analysts to effectively steer performance through model adjustments.

Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies.

PubMed

Palmer, Tom M; Holmes, Michael V; Keating, Brendan J; Sheehan, Nuala A

2017-11-01

Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors. © The Author(s) 2017. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. Conclusions The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate. PMID:23343408

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate.

Cardiac conduction velocity estimation from sequential mapping assuming known Gaussian distribution for activation time estimation error.

PubMed

Shariat, Mohammad Hassan; Gazor, Saeed; Redfearn, Damian

2016-08-01

In this paper, we study the problem of the cardiac conduction velocity (CCV) estimation for the sequential intracardiac mapping. We assume that the intracardiac electrograms of several cardiac sites are sequentially recorded, their activation times (ATs) are extracted, and the corresponding wavefronts are specified. The locations of the mapping catheter's electrodes and the ATs of the wavefronts are used here for the CCV estimation. We assume that the extracted ATs include some estimation errors, which we model with zero-mean white Gaussian noise values with known variances. Assuming stable planar wavefront propagation, we derive the maximum likelihood CCV estimator, when the synchronization times between various recording sites are unknown. We analytically evaluate the performance of the CCV estimator and provide its mean square estimation error. Our simulation results confirm the accuracy of the proposed method and the error analysis of the proposed CCV estimator.

Bone orientation and position estimation errors using Cosserat point elements and least squares methods: Application to gait.

PubMed

Solav, Dana; Camomilla, Valentina; Cereatti, Andrea; Barré, Arnaud; Aminian, Kamiar; Wolf, Alon

2017-09-06

The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects' knee prosthesis and a stereophotogrammetric system tracking skin-markers affected by soft tissue artifact. Femur orientation and position errors estimated from skin-marker clusters were computed for 18 subjects using clusters of up to 35 markers. Results based on gold-standard data revealed that instantaneous subsets of TCPEs exist which estimate the femur pose with reasonable accuracy (median root mean square error during stance/swing: 1.4/2.8deg for orientation, 1.5/4.2mm for position). A non-invasive and instantaneous criteria to select accurate TCPEs for pose estimation (4.8/7.3deg, 5.8/12.3mm), was compared with RBLS (4.3/6.6deg, 6.9/16.6mm) and HDLS (4.6/7.6deg, 6.7/12.5mm). Accounting for homogeneous deformation, using HDLS or selected TCPEs, yielded more accurate position estimations than RBLS method, which, conversely, yielded more accurate orientation estimations. Further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy. Copyright © 2017 Elsevier Ltd. All rights reserved.

The theory precision analyse of RFM localization of satellite remote sensing imagery

NASA Astrophysics Data System (ADS)

Zhang, Jianqing; Xv, Biao

2009-11-01

The tradition method of detecting precision of Rational Function Model(RFM) is to make use of a great deal check points, and it calculates mean square error through comparing calculational coordinate with known coordinate. This method is from theory of probability, through a large number of samples to statistic estimate value of mean square error, we can think its estimate value approaches in its true when samples are well enough. This paper is from angle of survey adjustment, take law of propagation of error as the theory basis, and it calculates theory precision of RFM localization. Then take the SPOT5 three array imagery as experiment data, and the result of traditional method and narrated method in the paper are compared, while has confirmed tradition method feasible, and answered its theory precision question from the angle of survey adjustment.

Computing daily mean streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration Curve Transfer statistical methods

USGS Publications Warehouse

Linhart, S. Mike; Nania, Jon F.; Sanders, Curtis L.; Archfield, Stacey A.

2012-01-01

The U.S. Geological Survey (USGS) maintains approximately 148 real-time streamgages in Iowa for which daily mean streamflow information is available, but daily mean streamflow data commonly are needed at locations where no streamgages are present. Therefore, the USGS conducted a study as part of a larger project in cooperation with the Iowa Department of Natural Resources to develop methods to estimate daily mean streamflow at locations in ungaged watersheds in Iowa by using two regression-based statistical methods. The regression equations for the statistical methods were developed from historical daily mean streamflow and basin characteristics from streamgages within the study area, which includes the entire State of Iowa and adjacent areas within a 50-mile buffer of Iowa in neighboring states. Results of this study can be used with other techniques to determine the best method for application in Iowa and can be used to produce a Web-based geographic information system tool to compute streamflow estimates automatically. The Flow Anywhere statistical method is a variation of the drainage-area-ratio method, which transfers same-day streamflow information from a reference streamgage to another location by using the daily mean streamflow at the reference streamgage and the drainage-area ratio of the two locations. The Flow Anywhere method modifies the drainage-area-ratio method in order to regionalize the equations for Iowa and determine the best reference streamgage from which to transfer same-day streamflow information to an ungaged location. Data used for the Flow Anywhere method were retrieved for 123 continuous-record streamgages located in Iowa and within a 50-mile buffer of Iowa. The final regression equations were computed by using either left-censored regression techniques with a low limit threshold set at 0.1 cubic feet per second (ft3/s) and the daily mean streamflow for the 15th day of every other month, or by using an ordinary-least-squares multiple linear regression method and the daily mean streamflow for the 15th day of every other month. The Flow Duration Curve Transfer method was used to estimate unregulated daily mean streamflow from the physical and climatic characteristics of gaged basins. For the Flow Duration Curve Transfer method, daily mean streamflow quantiles at the ungaged site were estimated with the parameter-based regression model, which results in a continuous daily flow-duration curve (the relation between exceedance probability and streamflow for each day of observed streamflow) at the ungaged site. By the use of a reference streamgage, the Flow Duration Curve Transfer is converted to a time series. Data used in the Flow Duration Curve Transfer method were retrieved for 113 continuous-record streamgages in Iowa and within a 50-mile buffer of Iowa. The final statewide regression equations for Iowa were computed by using a weighted-least-squares multiple linear regression method and were computed for the 0.01-, 0.05-, 0.10-, 0.15-, 0.20-, 0.30-, 0.40-, 0.50-, 0.60-, 0.70-, 0.80-, 0.85-, 0.90-, and 0.95-exceedance probability statistics determined from the daily mean streamflow with a reporting limit set at 0.1 ft3/s. The final statewide regression equation for Iowa computed by using left-censored regression techniques was computed for the 0.99-exceedance probability statistic determined from the daily mean streamflow with a low limit threshold and a reporting limit set at 0.1 ft3/s. For the Flow Anywhere method, results of the validation study conducted by using six streamgages show that differences between the root-mean-square error and the mean absolute error ranged from 1,016 to 138 ft3/s, with the larger value signifying a greater occurrence of outliers between observed and estimated streamflows. Root-mean-square-error values ranged from 1,690 to 237 ft3/s. Values of the percent root-mean-square error ranged from 115 percent to 26.2 percent. The logarithm (base 10) streamflow percent root-mean-square error ranged from 13.0 to 5.3 percent. Root-mean-square-error observations standard-deviation-ratio values ranged from 0.80 to 0.40. Percent-bias values ranged from 25.4 to 4.0 percent. Untransformed streamflow Nash-Sutcliffe efficiency values ranged from 0.84 to 0.35. The logarithm (base 10) streamflow Nash-Sutcliffe efficiency values ranged from 0.86 to 0.56. For the streamgage with the best agreement between observed and estimated streamflow, higher streamflows appear to be underestimated. For the streamgage with the worst agreement between observed and estimated streamflow, low flows appear to be overestimated whereas higher flows seem to be underestimated. Estimated cumulative streamflows for the period October 1, 2004, to September 30, 2009, are underestimated by -25.8 and -7.4 percent for the closest and poorest comparisons, respectively. For the Flow Duration Curve Transfer method, results of the validation study conducted by using the same six streamgages show that differences between the root-mean-square error and the mean absolute error ranged from 437 to 93.9 ft3/s, with the larger value signifying a greater occurrence of outliers between observed and estimated streamflows. Root-mean-square-error values ranged from 906 to 169 ft3/s. Values of the percent root-mean-square-error ranged from 67.0 to 25.6 percent. The logarithm (base 10) streamflow percent root-mean-square error ranged from 12.5 to 4.4 percent. Root-mean-square-error observations standard-deviation-ratio values ranged from 0.79 to 0.40. Percent-bias values ranged from 22.7 to 0.94 percent. Untransformed streamflow Nash-Sutcliffe efficiency values ranged from 0.84 to 0.38. The logarithm (base 10) streamflow Nash-Sutcliffe efficiency values ranged from 0.89 to 0.48. For the streamgage with the closest agreement between observed and estimated streamflow, there is relatively good agreement between observed and estimated streamflows. For the streamgage with the poorest agreement between observed and estimated streamflow, streamflows appear to be substantially underestimated for much of the time period. Estimated cumulative streamflow for the period October 1, 2004, to September 30, 2009, are underestimated by -9.3 and -22.7 percent for the closest and poorest comparisons, respectively.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

Rapid estimation of frequency response functions by close-range photogrammetry

NASA Technical Reports Server (NTRS)

Tripp, J. S.

1985-01-01

The accuracy of a rapid method which estimates the frequency response function from stereoscopic dynamic data is computed. It is shown that reversal of the order of the operations of coordinate transformation and Fourier transformation, which provides a significant increase in computational speed, introduces error. A portion of the error, proportional to the perturbation components normal to the camera focal planes, cannot be eliminated. The remaining error may be eliminated by proper scaling of frequency data prior to coordinate transformation. Methods are developed for least squares estimation of the full 3x3 frequency response matrix for a three dimensional structure.

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First,more » the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE PAGES

Zhou, Ping; Wang, Chenyu; Li, Mingjie; ...

2018-01-31

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Robust Mean and Covariance Structure Analysis through Iteratively Reweighted Least Squares.

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Bentler, Peter M.

2000-01-01

Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)

Utilization of electrical impedance imaging for estimation of in-vivo tissue resistivities

NASA Astrophysics Data System (ADS)

Eyuboglu, B. Murat; Pilkington, Theo C.

1993-08-01

In order to determine in vivo resistivity of tissues in the thorax, the possibility of combining electrical impedance imaging (EII) techniques with (1) anatomical data extracted from high resolution images, (2) a prior knowledge of tissue resistivities, and (3) a priori noise information was assessed in this study. A Least Square Error Estimator (LSEE) and a statistically constrained Minimum Mean Square Error Estimator (MiMSEE) were implemented to estimate regional electrical resistivities from potential measurements made on the body surface. A two dimensional boundary element model of the human thorax, which consists of four different conductivity regions (the skeletal muscle, the heart, the right lung, and the left lung) was adopted to simulate the measured EII torso potentials. The calculated potentials were then perturbed by simulated instrumentation noise. The signal information used to form the statistical constraint for the MiMSEE was obtained from a prior knowledge of the physiological range of tissue resistivities. The noise constraint was determined from a priori knowledge of errors due to linearization of the forward problem and to the instrumentation noise.

Cortical dipole imaging using truncated total least squares considering transfer matrix error.

PubMed

Hori, Junichi; Takeuchi, Kosuke

2013-01-01

Cortical dipole imaging has been proposed as a method to visualize electroencephalogram in high spatial resolution. We investigated the inverse technique of cortical dipole imaging using a truncated total least squares (TTLS). The TTLS is a regularization technique to reduce the influence from both the measurement noise and the transfer matrix error caused by the head model distortion. The estimation of the regularization parameter was also investigated based on L-curve. The computer simulation suggested that the estimation accuracy was improved by the TTLS compared with Tikhonov regularization. The proposed method was applied to human experimental data of visual evoked potentials. We confirmed the TTLS provided the high spatial resolution of cortical dipole imaging.

The Improved Estimation of Ratio of Two Population Proportions

ERIC Educational Resources Information Center

Solanki, Ramkrishna S.; Singh, Housila P.

2016-01-01

In this article, first we obtained the correct mean square error expression of Gupta and Shabbir's linear weighted estimator of the ratio of two population proportions. Later we suggested the general class of ratio estimators of two population proportions. The usual ratio estimator, Wynn-type estimator, Singh, Singh, and Kaur difference-type…

Three-dimensional holoscopic image coding scheme using high-efficiency video coding with kernel-based minimum mean-square-error estimation

NASA Astrophysics Data System (ADS)

Liu, Deyang; An, Ping; Ma, Ran; Yang, Chao; Shen, Liquan; Li, Kai

2016-07-01

Three-dimensional (3-D) holoscopic imaging, also known as integral imaging, light field imaging, or plenoptic imaging, can provide natural and fatigue-free 3-D visualization. However, a large amount of data is required to represent the 3-D holoscopic content. Therefore, efficient coding schemes for this particular type of image are needed. A 3-D holoscopic image coding scheme with kernel-based minimum mean square error (MMSE) estimation is proposed. In the proposed scheme, the coding block is predicted by an MMSE estimator under statistical modeling. In order to obtain the signal statistical behavior, kernel density estimation (KDE) is utilized to estimate the probability density function of the statistical modeling. As bandwidth estimation (BE) is a key issue in the KDE problem, we also propose a BE method based on kernel trick. The experimental results demonstrate that the proposed scheme can achieve a better rate-distortion performance and a better visual rendering quality.

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

August median streamflow on ungaged streams in Eastern Coastal Maine

USGS Publications Warehouse

Lombard, Pamela J.

2004-01-01

Methods for estimating August median streamflow were developed for ungaged, unregulated streams in eastern coastal Maine. The methods apply to streams with drainage areas ranging in size from 0.04 to 73.2 square miles and fraction of basin underlain by a sand and gravel aquifer ranging from 0 to 71 percent. The equations were developed with data from three long-term (greater than or equal to 10 years of record) continuous-record streamflow-gaging stations, 23 partial-record streamflow- gaging stations, and 5 short-term (less than 10 years of record) continuous-record streamflow-gaging stations. A mathematical technique for estimating a standard low-flow statistic, August median streamflow, at partial-record streamflow-gaging stations and short-term continuous-record streamflow-gaging stations was applied by relating base-flow measurements at these stations to concurrent daily streamflows at nearby long-term continuous-record streamflow-gaging stations (index stations). Generalized least-squares regression analysis (GLS) was used to relate estimates of August median streamflow at streamflow-gaging stations to basin characteristics at these same stations to develop equations that can be applied to estimate August median streamflow on ungaged streams. GLS accounts for different periods of record at the gaging stations and the cross correlation of concurrent streamflows among gaging stations. Thirty-one stations were used for the final regression equations. Two basin characteristics?drainage area and fraction of basin underlain by a sand and gravel aquifer?are used in the calculated regression equation to estimate August median streamflow for ungaged streams. The equation has an average standard error of prediction from -27 to 38 percent. A one-variable equation uses only drainage area to estimate August median streamflow when less accuracy is acceptable. This equation has an average standard error of prediction from -30 to 43 percent. Model error is larger than sampling error for both equations, indicating that additional or improved estimates of basin characteristics could be important to improved estimates of low-flow statistics. Weighted estimates of August median streamflow at partial- record or continuous-record gaging stations range from 0.003 to 31.0 cubic feet per second or from 0.1 to 0.6 cubic feet per second per square mile. Estimates of August median streamflow on ungaged streams in eastern coastal Maine, within the range of acceptable explanatory variables, range from 0.003 to 45 cubic feet per second or 0.1 to 0.6 cubic feet per second per square mile. Estimates of August median streamflow per square mile of drainage area generally increase as drainage area and fraction of basin underlain by a sand and gravel aquifer increase.

Hyperspectral analysis of soil organic matter in coal mining regions using wavelets, correlations, and partial least squares regression.

PubMed

Lin, Lixin; Wang, Yunjia; Teng, Jiyao; Wang, Xuchen

2016-02-01

Hyperspectral estimation of soil organic matter (SOM) in coal mining regions is an important tool for enhancing fertilization in soil restoration programs. The correlation--partial least squares regression (PLSR) method effectively solves the information loss problem of correlation--multiple linear stepwise regression, but results of the correlation analysis must be optimized to improve precision. This study considers the relationship between spectral reflectance and SOM based on spectral reflectance curves of soil samples collected from coal mining regions. Based on the major absorption troughs in the 400-1006 nm spectral range, PLSR analysis was performed using 289 independent bands of the second derivative (SDR) with three levels and measured SOM values. A wavelet-correlation-PLSR (W-C-PLSR) model was then constructed. By amplifying useful information that was previously obscured by noise, the W-C-PLSR model was optimal for estimating SOM content, with smaller prediction errors in both calibration (R(2) = 0.970, root mean square error (RMSEC) = 3.10, and mean relative error (MREC) = 8.75) and validation (RMSEV = 5.85 and MREV = 14.32) analyses, as compared with other models. Results indicate that W-C-PLSR has great potential to estimate SOM in coal mining regions.

Analysis of low flows and selected methods for estimating low-flow characteristics at partial-record and ungaged stream sites in western Washington

USGS Publications Warehouse

Curran, Christopher A.; Eng, Ken; Konrad, Christopher P.

2012-01-01

Regional low-flow regression models for estimating Q7,10 at ungaged stream sites are developed from the records of daily discharge at 65 continuous gaging stations (including 22 discontinued gaging stations) for the purpose of evaluating explanatory variables. By incorporating the base-flow recession time constant τ as an explanatory variable in the regression model, the root-mean square error for estimating Q7,10 at ungaged sites can be lowered to 72 percent (for known values of τ), which is 42 percent less than if only basin area and mean annual precipitation are used as explanatory variables. If partial-record sites are included in the regression data set, τ must be estimated from pairs of discharge measurements made during continuous periods of declining low flows. Eight measurement pairs are optimal for estimating τ at partial-record sites, and result in a lowering of the root-mean square error by 25 percent. A low-flow survey strategy that includes paired measurements at partial-record sites requires additional effort and planning beyond a standard strategy, but could be used to enhance regional estimates of τ and potentially reduce the error of regional regression models for estimating low-flow characteristics at ungaged sites.

Adaptive control of theophylline therapy: importance of blood sampling times.

PubMed

D'Argenio, D Z; Khakmahd, K

1983-10-01

A two-observation protocol for estimating theophylline clearance during a constant-rate intravenous infusion is used to examine the importance of blood sampling schedules with regard to the information content of resulting concentration data. Guided by a theory for calculating maximally informative sample times, population simulations are used to assess the effect of specific sampling times on the precision of resulting clearance estimates and subsequent predictions of theophylline plasma concentrations. The simulations incorporated noise terms for intersubject variability, dosing errors, sample collection errors, and assay error. Clearance was estimated using Chiou's method, least squares, and a Bayesian estimation procedure. The results of these simulations suggest that clinically significant estimation and prediction errors may result when using the above two-point protocol for estimating theophylline clearance if the time separating the two blood samples is less than one population mean elimination half-life.

An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

NASA Astrophysics Data System (ADS)

Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza

2018-03-01

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

A simple method for processing data with least square method

NASA Astrophysics Data System (ADS)

Wang, Chunyan; Qi, Liqun; Chen, Yongxiang; Pang, Guangning

2017-08-01

The least square method is widely used in data processing and error estimation. The mathematical method has become an essential technique for parameter estimation, data processing, regression analysis and experimental data fitting, and has become a criterion tool for statistical inference. In measurement data analysis, the distribution of complex rules is usually based on the least square principle, i.e., the use of matrix to solve the final estimate and to improve its accuracy. In this paper, a new method is presented for the solution of the method which is based on algebraic computation and is relatively straightforward and easy to understand. The practicability of this method is described by a concrete example.

First-Order System Least-Squares for the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Bochev, P.; Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.

Evaluation of Bayesian Sequential Proportion Estimation Using Analyst Labels

NASA Technical Reports Server (NTRS)

Lennington, R. K.; Abotteen, K. M. (Principal Investigator)

1980-01-01

The author has identified the following significant results. A total of ten Large Area Crop Inventory Experiment Phase 3 blind sites and analyst-interpreter labels were used in a study to compare proportional estimates obtained by the Bayes sequential procedure with estimates obtained from simple random sampling and from Procedure 1. The analyst error rate using the Bayes technique was shown to be no greater than that for the simple random sampling. Also, the segment proportion estimates produced using this technique had smaller bias and mean squared errors than the estimates produced using either simple random sampling or Procedure 1.

[Establishment of the Mathematical Model for PMI Estimation Using FTIR Spectroscopy and Data Mining Method].

PubMed

Wang, L; Qin, X C; Lin, H C; Deng, K F; Luo, Y W; Sun, Q R; Du, Q X; Wang, Z Y; Tuo, Y; Sun, J H

2018-02-01

To analyse the relationship between Fourier transform infrared （FTIR） spectrum of rat's spleen tissue and postmortem interval （PMI） for PMI estimation using FTIR spectroscopy combined with data mining method. Rats were sacrificed by cervical dislocation, and the cadavers were placed at 20 ℃. The FTIR spectrum data of rats' spleen tissues were taken and measured at different time points. After pretreatment, the data was analysed by data mining method. The absorption peak intensity of rat's spleen tissue spectrum changed with the PMI, while the absorption peak position was unchanged. The results of principal component analysis （PCA） showed that the cumulative contribution rate of the first three principal components was 96%. There was an obvious clustering tendency for the spectrum sample at each time point. The methods of partial least squares discriminant analysis （PLS-DA） and support vector machine classification （SVMC） effectively divided the spectrum samples with different PMI into four categories （0-24 h, 48-72 h, 96-120 h and 144-168 h）. The determination coefficient （ R ²） of the PMI estimation model established by PLS regression analysis was 0.96, and the root mean square error of calibration （RMSEC） and root mean square error of cross validation （RMSECV） were 9.90 h and 11.39 h respectively. In prediction set, the R ² was 0.97, and the root mean square error of prediction （RMSEP） was 10.49 h. The FTIR spectrum of the rat's spleen tissue can be effectively analyzed qualitatively and quantitatively by the combination of FTIR spectroscopy and data mining method, and the classification and PLS regression models can be established for PMI estimation. Copyright© by the Editorial Department of Journal of Forensic Medicine.

Sampling Errors of SSM/I and TRMM Rainfall Averages: Comparison with Error Estimates from Surface Data and a Sample Model

NASA Technical Reports Server (NTRS)

Bell, Thomas L.; Kundu, Prasun K.; Kummerow, Christian D.; Einaudi, Franco (Technical Monitor)

2000-01-01

Quantitative use of satellite-derived maps of monthly rainfall requires some measure of the accuracy of the satellite estimates. The rainfall estimate for a given map grid box is subject to both remote-sensing error and, in the case of low-orbiting satellites, sampling error due to the limited number of observations of the grid box provided by the satellite. A simple model of rain behavior predicts that Root-mean-square (RMS) random error in grid-box averages should depend in a simple way on the local average rain rate, and the predicted behavior has been seen in simulations using surface rain-gauge and radar data. This relationship was examined using satellite SSM/I data obtained over the western equatorial Pacific during TOGA COARE. RMS error inferred directly from SSM/I rainfall estimates was found to be larger than predicted from surface data, and to depend less on local rain rate than was predicted. Preliminary examination of TRMM microwave estimates shows better agreement with surface data. A simple method of estimating rms error in satellite rainfall estimates is suggested, based on quantities that can be directly computed from the satellite data.

Estimating pole/zero errors in GSN-IRIS/USGS network calibration metadata

USGS Publications Warehouse

Ringler, A.T.; Hutt, C.R.; Aster, R.; Bolton, H.; Gee, L.S.; Storm, T.

2012-01-01

Mapping the digital record of a seismograph into true ground motion requires the correction of the data by some description of the instrument's response. For the Global Seismographic Network (Butler et al., 2004), as well as many other networks, this instrument response is represented as a Laplace domain pole–zero model and published in the Standard for the Exchange of Earthquake Data (SEED) format. This Laplace representation assumes that the seismometer behaves as a linear system, with any abrupt changes described adequately via multiple time-invariant epochs. The SEED format allows for published instrument response errors as well, but these typically have not been estimated or provided to users. We present an iterative three-step method to estimate the instrument response parameters (poles and zeros) and their associated errors using random calibration signals. First, we solve a coarse nonlinear inverse problem using a least-squares grid search to yield a first approximation to the solution. This approach reduces the likelihood of poorly estimated parameters (a local-minimum solution) caused by noise in the calibration records and enhances algorithm convergence. Second, we iteratively solve a nonlinear parameter estimation problem to obtain the least-squares best-fit Laplace pole–zero–gain model. Third, by applying the central limit theorem, we estimate the errors in this pole–zero model by solving the inverse problem at each frequency in a two-thirds octave band centered at each best-fit pole–zero frequency. This procedure yields error estimates of the 99% confidence interval. We demonstrate the method by applying it to a number of recent Incorporated Research Institutions in Seismology/United States Geological Survey (IRIS/USGS) network calibrations (network code IU).

JASMINE -- Japan Astrometry Satellite Mission for INfrared Exploration: Data Analysis and Accuracy Assessment with a Kalman Filter

NASA Astrophysics Data System (ADS)

Yamada, Y.; Shimokawa, T.; Shinomoto, S. Yano, T.; Gouda, N.

2009-09-01

For the purpose of determining the celestial coordinates of stellar positions, consecutive observational images are laid overlapping each other with clues of stars belonging to multiple plates. In the analysis, one has to estimate not only the coordinates of individual plates, but also the possible expansion and distortion of the frame. This problem reduces to a least-squares fit that can in principle be solved by a huge matrix inversion, which is, however, impracticable. Here, we propose using Kalman filtering to perform the least-squares fit and implement a practical iterative algorithm. We also estimate errors associated with this iterative method and suggest a design of overlapping plates to minimize the error.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

Simulation of a long-term aquifer test conducted near the Rio Grande, Albuquerque, New Mexico

USGS Publications Warehouse

McAda, Douglas P.

2001-01-01

A long-term aquifer test was conducted near the Rio Grande in Albuquerque during January and February 1995 using 22 wells and piezometers at nine sites, with the City of Albuquerque Griegos 1 production well as the pumped well. Griegos 1 discharge averaged about 2,330 gallons per minute for 54.4 days. A three-dimensional finite-difference ground-water-flow model was used to estimate aquifer properties in the vicinity of the Griegos well field and the amount of infiltration induced into the aquifer system from the Rio Grande and riverside drains as a result of pumping during the test. The model was initially calibrated by trial-and-error adjustments of the aquifer properties. The model was recalibrated using a nonlinear least-squares regression technique. The aquifer system in the area includes the middle Tertiary to Quaternary Santa Fe Group and post-Santa Fe Group valley- and basin-fill deposits of the Albuquerque Basin. The Rio Grande and adjacent riverside drains are in hydraulic connection with the aquifer system. The hydraulic-conductivity values of the upper part of the Santa Fe Group resulting from the model calibrated by trial and error varied by zone in the model and ranged from 12 to 33 feet per day. The hydraulic conductivity of the inner-valley alluvium was 45 feet per day. The vertical to horizontal anisotropy ratio was 1:140. Specific storage was 4 x 10-6 per foot of aquifer thickness, and specific yield was 0.15 (dimensionless). The sum of squared errors between the observed and simulated drawdowns was 130 feet squared. Not all aquifer properties could be estimated using nonlinear regression because of model insensitivity to some aquifer properties at observation locations. Hydraulic conductivity of the inner-valley alluvium, middle part of the Santa Fe Group, and riverbed and riverside-drain bed and specific yield had low sensitivity values and therefore could not be estimated. Of the properties estimated, hydraulic conductivity of the upper part of the Santa Fe Group was estimated to be 12 feet per day, the vertical to horizontal anisotropy ratio was estimated to be 1:82, and specific storage was estimated to be 1.2 x 10-6 per foot of aquifer thickness. The overall sum of squared errors between the observed and simulated drawdowns was 87 feet squared, a significant improvement over the model calibrated by trial and error. At the end of aquifer-test pumping, induced infiltration from the Rio Grande and riverside drains was simulated to be 13 percent of the total amount of water pumped. The remainder was water removed from aquifer storage. After pumping stopped, induced infiltration continued to replenish aquifer storage. Simulations estimated that 5 years after pumping began (about 4.85 years after pumping stopped), 58 to 72 percent of the total amount of water pumped was replenished by induced infiltration from the Rio Grande surface-water system.

Channel estimation based on quantized MMP for FDD massive MIMO downlink

NASA Astrophysics Data System (ADS)

Guo, Yao-ting; Wang, Bing-he; Qu, Yi; Cai, Hua-jie

2016-10-01

In this paper, we consider channel estimation for Massive MIMO systems operating in frequency division duplexing mode. By exploiting the sparsity of propagation paths in Massive MIMO channel, we develop a compressed sensing(CS) based channel estimator which can reduce the pilot overhead. As compared with the conventional least squares (LS) and linear minimum mean square error(LMMSE) estimation, the proposed algorithm is based on the quantized multipath matching pursuit - MMP - reduced the pilot overhead and performs better than other CS algorithms. The simulation results demonstrate the advantage of the proposed algorithm over various existing methods including the LS, LMMSE, CoSaMP and conventional MMP estimators.

Parameter Estimation for Thurstone Choice Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vojnovic, Milan; Yun, Seyoung

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one ormore » more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.« less

Reliable estimation of orbit errors in spaceborne SAR interferometry. The network approach

NASA Astrophysics Data System (ADS)

Bähr, Hermann; Hanssen, Ramon F.

2012-12-01

An approach to improve orbital state vectors by orbit error estimates derived from residual phase patterns in synthetic aperture radar interferograms is presented. For individual interferograms, an error representation by two parameters is motivated: the baseline error in cross-range and the rate of change of the baseline error in range. For their estimation, two alternatives are proposed: a least squares approach that requires prior unwrapping and a less reliable gridsearch method handling the wrapped phase. In both cases, reliability is enhanced by mutual control of error estimates in an overdetermined network of linearly dependent interferometric combinations of images. Thus, systematic biases, e.g., due to unwrapping errors, can be detected and iteratively eliminated. Regularising the solution by a minimum-norm condition results in quasi-absolute orbit errors that refer to particular images. For the 31 images of a sample ENVISAT dataset, orbit corrections with a mutual consistency on the millimetre level have been inferred from 163 interferograms. The method itself qualifies by reliability and rigorous geometric modelling of the orbital error signal but does not consider interfering large scale deformation effects. However, a separation may be feasible in a combined processing with persistent scatterer approaches or by temporal filtering of the estimates.

Estimation of water level and steam temperature using ensemble Kalman filter square root (EnKF-SR)

NASA Astrophysics Data System (ADS)

Herlambang, T.; Mufarrikoh, Z.; Karya, D. F.; Rahmalia, D.

2018-04-01

The equipment unit which has the most vital role in the steam-powered electric power plant is boiler. Steam drum boiler is a tank functioning to separate fluida into has phase and liquid phase. The existence in boiler system has a vital role. The controlled variables in the steam drum boiler are water level and the steam temperature. If the water level is higher than the determined level, then the gas phase resulted will contain steam endangering the following process and making the resulted steam going to turbine get less, and the by causing damages to pipes in the boiler. On the contrary, if less than the height of determined water level, the resulted height will result in dry steam likely to endanger steam drum. Thus an error was observed between the determined. This paper studied the implementation of the Ensemble Kalman Filter Square Root (EnKF-SR) method in nonlinear model of the steam drum boiler equation. The computation to estimate the height of water level and the temperature of steam was by simulation using Matlab software. Thus an error was observed between the determined water level and the steam temperature, and that of estimated water level and steam temperature. The result of simulation by Ensemble Kalman Filter Square Root (EnKF-SR) on the nonlinear model of steam drum boiler showed that the error was less than 2%. The implementation of EnKF-SR on the steam drum boiler r model comprises of three simulations, each of which generates 200, 300 and 400 ensembles. The best simulation exhibited the error between the real condition and the estimated result, by generating 400 ensemble. The simulation in water level in order of 0.00002145 m, whereas in the steam temperature was some 0.00002121 kelvin.

Estimation of the daily global solar radiation based on the Gaussian process regression methodology in the Saharan climate

NASA Astrophysics Data System (ADS)

Guermoui, Mawloud; Gairaa, Kacem; Rabehi, Abdelaziz; Djafer, Djelloul; Benkaciali, Said

2018-06-01

Accurate estimation of solar radiation is the major concern in renewable energy applications. Over the past few years, a lot of machine learning paradigms have been proposed in order to improve the estimation performances, mostly based on artificial neural networks, fuzzy logic, support vector machine and adaptive neuro-fuzzy inference system. The aim of this work is the prediction of the daily global solar radiation, received on a horizontal surface through the Gaussian process regression (GPR) methodology. A case study of Ghardaïa region (Algeria) has been used in order to validate the above methodology. In fact, several combinations have been tested; it was found that, GPR-model based on sunshine duration, minimum air temperature and relative humidity gives the best results in term of mean absolute bias error (MBE), root mean square error (RMSE), relative mean square error (rRMSE), and correlation coefficient ( r) . The obtained values of these indicators are 0.67 MJ/m2, 1.15 MJ/m2, 5.2%, and 98.42%, respectively.

Methods of Fitting a Straight Line to Data: Examples in Water Resources

USGS Publications Warehouse

Hirsch, Robert M.; Gilroy, Edward J.

1984-01-01

Three methods of fitting straight lines to data are described and their purposes are discussed and contrasted in terms of their applicability in various water resources contexts. The three methods are ordinary least squares (OLS), least normal squares (LNS), and the line of organic correlation (OC). In all three methods the parameters are based on moment statistics of the data. When estimation of an individual value is the objective, OLS is the most appropriate. When estimation of many values is the objective and one wants the set of estimates to have the appropriate variance, then OC is most appropriate. When one wishes to describe the relationship between two variables and measurement error is unimportant, then OC is most appropriate. Where the error is important in descriptive problems or in calibration problems, then structural analysis techniques may be most appropriate. Finally, if the problem is one of describing some geographic trajectory, then LNS is most appropriate.

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov-Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard

2008-02-01

In a linear Gauss-Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov-Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.

Estimators of The Magnitude-Squared Spectrum and Methods for Incorporating SNR Uncertainty

PubMed Central

Lu, Yang; Loizou, Philipos C.

2011-01-01

Statistical estimators of the magnitude-squared spectrum are derived based on the assumption that the magnitude-squared spectrum of the noisy speech signal can be computed as the sum of the (clean) signal and noise magnitude-squared spectra. Maximum a posterior (MAP) and minimum mean square error (MMSE) estimators are derived based on a Gaussian statistical model. The gain function of the MAP estimator was found to be identical to the gain function used in the ideal binary mask (IdBM) that is widely used in computational auditory scene analysis (CASA). As such, it was binary and assumed the value of 1 if the local SNR exceeded 0 dB, and assumed the value of 0 otherwise. By modeling the local instantaneous SNR as an F-distributed random variable, soft masking methods were derived incorporating SNR uncertainty. The soft masking method, in particular, which weighted the noisy magnitude-squared spectrum by the a priori probability that the local SNR exceeds 0 dB was shown to be identical to the Wiener gain function. Results indicated that the proposed estimators yielded significantly better speech quality than the conventional MMSE spectral power estimators, in terms of yielding lower residual noise and lower speech distortion. PMID:21886543

Analysis and application of minimum variance discrete time system identification

NASA Technical Reports Server (NTRS)

Kaufman, H.; Kotob, S.

1975-01-01

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Coupling finite element and spectral methods: First results

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Debit, Naima; Maday, Yvon

1987-01-01

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Static Scene Statistical Non-Uniformity Correction

DTIC Science & Technology

2015-03-01

Error NUC Non-Uniformity Correction RMSE Root Mean Squared Error RSD Relative Standard Deviation S3NUC Static Scene Statistical Non-Uniformity...Deviation ( RSD ) which normalizes the standard deviation, σ, to the mean estimated value, µ using the equation RS D = σ µ × 100. The RSD plot of the gain...estimates is shown in Figure 4.1(b). The RSD plot shows that after a sample size of approximately 10, the different photocount values and the inclusion

Adjustment of Measurements with Multiplicative Errors: Error Analysis, Estimates of the Variance of Unit Weight, and Effect on Volume Estimation from LiDAR-Type Digital Elevation Models

PubMed Central

Shi, Yun; Xu, Peiliang; Peng, Junhuan; Shi, Chuang; Liu, Jingnan

2014-01-01

Modern observation technology has verified that measurement errors can be proportional to the true values of measurements such as GPS, VLBI baselines and LiDAR. Observational models of this type are called multiplicative error models. This paper is to extend the work of Xu and Shimada published in 2000 on multiplicative error models to analytical error analysis of quantities of practical interest and estimates of the variance of unit weight. We analytically derive the variance-covariance matrices of the three least squares (LS) adjustments, the adjusted measurements and the corrections of measurements in multiplicative error models. For quality evaluation, we construct five estimators for the variance of unit weight in association of the three LS adjustment methods. Although LiDAR measurements are contaminated with multiplicative random errors, LiDAR-based digital elevation models (DEM) have been constructed as if they were of additive random errors. We will simulate a model landslide, which is assumed to be surveyed with LiDAR, and investigate the effect of LiDAR-type multiplicative error measurements on DEM construction and its effect on the estimate of landslide mass volume from the constructed DEM. PMID:24434880

Application of square-root filtering for spacecraft attitude control

NASA Technical Reports Server (NTRS)

Sorensen, J. A.; Schmidt, S. F.; Goka, T.

1978-01-01

Suitable digital algorithms are developed and tested for providing on-board precision attitude estimation and pointing control for potential use in the Landsat-D spacecraft. These algorithms provide pointing accuracy of better than 0.01 deg. To obtain necessary precision with efficient software, a six state-variable square-root Kalman filter combines two star tracker measurements to update attitude estimates obtained from processing three gyro outputs. The validity of the estimation and control algorithms are established, and the sensitivity of their performance to various error sources and software parameters are investigated by detailed digital simulation. Spacecraft computer memory, cycle time, and accuracy requirements are estimated.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

The influence of a time-varying least squares parametric model when estimating SFOAEs evoked with swept-frequency tones

NASA Astrophysics Data System (ADS)

Hajicek, Joshua J.; Selesnick, Ivan W.; Henin, Simon; Talmadge, Carrick L.; Long, Glenis R.

2018-05-01

Stimulus frequency otoacoustic emissions (SFOAEs) were evoked and estimated using swept-frequency tones with and without the use of swept suppressor tones. SFOAEs were estimated using a least-squares fitting procedure. The estimated SFOAEs for the two paradigms (with- and without-suppression) were similar in amplitude and phase. The fitting procedure minimizes the square error between a parametric model of total ear-canal pressure (with unknown amplitudes and phases) and ear-canal pressure acquired during each paradigm. Modifying the parametric model to allow SFOAE amplitude and phase to vary over time revealed additional amplitude and phase fine structure in the without-suppressor, but not the with-suppressor paradigm. The use of a time-varying parametric model to estimate SFOAEs without-suppression may provide additional information about cochlear mechanics not available when using a with-suppressor paradigm.

Comparison of estimators of standard deviation for hydrologic time series

USGS Publications Warehouse

Tasker, Gary D.; Gilroy, Edward J.

1982-01-01

Unbiasing factors as a function of serial correlation, ρ, and sample size, n for the sample standard deviation of a lag one autoregressive model were generated by random number simulation. Monte Carlo experiments were used to compare the performance of several alternative methods for estimating the standard deviation σ of a lag one autoregressive model in terms of bias, root mean square error, probability of underestimation, and expected opportunity design loss. Three methods provided estimates of σ which were much less biased but had greater mean square errors than the usual estimate of σ: s = (1/(n - 1) ∑ (xi −x¯)2)½. The three methods may be briefly characterized as (1) a method using a maximum likelihood estimate of the unbiasing factor, (2) a method using an empirical Bayes estimate of the unbiasing factor, and (3) a robust nonparametric estimate of σ suggested by Quenouille. Because s tends to underestimate σ, its use as an estimate of a model parameter results in a tendency to underdesign. If underdesign losses are considered more serious than overdesign losses, then the choice of one of the less biased methods may be wise.

Estimation of population mean under systematic sampling

NASA Astrophysics Data System (ADS)

Noor-ul-amin, Muhammad; Javaid, Amjad

2017-11-01

In this study we propose a generalized ratio estimator under non-response for systematic random sampling. We also generate a class of estimators through special cases of generalized estimator using different combinations of coefficients of correlation, kurtosis and variation. The mean square errors and mathematical conditions are also derived to prove the efficiency of proposed estimators. Numerical illustration is included using three populations to support the results.

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

New method for propagating the square root covariance matrix in triangular form. [using Kalman-Bucy filter

NASA Technical Reports Server (NTRS)

Choe, C. Y.; Tapley, B. D.

1975-01-01

A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.

Performance analysis of adaptive equalization for coherent acoustic communications in the time-varying ocean environment.

PubMed

Preisig, James C

2005-07-01

Equations are derived for analyzing the performance of channel estimate based equalizers. The performance is characterized in terms of the mean squared soft decision error (sigma2(s)) of each equalizer. This error is decomposed into two components. These are the minimum achievable error (sigma2(0)) and the excess error (sigma2(e)). The former is the soft decision error that would be realized by the equalizer if the filter coefficient calculation were based upon perfect knowledge of the channel impulse response and statistics of the interfering noise field. The latter is the additional soft decision error that is realized due to errors in the estimates of these channel parameters. These expressions accurately predict the equalizer errors observed in the processing of experimental data by a channel estimate based decision feedback equalizer (DFE) and a passive time-reversal equalizer. Further expressions are presented that allow equalizer performance to be predicted given the scattering function of the acoustic channel. The analysis using these expressions yields insights into the features of surface scattering that most significantly impact equalizer performance in shallow water environments and motivates the implementation of a DFE that is robust with respect to channel estimation errors.

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

Estimating standard errors in feature network models.

PubMed

Frank, Laurence E; Heiser, Willem J

2007-05-01

Feature network models are graphical structures that represent proximity data in a discrete space while using the same formalism that is the basis of least squares methods employed in multidimensional scaling. Existing methods to derive a network model from empirical data only give the best-fitting network and yield no standard errors for the parameter estimates. The additivity properties of networks make it possible to consider the model as a univariate (multiple) linear regression problem with positivity restrictions on the parameters. In the present study, both theoretical and empirical standard errors are obtained for the constrained regression parameters of a network model with known features. The performance of both types of standard error is evaluated using Monte Carlo techniques.

A Fortran 77 computer code for damped least-squares inversion of Slingram electromagnetic anomalies over thin tabular conductors

NASA Astrophysics Data System (ADS)

Dondurur, Derman; Sarı, Coşkun

2004-07-01

A FORTRAN 77 computer code is presented that permits the inversion of Slingram electromagnetic anomalies to an optimal conductor model. Damped least-squares inversion algorithm is used to estimate the anomalous body parameters, e.g. depth, dip and surface projection point of the target. Iteration progress is controlled by maximum relative error value and iteration continued until a tolerance value was satisfied, while the modification of Marquardt's parameter is controlled by sum of the squared errors value. In order to form the Jacobian matrix, the partial derivatives of theoretical anomaly expression with respect to the parameters being optimised are calculated by numerical differentiation by using first-order forward finite differences. A theoretical and two field anomalies are inserted to test the accuracy and applicability of the present inversion program. Inversion of the field data indicated that depth and the surface projection point parameters of the conductor are estimated correctly, however, considerable discrepancies appeared on the estimated dip angles. It is therefore concluded that the most important factor resulting in the misfit between observed and calculated data is due to the fact that the theory used for computing Slingram anomalies is valid for only thin conductors and this assumption might have caused incorrect dip estimates in the case of wide conductors.

A comparison of two indices for the intraclass correlation coefficient.

PubMed

Shieh, Gwowen

2012-12-01

In the present study, we examined the behavior of two indices for measuring the intraclass correlation in the one-way random effects model: the prevailing ICC(1) (Fisher, 1938) and the corrected eta-squared (Bliese & Halverson, 1998). These two procedures differ both in their methods of estimating the variance components that define the intraclass correlation coefficient and in their performance of bias and mean squared error in the estimation of the intraclass correlation coefficient. In contrast with the natural unbiased principle used to construct ICC(1), in the present study it was analytically shown that the corrected eta-squared estimator is identical to the maximum likelihood estimator and the pairwise estimator under equal group sizes. Moreover, the empirical results obtained from the present Monte Carlo simulation study across various group structures revealed the mutual dominance relationship between their truncated versions for negative values. The corrected eta-squared estimator performs better than the ICC(1) estimator when the underlying population intraclass correlation coefficient is small. Conversely, ICC(1) has a clear advantage over the corrected eta-squared for medium and large magnitudes of population intraclass correlation coefficient. The conceptual description and numerical investigation provide guidelines to help researchers choose between the two indices for more accurate reliability analysis in multilevel research.

Error in telemetry studies: Effects of animal movement on triangulation

USGS Publications Warehouse

Schmutz, Joel A.; White, Gary C.

1990-01-01

We used Monte Carlo simulations to investigate the effects of animal movement on error of estimated animal locations derived from radio-telemetry triangulation of sequentially obtained bearings. Simulated movements of 0-534 m resulted in up to 10-fold increases in average location error but <10% decreases in location precision when observer-to-animal distances were <1,000 m. Location error and precision were minimally affected by censorship of poor locations with Chi-square goodness-of-fit tests. Location error caused by animal movement can only be eliminated by taking simultaneous bearings.

Support vector regression methodology for estimating global solar radiation in Algeria

NASA Astrophysics Data System (ADS)

Guermoui, Mawloud; Rabehi, Abdelaziz; Gairaa, Kacem; Benkaciali, Said

2018-01-01

Accurate estimation of Daily Global Solar Radiation (DGSR) has been a major goal for solar energy applications. In this paper we show the possibility of developing a simple model based on the Support Vector Regression (SVM-R), which could be used to estimate DGSR on the horizontal surface in Algeria based only on sunshine ratio as input. The SVM model has been developed and tested using a data set recorded over three years (2005-2007). The data was collected at the Applied Research Unit for Renewable Energies (URAER) in Ghardaïa city. The data collected between 2005-2006 are used to train the model while the 2007 data are used to test the performance of the selected model. The measured and the estimated values of DGSR were compared during the testing phase statistically using the Root Mean Square Error (RMSE), Relative Square Error (rRMSE), and correlation coefficient (r2), which amount to 1.59(MJ/m2), 8.46 and 97,4%, respectively. The obtained results show that the SVM-R is highly qualified for DGSR estimation using only sunshine ratio.

Estimating 1970-99 average annual groundwater recharge in Wisconsin using streamflow data

USGS Publications Warehouse

Gebert, Warren A.; Walker, John F.; Kennedy, James L.

2011-01-01

Average annual recharge in Wisconsin for the period 1970-99 was estimated using streamflow data from U.S. Geological Survey continuous-record streamflow-gaging stations and partial-record sites. Partial-record sites have discharge measurements collected during low-flow conditions. The average annual base flow of a stream divided by the drainage area is a good approximation of the recharge rate; therefore, once average annual base flow is determined recharge can be calculated. Estimates of recharge for nearly 72 percent of the surface area of the State are provided. The results illustrate substantial spatial variability of recharge across the State, ranging from less than 1 inch to more than 12 inches per year. The average basin size for partial-record sites (50 square miles) was less than the average basin size for the gaging stations (305 square miles). Including results for smaller basins reveals a spatial variability that otherwise would be smoothed out using only estimates for larger basins. An error analysis indicates that the techniques used provide base flow estimates with standard errors ranging from 5.4 to 14 percent.

Network Adjustment of Orbit Errors in SAR Interferometry

NASA Astrophysics Data System (ADS)

Bahr, Hermann; Hanssen, Ramon

2010-03-01

Orbit errors can induce significant long wavelength error signals in synthetic aperture radar (SAR) interferograms and thus bias estimates of wide-scale deformation phenomena. The presented approach aims for correcting orbit errors in a preprocessing step to deformation analysis by modifying state vectors. Whereas absolute errors in the orbital trajectory are negligible, the influence of relative errors (baseline errors) is parametrised by their parallel and perpendicular component as a linear function of time. As the sensitivity of the interferometric phase is only significant with respect to the perpendicular base-line and the rate of change of the parallel baseline, the algorithm focuses on estimating updates to these two parameters. This is achieved by a least squares approach, where the unwrapped residual interferometric phase is observed and atmospheric contributions are considered to be stochastic with constant mean. To enhance reliability, baseline errors are adjusted in an overdetermined network of interferograms, yielding individual orbit corrections per acquisition.

Spectral combination of spherical gravitational curvature boundary-value problems

NASA Astrophysics Data System (ADS)

PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel

2018-04-01

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error of the combined solutions and improves standard deviation of the solution based only on the least accurate components.

Estimating riparian understory vegetation cover with beta regression and copula models

USGS Publications Warehouse

Eskelson, Bianca N.I.; Madsen, Lisa; Hagar, Joan C.; Temesgen, Hailemariam

2011-01-01

Understory vegetation communities are critical components of forest ecosystems. As a result, the importance of modeling understory vegetation characteristics in forested landscapes has become more apparent. Abundance measures such as shrub cover are bounded between 0 and 1, exhibit heteroscedastic error variance, and are often subject to spatial dependence. These distributional features tend to be ignored when shrub cover data are analyzed. The beta distribution has been used successfully to describe the frequency distribution of vegetation cover. Beta regression models ignoring spatial dependence (BR) and accounting for spatial dependence (BRdep) were used to estimate percent shrub cover as a function of topographic conditions and overstory vegetation structure in riparian zones in western Oregon. The BR models showed poor explanatory power (pseudo-R2 ≤ 0.34) but outperformed ordinary least-squares (OLS) and generalized least-squares (GLS) regression models with logit-transformed response in terms of mean square prediction error and absolute bias. We introduce a copula (COP) model that is based on the beta distribution and accounts for spatial dependence. A simulation study was designed to illustrate the effects of incorrectly assuming normality, equal variance, and spatial independence. It showed that BR, BRdep, and COP models provide unbiased parameter estimates, whereas OLS and GLS models result in slightly biased estimates for two of the three parameters. On the basis of the simulation study, 93–97% of the GLS, BRdep, and COP confidence intervals covered the true parameters, whereas OLS and BR only resulted in 84–88% coverage, which demonstrated the superiority of GLS, BRdep, and COP over OLS and BR models in providing standard errors for the parameter estimates in the presence of spatial dependence.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Augmented GNSS Differential Corrections Minimum Mean Square Error Estimation Sensitivity to Spatial Correlation Modeling Errors

PubMed Central

Kassabian, Nazelie; Presti, Letizia Lo; Rispoli, Francesco

2014-01-01

Railway signaling is a safety system that has evolved over the last couple of centuries towards autonomous functionality. Recently, great effort is being devoted in this field, towards the use and exploitation of Global Navigation Satellite System (GNSS) signals and GNSS augmentation systems in view of lower railway track equipments and maintenance costs, that is a priority to sustain the investments for modernizing the local and regional lines most of which lack automatic train protection systems and are still manually operated. The objective of this paper is to assess the sensitivity of the Linear Minimum Mean Square Error (LMMSE) algorithm to modeling errors in the spatial correlation function that characterizes true pseudorange Differential Corrections (DCs). This study is inspired by the railway application; however, it applies to all transportation systems, including the road sector, that need to be complemented by an augmentation system in order to deliver accurate and reliable positioning with integrity specifications. A vector of noisy pseudorange DC measurements are simulated, assuming a Gauss-Markov model with a decay rate parameter inversely proportional to the correlation distance that exists between two points of a certain environment. The LMMSE algorithm is applied on this vector to estimate the true DC, and the estimation error is compared to the noise added during simulation. The results show that for large enough correlation distance to Reference Stations (RSs) distance separation ratio values, the LMMSE brings considerable advantage in terms of estimation error accuracy and precision. Conversely, the LMMSE algorithm may deteriorate the quality of the DC measurements whenever the ratio falls below a certain threshold. PMID:24922454

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Estimation of geopotential differences over intercontinental locations using satellite and terrestrial measurements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Pavlis, Nikolaos K.

1991-01-01

An error analysis study was conducted in order to assess the current accuracies and the future anticipated improvements in the estimation of geopotential differences over intercontinental locations. An observation/estimation scheme was proposed and studied, whereby gravity disturbance measurements on the Earth's surface, in caps surrounding the estimation points, are combined with corresponding data in caps directly over these points at the altitude of a low orbiting satellite, for the estimation of the geopotential difference between the terrestrial stations. The mathematical modeling required to relate the primary observables to the parameters to be estimated, was studied for the terrestrial data and the data at altitude. Emphasis was placed on the examination of systematic effects and on the corresponding reductions that need to be applied to the measurements to avoid systematic errors. The error estimation for the geopotential differences was performed using both truncation theory and least squares collocation with ring averages, in case observations on the Earth's surface only are used. The error analysis indicated that with the currently available global geopotential model OSU89B and with gravity disturbance data in 2 deg caps surrounding the estimation points, the error of the geopotential difference arising from errors in the reference model and the cap data is about 23 kgal cm, for 30 deg station separation.

Tests of Independence in Contingency Tables with Small Samples: A Comparison of Statistical Power.

ERIC Educational Resources Information Center

Parshall, Cynthia G.; Kromrey, Jeffrey D.

1996-01-01

Power and Type I error rates were estimated for contingency tables with small sample sizes for the following four types of tests: (1) Pearson's chi-square; (2) chi-square with Yates's continuity correction; (3) the likelihood ratio test; and (4) Fisher's Exact Test. Various marginal distributions, sample sizes, and effect sizes were examined. (SLD)

A Generalized Least Squares Regression Approach for Computing Effect Sizes in Single-Case Research: Application Examples

ERIC Educational Resources Information Center

Maggin, Daniel M.; Swaminathan, Hariharan; Rogers, Helen J.; O'Keeffe, Breda V.; Sugai, George; Horner, Robert H.

2011-01-01

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of…

Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO With Arbitrary Statistics

NASA Astrophysics Data System (ADS)

Shariati, Nafiseh; Bjornson, Emil; Bengtsson, Mats; Debbah, Merouane

2014-10-01

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we ...

Optimal Tuner Selection for Kalman Filter-Based Aircraft Engine Performance Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2010-01-01

A linear point design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. This paper derives theoretical Kalman filter estimation error bias and variance values at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the conventional approach of tuner selection. Experimental simulation results are found to be in agreement with theoretical predictions. The new methodology is shown to yield a significant improvement in on-line engine performance estimation accuracy

Least-squares dual characterization for ROI assessment in emission tomography

NASA Astrophysics Data System (ADS)

Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.

2013-06-01

Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.

Adaptation of a Fast Optimal Interpolation Algorithm to the Mapping of Oceangraphic Data

NASA Technical Reports Server (NTRS)

Menemenlis, Dimitris; Fieguth, Paul; Wunsch, Carl; Willsky, Alan

1997-01-01

A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least squares, that is, problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. In contrast to methods previously proposed for solving large least squares problems, our approach provides estimation error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations. The multiscale algorithm itself, published elsewhere, is not the focus of this paper. However, the algorithm requires statistical models having a very particular multiscale structure; it is the development of a class of multiscale statistical models, appropriate for oceanographic mapping problems, with which we concern ourselves in this paper. The approach is illustrated by mapping temperature in the northeastern Pacific. The number of hydrographic stations is kept deliberately small to show that multiscale and exact least squares results are comparable. A portion of the data were not used in the analysis; these data serve to test the multiscale estimates. A major advantage of the present approach is the ability to repeat the estimation procedure a large number of times for sensitivity studies, parameter estimation, and model testing. We have made available by anonymous Ftp a set of MATLAB-callable routines which implement the multiscale algorithm and the statistical models developed in this paper.

Effects of Employing Ridge Regression in Structural Equation Models.

ERIC Educational Resources Information Center

McQuitty, Shaun

1997-01-01

LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)

Estimating cell populations

NASA Technical Reports Server (NTRS)

White, B. S.; Castleman, K. R.

1981-01-01

An important step in the diagnosis of a cervical cytology specimen is estimating the proportions of the various cell types present. This is usually done with a cell classifier, the error rates of which can be expressed as a confusion matrix. We show how to use the confusion matrix to obtain an unbiased estimate of the desired proportions. We show that the mean square error of this estimate depends on a 'befuddlement matrix' derived from the confusion matrix, and how this, in turn, leads to a figure of merit for cell classifiers. Finally, we work out the two-class problem in detail and present examples to illustrate the theory.

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yunlong; Wang, Aiping; Guo, Lei

This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Validation of Nimbus-7 temperature-humidity infrared radiometer estimates of cloud type and amount

NASA Technical Reports Server (NTRS)

Stowe, L. L.

1982-01-01

Estimates of clear and low, middle and high cloud amount in fixed geographical regions approximately (160 km) squared are being made routinely from 11.5 micron radiance measurements of the Nimbus-7 Temperature-Humidity Infrared Radiometer (THIR). The purpose of validation is to determine the accuracy of the THIR cloud estimates. Validation requires that a comparison be made between the THIR estimates of cloudiness and the 'true' cloudiness. The validation results reported in this paper use human analysis of concurrent but independent satellite images with surface meteorological and radiosonde observations to approximate the 'true' cloudiness. Regression and error analyses are used to estimate the systematic and random errors of THIR derived clear amount.

Development of a Nonlinear Soft-Sensor Using a GMDH Network for a Refinery Crude Distillation Tower

NASA Astrophysics Data System (ADS)

Fujii, Kenzo; Yamamoto, Toru

In atmospheric distillation processes, the stabilization of processes is required in order to optimize the crude-oil composition that corresponds to product market conditions. However, the process control systems sometimes fall into unstable states in the case where unexpected disturbances are introduced, and these unusual phenomena have had an undesirable affect on certain products. Furthermore, a useful chemical engineering model has not yet been established for these phenomena. This remains a serious problem in the atmospheric distillation process. This paper describes a new modeling scheme to predict unusual phenomena in the atmospheric distillation process using the GMDH (Group Method of Data Handling) network which is one type of network model. According to the GMDH network, the model structure can be determined systematically. However, the least squares method has been commonly utilized in determining weight coefficients (model parameters). Estimation accuracy is not entirely expected, because the sum of squared errors between the measured values and estimates is evaluated. Therefore, instead of evaluating the sum of squared errors, the sum of absolute value of errors is introduced and the Levenberg-Marquardt method is employed in order to determine model parameters. The effectiveness of the proposed method is evaluated by the foaming prediction in the crude oil switching operation in the atmospheric distillation process.

Alcohol consumption, beverage prices and measurement error.

PubMed

Young, Douglas J; Bielinska-Kwapisz, Agnieszka

2003-03-01

Alcohol price data collected by the American Chamber of Commerce Researchers Association (ACCRA) have been widely used in studies of alcohol consumption and related behaviors. A number of problems with these data suggest that they contain substantial measurement error, which biases conventional statistical estimators toward a finding of little or no effect of prices on behavior. We test for measurement error, assess the magnitude of the bias and provide an alternative estimator that is likely to be superior. The study utilizes data on per capita alcohol consumption across U.S. states and the years 1982-1997. State and federal alcohol taxes are used as instrumental variables for prices. Formal tests strongly confim the hypothesis of measurement error. Instrumental variable estimates of the price elasticity of demand range from -0.53 to -1.24. These estimates are substantially larger in absolute value than ordinary least squares estimates, which sometimes are not significantly different from zero or even positive. The ACCRA price data are substantially contaminated with measurement error, but using state and federal taxes as instrumental variables mitigates the problem.

Determining the Uncertainty of X-Ray Absorption Measurements

PubMed Central

Wojcik, Gary S.

2004-01-01

X-ray absorption (or more properly, x-ray attenuation) techniques have been applied to study the moisture movement in and moisture content of materials like cement paste, mortar, and wood. An increase in the number of x-ray counts with time at a location in a specimen may indicate a decrease in moisture content. The uncertainty of measurements from an x-ray absorption system, which must be known to properly interpret the data, is often assumed to be the square root of the number of counts, as in a Poisson process. No detailed studies have heretofore been conducted to determine the uncertainty of x-ray absorption measurements or the effect of averaging data on the uncertainty. In this study, the Poisson estimate was found to adequately approximate normalized root mean square errors (a measure of uncertainty) of counts for point measurements and profile measurements of water specimens. The Poisson estimate, however, was not reliable in approximating the magnitude of the uncertainty when averaging data from paste and mortar specimens. Changes in uncertainty from differing averaging procedures were well-approximated by a Poisson process. The normalized root mean square errors decreased when the x-ray source intensity, integration time, collimator size, and number of scanning repetitions increased. Uncertainties in mean paste and mortar count profiles were kept below 2 % by averaging vertical profiles at horizontal spacings of 1 mm or larger with counts per point above 4000. Maximum normalized root mean square errors did not exceed 10 % in any of the tests conducted. PMID:27366627

Sequential Least-Squares Using Orthogonal Transformations. [spacecraft communication/spacecraft tracking-data smoothing

NASA Technical Reports Server (NTRS)

Bierman, G. J.

1975-01-01

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission.

A Monte Carlo comparison of the recovery of winds near upwind and downwind from the SASS-1 model function by means of the sum of squares algorithm and a maximum likelihood estimator

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.

1984-01-01

Backscatter measurements at upwind and crosswind are simulated for five incidence angles by means of the SASS-1 model function. The effects of communication noise and attitude errors are simulated by Monte Carlo methods, and the winds are recovered by both the Sum of Square (SOS) algorithm and a Maximum Likelihood Estimater (MLE). The SOS algorithm is shown to fail for light enough winds at all incidence angles and to fail to show areas of calm because backscatter estimates that were negative or that produced incorrect values of K sub p greater than one were discarded. The MLE performs well for all input backscatter estimates and returns calm when both are negative. The use of the SOS algorithm is shown to have introduced errors in the SASS-1 model function that, in part, cancel out the errors that result from using it, but that also cause disagreement with other data sources such as the AAFE circle flight data at light winds. Implications for future scatterometer systems are given.

Improved estimation of anomalous diffusion exponents in single-particle tracking experiments

NASA Astrophysics Data System (ADS)

Kepten, Eldad; Bronshtein, Irena; Garini, Yuval

2013-05-01

The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.

Asymptotic Analysis Of The Total Least Squares ESPRIT Algorithm'

NASA Astrophysics Data System (ADS)

Ottersten, B. E.; Viberg, M.; Kailath, T.

1989-11-01

This paper considers the problem of estimating the parameters of multiple narrowband signals arriving at an array of sensors. Modern approaches to this problem often involve costly procedures for calculating the estimates. The ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm was recently proposed as a means for obtaining accurate estimates without requiring a costly search of the parameter space. This method utilizes an array invariance to arrive at a computationally efficient multidimensional estimation procedure. Herein, the asymptotic distribution of the estimation error is derived for the Total Least Squares (TLS) version of ESPRIT. The Cramer-Rao Bound (CRB) for the ESPRIT problem formulation is also derived and found to coincide with the variance of the asymptotic distribution through numerical examples. The method is also compared to least squares ESPRIT and MUSIC as well as to the CRB for a calibrated array. Simulations indicate that the theoretic expressions can be used to accurately predict the performance of the algorithm.

Nonlinear filtering properties of detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Tsujimoto, Yutaka

2016-11-01

Detrended fluctuation analysis (DFA) has been widely used for quantifying long-range correlation and fractal scaling behavior. In DFA, to avoid spurious detection of scaling behavior caused by a nonstationary trend embedded in the analyzed time series, a detrending procedure using piecewise least-squares fitting has been applied. However, it has been pointed out that the nonlinear filtering properties involved with detrending may induce instabilities in the scaling exponent estimation. To understand this issue, we investigate the adverse effects of the DFA detrending procedure on the statistical estimation. We show that the detrending procedure using piecewise least-squares fitting results in the nonuniformly weighted estimation of the root-mean-square deviation and that this property could induce an increase in the estimation error. In addition, for comparison purposes, we investigate the performance of a centered detrending moving average analysis with a linear detrending filter and sliding window DFA and show that these methods have better performance than the standard DFA.

Doppler-shift estimation of flat underwater channel using data-aided least-square approach

NASA Astrophysics Data System (ADS)

Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing

2015-06-01

In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes

PubMed Central

2018-01-01

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G‐computation. All methods resulted in essentially unbiased estimation of the population dose‐response function. However, GPS‐based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. PMID:29508424

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes.

PubMed

Austin, Peter C

2018-05-20

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G-computation. All methods resulted in essentially unbiased estimation of the population dose-response function. However, GPS-based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. © 2018 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Identification and compensation of the temperature influences in a miniature three-axial accelerometer based on the least squares method

NASA Astrophysics Data System (ADS)

Grigorie, Teodor Lucian; Corcau, Ileana Jenica; Tudosie, Alexandru Nicolae

2017-06-01

The paper presents a way to obtain an intelligent miniaturized three-axial accelerometric sensor, based on the on-line estimation and compensation of the sensor errors generated by the environmental temperature variation. Taking into account that this error's value is a strongly nonlinear complex function of the values of environmental temperature and of the acceleration exciting the sensor, its correction may not be done off-line and it requires the presence of an additional temperature sensor. The proposed identification methodology for the error model is based on the least square method which process off-line the numerical values obtained from the accelerometer experimental testing for different values of acceleration applied to its axes of sensitivity and for different values of operating temperature. A final analysis of the error level after the compensation highlights the best variant for the matrix in the error model. In the sections of the paper are shown the results of the experimental testing of the accelerometer on all the three sensitivity axes, the identification of the error models on each axis by using the least square method, and the validation of the obtained models with experimental values. For all of the three detection channels was obtained a reduction by almost two orders of magnitude of the acceleration absolute maximum error due to environmental temperature variation.

Estimation of the simple correlation coefficient.

PubMed

Shieh, Gwowen

2010-11-01

This article investigates some unfamiliar properties of the Pearson product-moment correlation coefficient for the estimation of simple correlation coefficient. Although Pearson's r is biased, except for limited situations, and the minimum variance unbiased estimator has been proposed in the literature, researchers routinely employ the sample correlation coefficient in their practical applications, because of its simplicity and popularity. In order to support such practice, this study examines the mean squared errors of r and several prominent formulas. The results reveal specific situations in which the sample correlation coefficient performs better than the unbiased and nearly unbiased estimators, facilitating recommendation of r as an effect size index for the strength of linear association between two variables. In addition, related issues of estimating the squared simple correlation coefficient are also considered.

Super-linear Precision in Simple Neural Population Codes

NASA Astrophysics Data System (ADS)

Schwab, David; Fiete, Ila

2015-03-01

A widely used tool for quantifying the precision with which a population of noisy sensory neurons encodes the value of an external stimulus is the Fisher Information (FI). Maximizing the FI is also a commonly used objective for constructing optimal neural codes. The primary utility and importance of the FI arises because it gives, through the Cramer-Rao bound, the smallest mean-squared error achievable by any unbiased stimulus estimator. However, it is well-known that when neural firing is sparse, optimizing the FI can result in codes that perform very poorly when considering the resulting mean-squared error, a measure with direct biological relevance. Here we construct optimal population codes by minimizing mean-squared error directly and study the scaling properties of the resulting network, focusing on the optimal tuning curve width. We then extend our results to continuous attractor networks that maintain short-term memory of external stimuli in their dynamics. Here we find similar scaling properties in the structure of the interactions that minimize diffusive information loss.

Methods for estimating aboveground biomass and its components for Douglas-fir and lodgepole pine trees

Treesearch

K.P. Poudel; H. Temesgen

2016-01-01

Estimating aboveground biomass and its components requires sound statistical formulation and evaluation. Using data collected from 55 destructively sampled trees in different parts of Oregon, we evaluated the performance of three groups of methods to estimate total aboveground biomass and (or) its components based on the bias and root mean squared error (RMSE) that...

Smoothness of In vivo Spectral Baseline Determined by Mean Squared Error

PubMed Central

Zhang, Yan; Shen, Jun

2013-01-01

Purpose A nonparametric smooth line is usually added to spectral model to account for background signals in vivo magnetic resonance spectroscopy (MRS). The assumed smoothness of the baseline significantly influences quantitative spectral fitting. In this paper, a method is proposed to minimize baseline influences on estimated spectral parameters. Methods In this paper, the non-parametric baseline function with a given smoothness was treated as a function of spectral parameters. Its uncertainty was measured by root-mean-squared error (RMSE). The proposed method was demonstrated with a simulated spectrum and in vivo spectra of both short echo time (TE) and averaged echo times. The estimated in vivo baselines were compared with the metabolite-nulled spectra, and the LCModel-estimated baselines. The accuracies of estimated baseline and metabolite concentrations were further verified by cross-validation. Results An optimal smoothness condition was found that led to the minimal baseline RMSE. In this condition, the best fit was balanced against minimal baseline influences on metabolite concentration estimates. Conclusion Baseline RMSE can be used to indicate estimated baseline uncertainties and serve as the criterion for determining the baseline smoothness of in vivo MRS. PMID:24259436

Past observable dynamics of a continuously monitored qubit

NASA Astrophysics Data System (ADS)

García-Pintos, Luis Pedro; Dressel, Justin

2017-12-01

Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process, such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit, this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.

Distribution of kriging errors, the implications and how to communicate them

NASA Astrophysics Data System (ADS)

Li, Hong Yi; Milne, Alice; Webster, Richard

2016-04-01

Kriging in one form or another has become perhaps the most popular method for spatial prediction in environmental science. Each prediction is unbiased and of minimum variance, which itself is estimated. The kriging variances depend on the mathematical model chosen to describe the spatial variation; different models, however plausible, give rise to different minimized variances. Practitioners often compare models by so-called cross-validation before finally choosing the most appropriate for their kriging. One proceeds as follows. One removes a unit (a sampling point) from the whole set, kriges the value there and compares the kriged value with the value observed to obtain the deviation or error. One repeats the process for each and every point in turn and for all plausible models. One then computes the mean errors (MEs) and the mean of the squared errors (MSEs). Ideally a squared error should equal the corresponding kriging variance (σK2), and so one is advised to choose the model for which on average the squared errors most nearly equal the kriging variances, i.e. the ratio MSDR = MSE/σK2 ≈ 1. Maximum likelihood estimation of models almost guarantees that the MSDR equals 1, and so the kriging variances are unbiased predictors of the squared error across the region. The method is based on the assumption that the errors have a normal distribution. The squared deviation ratio (SDR) should therefore be distributed as χ2 with one degree of freedom with a median of 0.455. We have found that often the median of the SDR (MedSDR) is less, in some instances much less, than 0.455 even though the mean of the SDR is close to 1. It seems that in these cases the distributions of the errors are leptokurtic, i.e. they have an excess of predictions close to the true values, excesses near the extremes and a dearth of predictions in between. In these cases the kriging variances are poor measures of the uncertainty at individual sites. The uncertainty is typically under-estimated for the extreme observations and compensated for by over estimating for other observations. Statisticians must tell users when they present maps of predictions. We illustrate the situation with results from mapping salinity in land reclaimed from the Yangtze delta in the Gulf of Hangzhou, China. There the apparent electrical conductivity (ECa) of the topsoil was measured at 525 points in a field of 2.3 ha. The marginal distribution of the observations was strongly positively skewed, and so the observed ECas were transformed to their logarithms to give an approximately symmetric distribution. That distribution was strongly platykurtic with short tails and no evident outliers. The logarithms were analysed as a mixed model of quadratic drift plus correlated random residuals with a spherical variogram. The kriged predictions that deviated from their true values with an MSDR of 0.993, but with a medSDR=0.324. The coefficient of kurtosis of the deviations was 1.45, i.e. substantially larger than 0 for a normal distribution. The reasons for this behaviour are being sought. The most likely explanation is that there are spatial outliers, i.e. points at which the observed values that differ markedly from those at their their closest neighbours.

Distribution of kriging errors, the implications and how to communicate them

NASA Astrophysics Data System (ADS)

Li, HongYi; Milne, Alice; Webster, Richard

2015-04-01

Kriging in one form or another has become perhaps the most popular method for spatial prediction in environmental science. Each prediction is unbiased and of minimum variance, which itself is estimated. The kriging variances depend on the mathematical model chosen to describe the spatial variation; different models, however plausible, give rise to different minimized variances. Practitioners often compare models by so-called cross-validation before finally choosing the most appropriate for their kriging. One proceeds as follows. One removes a unit (a sampling point) from the whole set, kriges the value there and compares the kriged value with the value observed to obtain the deviation or error. One repeats the process for each and every point in turn and for all plausible models. One then computes the mean errors (MEs) and the mean of the squared errors (MSEs). Ideally a squared error should equal the corresponding kriging variance (σ_K^2), and so one is advised to choose the model for which on average the squared errors most nearly equal the kriging variances, i.e. the ratio MSDR=MSE/ σ_K2 ≈1. Maximum likelihood estimation of models almost guarantees that the MSDR equals 1, and so the kriging variances are unbiased predictors of the squared error across the region. The method is based on the assumption that the errors have a normal distribution. The squared deviation ratio (SDR) should therefore be distributed as χ2 with one degree of freedom with a median of 0.455. We have found that often the median of the SDR (MedSDR) is less, in some instances much less, than 0.455 even though the mean of the SDR is close to 1. It seems that in these cases the distributions of the errors are leptokurtic, i.e. they have an excess of predictions close to the true values, excesses near the extremes and a dearth of predictions in between. In these cases the kriging variances are poor measures of the uncertainty at individual sites. The uncertainty is typically under-estimated for the extreme observations and compensated for by over estimating for other observations. Statisticians must tell users when they present maps of predictions. We illustrate the situation with results from mapping salinity in land reclaimed from the Yangtze delta in the Gulf of Hangzhou, China. There the apparent electrical conductivity (EC_a) of the topsoil was measured at 525 points in a field of 2.3~ha. The marginal distribution of the observations was strongly positively skewed, and so the observed EC_as were transformed to their logarithms to give an approximately symmetric distribution. That distribution was strongly platykurtic with short tails and no evident outliers. The logarithms were analysed as a mixed model of quadratic drift plus correlated random residuals with a spherical variogram. The kriged predictions that deviated from their true values with an MSDR of 0.993, but with a medSDR=0.324. The coefficient of kurtosis of the deviations was 1.45, i.e. substantially larger than 0 for a normal distribution. The reasons for this behaviour are being sought. The most likely explanation is that there are spatial outliers, i.e. points at which the observed values that differ markedly from those at their their closest neighbours.

A method to estimate statistical errors of properties derived from charge-density modelling

PubMed Central

Lecomte, Claude

2018-01-01

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This ‘SSD methodology’ procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling. PMID:29724964

Estimation of time averages from irregularly spaced observations - With application to coastal zone color scanner estimates of chlorophyll concentration

NASA Technical Reports Server (NTRS)

Chelton, Dudley B.; Schlax, Michael G.

1991-01-01

The sampling error of an arbitrary linear estimate of a time-averaged quantity constructed from a time series of irregularly spaced observations at a fixed located is quantified through a formalism. The method is applied to satellite observations of chlorophyll from the coastal zone color scanner. The two specific linear estimates under consideration are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all the observations in the time series. The resulting suboptimal estimates are shown to be more accurate than composite averages. Suboptimal estimates are also found to be nearly as accurate as optimal estimates using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters, which makes it a viable practical alternative to the composite average method generally employed at present.

A robust pseudo-inverse spectral filter applied to the Earth Radiation Budget Experiment (ERBE) scanning channels

NASA Technical Reports Server (NTRS)

Avis, L. M.; Green, R. N.; Suttles, J. T.; Gupta, S. K.

1984-01-01

Computer simulations of a least squares estimator operating on the ERBE scanning channels are discussed. The estimator is designed to minimize the errors produced by nonideal spectral response to spectrally varying and uncertain radiant input. The three ERBE scanning channels cover a shortwave band a longwave band and a ""total'' band from which the pseudo inverse spectral filter estimates the radiance components in the shortwave band and a longwave band. The radiance estimator draws on instantaneous field of view (IFOV) scene type information supplied by another algorithm of the ERBE software, and on a priori probabilistic models of the responses of the scanning channels to the IFOV scene types for given Sun scene spacecraft geometry. It is found that the pseudoinverse spectral filter is stable, tolerant of errors in scene identification and in channel response modeling, and, in the absence of such errors, yields minimum variance and essentially unbiased radiance estimates.

Minimization of model representativity errors in identification of point source emission from atmospheric concentration measurements

NASA Astrophysics Data System (ADS)

Sharan, Maithili; Singh, Amit Kumar; Singh, Sarvesh Kumar

2017-11-01

Estimation of an unknown atmospheric release from a finite set of concentration measurements is considered an ill-posed inverse problem. Besides ill-posedness, the estimation process is influenced by the instrumental errors in the measured concentrations and model representativity errors. The study highlights the effect of minimizing model representativity errors on the source estimation. This is described in an adjoint modelling framework and followed in three steps. First, an estimation of point source parameters (location and intensity) is carried out using an inversion technique. Second, a linear regression relationship is established between the measured concentrations and corresponding predicted using the retrieved source parameters. Third, this relationship is utilized to modify the adjoint functions. Further, source estimation is carried out using these modified adjoint functions to analyse the effect of such modifications. The process is tested for two well known inversion techniques, called renormalization and least-square. The proposed methodology and inversion techniques are evaluated for a real scenario by using concentrations measurements from the Idaho diffusion experiment in low wind stable conditions. With both the inversion techniques, a significant improvement is observed in the retrieval of source estimation after minimizing the representativity errors.

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

An empirical model for estimating solar radiation in the Algerian Sahara

NASA Astrophysics Data System (ADS)

Benatiallah, Djelloul; Benatiallah, Ali; Bouchouicha, Kada; Hamouda, Messaoud; Nasri, Bahous

2018-05-01

The present work aims to determine the empirical model R.sun that will allow us to evaluate the solar radiation flues on a horizontal plane and in clear-sky on the located Adrar city (27°18 N and 0°11 W) of Algeria and compare with the results measured at the localized site. The expected results of this comparison are of importance for the investment study of solar systems (solar power plants for electricity production, CSP) and also for the design and performance analysis of any system using the solar energy. Statistical indicators used to evaluate the accuracy of the model where the mean bias error (MBE), root mean square error (RMSE) and coefficient of determination. The results show that for global radiation, the daily correlation coefficient is 0.9984. The mean absolute percentage error is 9.44 %. The daily mean bias error is -7.94 %. The daily root mean square error is 12.31 %.

Stock price estimation using ensemble Kalman Filter square root method

NASA Astrophysics Data System (ADS)

Karya, D. F.; Katias, P.; Herlambang, T.

2018-04-01

Shares are securities as the possession or equity evidence of an individual or corporation over an enterprise, especially public companies whose activity is stock trading. Investment in stocks trading is most likely to be the option of investors as stocks trading offers attractive profits. In determining a choice of safe investment in the stocks, the investors require a way of assessing the stock prices to buy so as to help optimize their profits. An effective method of analysis which will reduce the risk the investors may bear is by predicting or estimating the stock price. Estimation is carried out as a problem sometimes can be solved by using previous information or data related or relevant to the problem. The contribution of this paper is that the estimates of stock prices in high, low, and close categorycan be utilized as investors’ consideration for decision making in investment. In this paper, stock price estimation was made by using the Ensemble Kalman Filter Square Root method (EnKF-SR) and Ensemble Kalman Filter method (EnKF). The simulation results showed that the resulted estimation by applying EnKF method was more accurate than that by the EnKF-SR, with an estimation error of about 0.2 % by EnKF and an estimation error of 2.6 % by EnKF-SR.

Variable is better than invariable: sparse VSS-NLMS algorithms with application to adaptive MIMO channel estimation.

PubMed

Gui, Guan; Chen, Zhang-xin; Xu, Li; Wan, Qun; Huang, Jiyan; Adachi, Fumiyuki

2014-01-01

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics.

Variable Is Better Than Invariable: Sparse VSS-NLMS Algorithms with Application to Adaptive MIMO Channel Estimation

PubMed Central

Gui, Guan; Chen, Zhang-xin; Xu, Li; Wan, Qun; Huang, Jiyan; Adachi, Fumiyuki

2014-01-01

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics. PMID:25089286

Reference-free error estimation for multiple measurement methods.

PubMed

Madan, Hennadii; Pernuš, Franjo; Špiclin, Žiga

2018-01-01

We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the random errors are modeled jointly across all methods, thereby enabling the framework to analyze measurement methods based on similar principles, which may have correlated random errors. Furthermore, the posterior distribution of the error model parameters is estimated from samples obtained by Markov chain Monte-Carlo and analyzed to estimate the parameter values and the unknown true values of the measurand. The framework was validated on six synthetic and one clinical dataset containing measurements of total lesion load, a biomarker of neurodegenerative diseases, which was obtained with four automatic methods by analyzing brain magnetic resonance images. The estimates of bias and random error were in a good agreement with the corresponding least squares regression estimates against a reference.

North Alabama Lightning Mapping Array (LMA): VHF Source Retrieval Algorithm and Error Analyses

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Solakiewicz, R. J.; Blakeslee, R. J.; Goodman, S. J.; Christian, H. J.; Hall, J.; Bailey, J.; Krider, E. P.; Bateman, M. G.; Boccippio, D.

2003-01-01

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results. However, for many source locations, the Curvature Matrix Theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Identifying model error in metabolic flux analysis - a generalized least squares approach.

PubMed

Sokolenko, Stanislav; Quattrociocchi, Marco; Aucoin, Marc G

2016-09-13

The estimation of intracellular flux through traditional metabolic flux analysis (MFA) using an overdetermined system of equations is a well established practice in metabolic engineering. Despite the continued evolution of the methodology since its introduction, there has been little focus on validation and identification of poor model fit outside of identifying "gross measurement error". The growing complexity of metabolic models, which are increasingly generated from genome-level data, has necessitated robust validation that can directly assess model fit. In this work, MFA calculation is framed as a generalized least squares (GLS) problem, highlighting the applicability of the common t-test for model validation. To differentiate between measurement and model error, we simulate ideal flux profiles directly from the model, perturb them with estimated measurement error, and compare their validation to real data. Application of this strategy to an established Chinese Hamster Ovary (CHO) cell model shows how fluxes validated by traditional means may be largely non-significant due to a lack of model fit. With further simulation, we explore how t-test significance relates to calculation error and show that fluxes found to be non-significant have 2-4 fold larger error (if measurement uncertainty is in the 5-10 % range). The proposed validation method goes beyond traditional detection of "gross measurement error" to identify lack of fit between model and data. Although the focus of this work is on t-test validation and traditional MFA, the presented framework is readily applicable to other regression analysis methods and MFA formulations.

Accounting for measurement error in log regression models with applications to accelerated testing.

PubMed

Richardson, Robert; Tolley, H Dennis; Evenson, William E; Lunt, Barry M

2018-01-01

In regression settings, parameter estimates will be biased when the explanatory variables are measured with error. This bias can significantly affect modeling goals. In particular, accelerated lifetime testing involves an extrapolation of the fitted model, and a small amount of bias in parameter estimates may result in a significant increase in the bias of the extrapolated predictions. Additionally, bias may arise when the stochastic component of a log regression model is assumed to be multiplicative when the actual underlying stochastic component is additive. To account for these possible sources of bias, a log regression model with measurement error and additive error is approximated by a weighted regression model which can be estimated using Iteratively Re-weighted Least Squares. Using the reduced Eyring equation in an accelerated testing setting, the model is compared to previously accepted approaches to modeling accelerated testing data with both simulations and real data.

Recursive least squares estimation and its application to shallow trench isolation

NASA Astrophysics Data System (ADS)

Wang, Jin; Qin, S. Joe; Bode, Christopher A.; Purdy, Matthew A.

2003-06-01

In recent years, run-to-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Guo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA.

LS Channel Estimation and Signal Separation for UHF RFID Tag Collision Recovery on the Physical Layer.

PubMed

Duan, Hanjun; Wu, Haifeng; Zeng, Yu; Chen, Yuebin

2016-03-26

In a passive ultra-high frequency (UHF) radio-frequency identification (RFID) system, tag collision is generally resolved on a medium access control (MAC) layer. However, some of collided tag signals could be recovered on a physical (PHY) layer and, thus, enhance the identification efficiency of the RFID system. For the recovery on the PHY layer, channel estimation is a critical issue. Good channel estimation will help to recover the collided signals. Existing channel estimates work well for two collided tags. When the number of collided tags is beyond two, however, the existing estimates have more estimation errors. In this paper, we propose a novel channel estimate for the UHF RFID system. It adopts an orthogonal matrix based on the information of preambles which is known for a reader and applies a minimum-mean-square-error (MMSE) criterion to estimate channels. From the estimated channel, we could accurately separate the collided signals and recover them. By means of numerical results, we show that the proposed estimate has lower estimation errors and higher separation efficiency than the existing estimates.

Objective Analysis of Oceanic Data for Coast Guard Trajectory Models Phase II

DTIC Science & Technology

1997-12-01

as outliers depends on the desired probability of false alarm, Pfa values, which is the probability of marking a valid point as an outlier. Table 2-2...constructed to minimize the mean-squared prediction error of the grid point estimate under the constraint that the estimate is unbiased . The...prediction error, e= Zl(S) _oizl(Si)+oC1iZz(S) (2.44) subject to the constraints of unbiasedness , • c/1 = 1,and (2.45) i SCC12 = 0. (2.46) Denoting

Signal-to-noise ratio estimation in digital computer simulation of lowpass and bandpass systems with applications to analog and digital communications, volume 3

NASA Technical Reports Server (NTRS)

Tranter, W. H.; Turner, M. D.

1977-01-01

Techniques are developed to estimate power gain, delay, signal-to-noise ratio, and mean square error in digital computer simulations of lowpass and bandpass systems. The techniques are applied to analog and digital communications. The signal-to-noise ratio estimates are shown to be maximum likelihood estimates in additive white Gaussian noise. The methods are seen to be especially useful for digital communication systems where the mapping from the signal-to-noise ratio to the error probability can be obtained. Simulation results show the techniques developed to be accurate and quite versatile in evaluating the performance of many systems through digital computer simulation.

Finite-error metrological bounds on multiparameter Hamiltonian estimation

NASA Astrophysics Data System (ADS)

Kura, Naoto; Ueda, Masahito

2018-01-01

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance δ . The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

Modelling of the batch biosorption system: study on exchange of protons with cell wall-bound mineral ions.

PubMed

Mishra, Vishal

2015-01-01

The interchange of the protons with the cell wall-bound calcium and magnesium ions at the interface of solution/bacterial cell surface in the biosorption system at various concentrations of protons has been studied in the present work. A mathematical model for establishing the correlation between concentration of protons and active sites was developed and optimized. The sporadic limited residence time reactor was used to titrate the calcium and magnesium ions at the individual data point. The accuracy of the proposed mathematical model was estimated using error functions such as nonlinear regression, adjusted nonlinear regression coefficient, the chi-square test, P-test and F-test. The values of the chi-square test (0.042-0.017), P-test (<0.001-0.04), sum of square errors (0.061-0.016), root mean square error (0.01-0.04) and F-test (2.22-19.92) reported in the present research indicated the suitability of the model over a wide range of proton concentrations. The zeta potential of the bacterium surface at various concentrations of protons was observed to validate the denaturation of active sites.

Novel SVM-based technique to improve rainfall estimation over the Mediterranean region (north of Algeria) using the multispectral MSG SEVIRI imagery

NASA Astrophysics Data System (ADS)

Sehad, Mounir; Lazri, Mourad; Ameur, Soltane

2017-03-01

In this work, a new rainfall estimation technique based on the high spatial and temporal resolution of the Spinning Enhanced Visible and Infra Red Imager (SEVIRI) aboard the Meteosat Second Generation (MSG) is presented. This work proposes efficient scheme rainfall estimation based on two multiclass support vector machine (SVM) algorithms: SVM_D for daytime and SVM_N for night time rainfall estimations. Both SVM models are trained using relevant rainfall parameters based on optical, microphysical and textural cloud proprieties. The cloud parameters are derived from the Spectral channels of the SEVIRI MSG radiometer. The 3-hourly and daily accumulated rainfall are derived from the 15 min-rainfall estimation given by the SVM classifiers for each MSG observation image pixel. The SVMs were trained with ground meteorological radar precipitation scenes recorded from November 2006 to March 2007 over the north of Algeria located in the Mediterranean region. Further, the SVM_D and SVM_N models were used to estimate 3-hourly and daily rainfall using data set gathered from November 2010 to March 2011 over north Algeria. The results were validated against collocated rainfall observed by rain gauge network. Indeed, the statistical scores given by correlation coefficient, bias, root mean square error and mean absolute error, showed good accuracy of rainfall estimates by the present technique. Moreover, rainfall estimates of our technique were compared with two high accuracy rainfall estimates methods based on MSG SEVIRI imagery namely: random forests (RF) based approach and an artificial neural network (ANN) based technique. The findings of the present technique indicate higher correlation coefficient (3-hourly: 0.78; daily: 0.94), and lower mean absolute error and root mean square error values. The results show that the new technique assign 3-hourly and daily rainfall with good and better accuracy than ANN technique and (RF) model.

Technique for estimating the 2- to 500-year flood discharges on unregulated streams in rural Missouri

USGS Publications Warehouse

Alexander, Terry W.; Wilson, Gary L.

1995-01-01

A generalized least-squares regression technique was used to relate the 2- to 500-year flood discharges from 278 selected streamflow-gaging stations to statistically significant basin characteristics. The regression relations (estimating equations) were defined for three hydrologic regions (I, II, and III) in rural Missouri. Ordinary least-squares regression analyses indicate that drainage area (Regions I, II, and III) and main-channel slope (Regions I and II) are the only basin characteristics needed for computing the 2- to 500-year design-flood discharges at gaged or ungaged stream locations. The resulting generalized least-squares regression equations provide a technique for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges on unregulated streams in rural Missouri. The regression equations for Regions I and II were developed from stream-flow-gaging stations with drainage areas ranging from 0.13 to 11,500 square miles and 0.13 to 14,000 square miles, and main-channel slopes ranging from 1.35 to 150 feet per mile and 1.20 to 279 feet per mile. The regression equations for Region III were developed from streamflow-gaging stations with drainage areas ranging from 0.48 to 1,040 square miles. Standard errors of estimate for the generalized least-squares regression equations in Regions I, II, and m ranged from 30 to 49 percent.

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

Accuracy of maximum likelihood and least-squares estimates in the lidar slope method with noisy data.

PubMed

Eberhard, Wynn L

2017-04-01

The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

NASA Astrophysics Data System (ADS)

Cheung, KW; So, HC; Ma, W.-K.; Chan, YT

2006-12-01

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

Gene expression programming approach for the estimation of moisture ratio in herbal plants drying with vacuum heat pump dryer

NASA Astrophysics Data System (ADS)

Dikmen, Erkan; Ayaz, Mahir; Gül, Doğan; Şahin, Arzu Şencan

2017-07-01

The determination of drying behavior of herbal plants is a complex process. In this study, gene expression programming (GEP) model was used to determine drying behavior of herbal plants as fresh sweet basil, parsley and dill leaves. Time and drying temperatures are input parameters for the estimation of moisture ratio of herbal plants. The results of the GEP model are compared with experimental drying data. The statistical values as mean absolute percentage error, root-mean-squared error and R-square are used to calculate the difference between values predicted by the GEP model and the values actually observed from the experimental study. It was found that the results of the GEP model and experimental study are in moderately well agreement. The results have shown that the GEP model can be considered as an efficient modelling technique for the prediction of moisture ratio of herbal plants.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Retrieving air humidity, global solar radiation, and reference evapotranspiration from daily temperatures: development and validation of new methods for Mexico. Part I: humidity

NASA Astrophysics Data System (ADS)

Lobit, P.; López Pérez, L.; Lhomme, J. P.; Gómez Tagle, A.

2017-07-01

This study evaluates the dew point method (Allen et al. 1998) to estimate atmospheric vapor pressure from minimum temperature, and proposes an improved model to estimate it from maximum and minimum temperature. Both methods were evaluated on 786 weather stations in Mexico. The dew point method induced positive bias in dry areas but also negative bias in coastal areas, and its average root mean square error for all evaluated stations was 0.38 kPa. The improved model assumed a bi-linear relation between estimated vapor pressure deficit (difference between saturated vapor pressure at minimum and average temperature) and measured vapor pressure deficit. The parameters of these relations were estimated from historical annual median values of relative humidity. This model removed bias and allowed for a root mean square error of 0.31 kPa. When no historical measurements of relative humidity were available, empirical relations were proposed to estimate it from latitude and altitude, with only a slight degradation on the model accuracy (RMSE = 0.33 kPa, bias = -0.07 kPa). The applicability of the method to other environments is discussed.

Analysis of Learning Curve Fitting Techniques.

DTIC Science & Technology

1987-09-01

1986. 15. Neter, John and others. Applied Linear Regression Models. Homewood IL: Irwin, 19-33. 16. SAS User’s Guide: Basics, Version 5 Edition. SAS... Linear Regression Techniques (15:23-52). Random errors are assumed to be normally distributed when using -# ordinary least-squares, according to Johnston...lot estimated by the improvement curve formula. For a more detailed explanation of the ordinary least-squares technique, see Neter, et. al., Applied

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Simultaneous Estimation of Microphysical Parameters and Atmospheric State Variables With Radar Data and Ensemble Square-root Kalman Filter

NASA Astrophysics Data System (ADS)

Tong, M.; Xue, M.

2006-12-01

An important source of model error for convective-scale data assimilation and prediction is microphysical parameterization. This study investigates the possibility of estimating up to five fundamental microphysical parameters, which are closely involved in the definition of drop size distribution of microphysical species in a commonly used single-moment ice microphysics scheme, using radar observations and the ensemble Kalman filter method. The five parameters include the intercept parameters for rain, snow and hail/graupel, and the bulk densities of hail/graupel and snow. Parameter sensitivity and identifiability are first examined. The ensemble square-root Kalman filter (EnSRF) is employed for simultaneous state and parameter estimation. OSS experiments are performed for a model-simulated supercell storm, in which the five microphysical parameters are estimated individually or in different combinations starting from different initial guesses. When error exists in only one of the microphysical parameters, the parameter can be successfully estimated without exception. The estimation of multiple parameters is found to be less robust, with end results of estimation being sensitive to the realization of the initial parameter perturbation. This is believed to be because of the reduced parameter identifiability and the existence of non-unique solutions. The results of state estimation are, however, always improved when simultaneous parameter estimation is performed, even when the estimated parameters values are not accurate.

Relative Performance of Rescaling and Resampling Approaches to Model Chi Square and Parameter Standard Error Estimation in Structural Equation Modeling.

ERIC Educational Resources Information Center

Nevitt, Johnathan; Hancock, Gregory R.

Though common structural equation modeling (SEM) methods are predicated upon the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to use distribution-free estimation methods. Fortunately, promising alternatives are being integrated into…

Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories

Treesearch

Steen Magnussen; Ronald E. McRoberts; Erkki O. Tomppo

2009-01-01

New model-based estimators of the uncertainty of pixel-level and areal k-nearest neighbour (knn) predictions of attribute Y from remotely-sensed ancillary data X are presented. Non-parametric functions predict Y from scalar 'Single Index Model' transformations of X. Variance functions generated...

Adaptive optimisation-offline cyber attack on remote state estimator

NASA Astrophysics Data System (ADS)

Huang, Xin; Dong, Jiuxiang

2017-10-01

Security issues of cyber-physical systems have received increasing attentions in recent years. In this paper, deception attacks on the remote state estimator equipped with the chi-squared failure detector are considered, and it is assumed that the attacker can monitor and modify all the sensor data. A novel adaptive optimisation-offline cyber attack strategy is proposed, where using the current and previous sensor data, the attack can yield the largest estimation error covariance while ensuring to be undetected by the chi-squared monitor. From the attacker's perspective, the attack is better than the existing linear deception attacks to degrade the system performance. Finally, some numerical examples are provided to demonstrate theoretical results.

Evaluation of spatial filtering on the accuracy of wheat area estimate

NASA Technical Reports Server (NTRS)

Dejesusparada, N. (Principal Investigator); Moreira, M. A.; Chen, S. C.; Delima, A. M.

1982-01-01

A 3 x 3 pixel spatial filter for postclassification was used for wheat classification to evaluate the effects of this procedure on the accuracy of area estimation using LANDSAT digital data obtained from a single pass. Quantitative analyses were carried out in five test sites (approx 40 sq km each) and t tests showed that filtering with threshold values significantly decreased errors of commission and omission. In area estimation filtering improved the overestimate of 4.5% to 2.7% and the root-mean-square error decreased from 126.18 ha to 107.02 ha. Extrapolating the same procedure of automatic classification using spatial filtering for postclassification to the whole study area, the accuracy in area estimate was improved from the overestimate of 10.9% to 9.7%. It is concluded that when single pass LANDSAT data is used for crop identification and area estimation the postclassification procedure using a spatial filter provides a more accurate area estimate by reducing classification errors.

Robust estimation of thermodynamic parameters (ΔH, ΔS and ΔCp) for prediction of retention time in gas chromatography - Part II (Application).

PubMed

Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira

2015-12-18

For this work, an analysis of parameter estimation for the retention factor in GC model was performed, considering two different criteria: sum of square error, and maximum error in absolute value; relevant statistics are described for each case. The main contribution of this work is the implementation of an initialization scheme (specialized) for the estimated parameters, which features fast convergence (low computational time) and is based on knowledge of the surface of the error criterion. In an application to a series of alkanes, specialized initialization resulted in significant reduction to the number of evaluations of the objective function (reducing computational time) in the parameter estimation. The obtained reduction happened between one and two orders of magnitude, compared with the simple random initialization. Copyright © 2015 Elsevier B.V. All rights reserved.

Inertial and time-of-arrival ranging sensor fusion.

PubMed

Vasilyev, Paul; Pearson, Sean; El-Gohary, Mahmoud; Aboy, Mateo; McNames, James

2017-05-01

Wearable devices with embedded kinematic sensors including triaxial accelerometers, gyroscopes, and magnetometers are becoming widely used in applications for tracking human movement in domains that include sports, motion gaming, medicine, and wellness. The kinematic sensors can be used to estimate orientation, but can only estimate changes in position over short periods of time. We developed a prototype sensor that includes ultra wideband ranging sensors and kinematic sensors to determine the feasibility of fusing the two sensor technologies to estimate both orientation and position. We used a state space model and applied the unscented Kalman filter to fuse the sensor information. Our results demonstrate that it is possible to estimate orientation and position with less error than is possible with either sensor technology alone. In our experiment we obtained a position root mean square error of 5.2cm and orientation error of 4.8° over a 15min recording. Copyright © 2017 Elsevier B.V. All rights reserved.

Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments

PubMed Central

Erkoc, Ali; Emiroglu, Esra

2014-01-01

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set. PMID:25202738

Graphical evaluation of the ridge-type robust regression estimators in mixture experiments.

PubMed

Erkoc, Ali; Emiroglu, Esra; Akay, Kadri Ulas

2014-01-01

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.

Estimating random errors due to shot noise in backscatter lidar observations.

PubMed

Liu, Zhaoyan; Hunt, William; Vaughan, Mark; Hostetler, Chris; McGill, Matthew; Powell, Kathleen; Winker, David; Hu, Yongxiang

2006-06-20

We discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson- distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root mean square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF, uncertainties can be reliably calculated from or for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations lidar and tested using data from the Lidar In-space Technology Experiment.

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

NASA Technical Reports Server (NTRS)

Liu, Zhaoyan; Hunt, William; Vaughan, Mark A.; Hostetler, Chris A.; McGill, Matthew J.; Powell, Kathy; Winker, David M.; Hu, Yongxiang

2006-01-01

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Use of historical control data for assessing treatment effects in clinical trials.

PubMed

Viele, Kert; Berry, Scott; Neuenschwander, Beat; Amzal, Billy; Chen, Fang; Enas, Nathan; Hobbs, Brian; Ibrahim, Joseph G; Kinnersley, Nelson; Lindborg, Stacy; Micallef, Sandrine; Roychoudhury, Satrajit; Thompson, Laura

2014-01-01

Clinical trials rarely, if ever, occur in a vacuum. Generally, large amounts of clinical data are available prior to the start of a study, particularly on the current study's control arm. There is obvious appeal in using (i.e., 'borrowing') this information. With historical data providing information on the control arm, more trial resources can be devoted to the novel treatment while retaining accurate estimates of the current control arm parameters. This can result in more accurate point estimates, increased power, and reduced type I error in clinical trials, provided the historical information is sufficiently similar to the current control data. If this assumption of similarity is not satisfied, however, one can acquire increased mean square error of point estimates due to bias and either reduced power or increased type I error depending on the direction of the bias. In this manuscript, we review several methods for historical borrowing, illustrating how key parameters in each method affect borrowing behavior, and then, we compare these methods on the basis of mean square error, power and type I error. We emphasize two main themes. First, we discuss the idea of 'dynamic' (versus 'static') borrowing. Second, we emphasize the decision process involved in determining whether or not to include historical borrowing in terms of the perceived likelihood that the current control arm is sufficiently similar to the historical data. Our goal is to provide a clear review of the key issues involved in historical borrowing and provide a comparison of several methods useful for practitioners. Copyright © 2013 John Wiley & Sons, Ltd.

Use of historical control data for assessing treatment effects in clinical trials

PubMed Central

Viele, Kert; Berry, Scott; Neuenschwander, Beat; Amzal, Billy; Chen, Fang; Enas, Nathan; Hobbs, Brian; Ibrahim, Joseph G.; Kinnersley, Nelson; Lindborg, Stacy; Micallef, Sandrine; Roychoudhury, Satrajit; Thompson, Laura

2014-01-01

Clinical trials rarely, if ever, occur in a vacuum. Generally, large amounts of clinical data are available prior to the start of a study, particularly on the current study’s control arm. There is obvious appeal in using (i.e., ‘borrowing’) this information. With historical data providing information on the control arm, more trial resources can be devoted to the novel treatment while retaining accurate estimates of the current control arm parameters. This can result in more accurate point estimates, increased power, and reduced type I error in clinical trials, provided the historical information is sufficiently similar to the current control data. If this assumption of similarity is not satisfied, however, one can acquire increased mean square error of point estimates due to bias and either reduced power or increased type I error depending on the direction of the bias. In this manuscript, we review several methods for historical borrowing, illustrating how key parameters in each method affect borrowing behavior, and then, we compare these methods on the basis of mean square error, power and type I error. We emphasize two main themes. First, we discuss the idea of ‘dynamic’ (versus ‘static’) borrowing. Second, we emphasize the decision process involved in determining whether or not to include historical borrowing in terms of the perceived likelihood that the current control arm is sufficiently similar to the historical data. Our goal is to provide a clear review of the key issues involved in historical borrowing and provide a comparison of several methods useful for practitioners. PMID:23913901

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research. PMID:26579002

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice

PubMed Central

Wang, Yong; Ma, Xiaolei; Liu, Yong; Gong, Ke; Henricakson, Kristian C.; Xu, Maozeng; Wang, Yinhai

2016-01-01

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior. PMID:26761209

A comparison of abundance estimates from extended batch-marking and Jolly–Seber-type experiments

PubMed Central

Cowen, Laura L E; Besbeas, Panagiotis; Morgan, Byron J T; Schwarz, Carl J

2014-01-01

Little attention has been paid to the use of multi-sample batch-marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. (2010) present a pseudo-likelihood for a multi-sample batch-marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz–Thompson-type estimator. We have developed and maximized the likelihood for batch-marking studies. We use data simulated from a Jolly–Seber-type study and convert this to what would have been obtained from an extended batch-marking study. We compare our abundance estimates obtained from the Crosbie–Manly–Arnason–Schwarz (CMAS) model with those of the extended batch-marking model to determine the efficiency of collecting and analyzing batch-marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo-likelihood method of Huggins et al. (2010). When faced with designing a batch-marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size. PMID:24558576

Least Squares Neural Network-Based Wireless E-Nose System Using an SnO₂ Sensor Array.

PubMed

Shahid, Areej; Choi, Jong-Hyeok; Rana, Abu Ul Hassan Sarwar; Kim, Hyun-Seok

2018-05-06

Over the last few decades, the development of the electronic nose (E-nose) for detection and quantification of dangerous and odorless gases, such as methane (CH₄) and carbon monoxide (CO), using an array of SnO₂ gas sensors has attracted considerable attention. This paper addresses sensor cross sensitivity by developing a classifier and estimator using an artificial neural network (ANN) and least squares regression (LSR), respectively. Initially, the ANN was implemented using a feedforward pattern recognition algorithm to learn the collective behavior of an array as the signature of a particular gas. In the second phase, the classified gas was quantified by minimizing the mean square error using LSR. The combined approach produced 98.7% recognition probability, with 95.5 and 94.4% estimated gas concentration accuracies for CH₄ and CO, respectively. The classifier and estimator parameters were deployed in a remote microcontroller for the actualization of a wireless E-nose system.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Increasing point-count duration increases standard error

USGS Publications Warehouse

Smith, W.P.; Twedt, D.J.; Hamel, P.B.; Ford, R.P.; Wiedenfeld, D.A.; Cooper, R.J.

1998-01-01

We examined data from point counts of varying duration in bottomland forests of west Tennessee and the Mississippi Alluvial Valley to determine if counting interval influenced sampling efficiency. Estimates of standard error increased as point count duration increased both for cumulative number of individuals and species in both locations. Although point counts appear to yield data with standard errors proportional to means, a square root transformation of the data may stabilize the variance. Using long (>10 min) point counts may reduce sample size and increase sampling error, both of which diminish statistical power and thereby the ability to detect meaningful changes in avian populations.

A general model for attitude determination error analysis

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Seidewitz, ED; Nicholson, Mark

1988-01-01

An overview is given of a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The models presented include both batch least-squares and sequential attitude estimation processes for both spin-stabilized and three-axis stabilized spacecraft. The discussion includes a brief description of a dynamics model of strapdown gyros, but it does not cover other sensor models. Model parameters can be chosen to be solve-for parameters, which are assumed to be estimated as part of the determination process, or consider parameters, which are assumed to have errors but not to be estimated. The only restriction on this choice is that the time evolution of the consider parameters must not depend on any of the solve-for parameters. The result of an error analysis is an indication of the contributions of the various error sources to the uncertainties in the determination of the spacecraft solve-for parameters. The model presented gives the uncertainty due to errors in the a priori estimates of the solve-for parameters, the uncertainty due to measurement noise, the uncertainty due to dynamic noise (also known as process noise or measurement noise), the uncertainty due to the consider parameters, and the overall uncertainty due to all these sources of error.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Region of influence regression for estimating the 50-year flood at ungaged sites

USGS Publications Warehouse

Tasker, Gary D.; Hodge, S.A.; Barks, C.S.

1996-01-01

Five methods of developing regional regression models to estimate flood characteristics at ungaged sites in Arkansas are examined. The methods differ in the manner in which the State is divided into subrogions. Each successive method (A to E) is computationally more complex than the previous method. Method A makes no subdivision. Methods B and C define two and four geographic subrogions, respectively. Method D uses cluster/discriminant analysis to define subrogions on the basis of similarities in watershed characteristics. Method E, the new region of influence method, defines a unique subregion for each ungaged site. Split-sample results indicate that, in terms of root-mean-square error, method E (38 percent error) is best. Methods C and D (42 and 41 percent error) were in a virtual tie for second, and methods B (44 percent error) and A (49 percent error) were fourth and fifth best.

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Sulcal set optimization for cortical surface registration.

PubMed

Joshi, Anand A; Pantazis, Dimitrios; Li, Quanzheng; Damasio, Hanna; Shattuck, David W; Toga, Arthur W; Leahy, Richard M

2010-04-15

Flat mapping based cortical surface registration constrained by manually traced sulcal curves has been widely used for inter subject comparisons of neuroanatomical data. Even for an experienced neuroanatomist, manual sulcal tracing can be quite time consuming, with the cost increasing with the number of sulcal curves used for registration. We present a method for estimation of an optimal subset of size N(C) from N possible candidate sulcal curves that minimizes a mean squared error metric over all combinations of N(C) curves. The resulting procedure allows us to estimate a subset with a reduced number of curves to be traced as part of the registration procedure leading to optimal use of manual labeling effort for registration. To minimize the error metric we analyze the correlation structure of the errors in the sulcal curves by modeling them as a multivariate Gaussian distribution. For a given subset of sulci used as constraints in surface registration, the proposed model estimates registration error based on the correlation structure of the sulcal errors. The optimal subset of constraint curves consists of the N(C) sulci that jointly minimize the estimated error variance for the subset of unconstrained curves conditioned on the N(C) constraint curves. The optimal subsets of sulci are presented and the estimated and actual registration errors for these subsets are computed. Copyright 2009 Elsevier Inc. All rights reserved.

Estimating Root Mean Square Errors in Remotely Sensed Soil Moisture over Continental Scale Domains

NASA Technical Reports Server (NTRS)

Draper, Clara S.; Reichle, Rolf; de Jeu, Richard; Naeimi, Vahid; Parinussa, Robert; Wagner, Wolfgang

2013-01-01

Root Mean Square Errors (RMSE) in the soil moisture anomaly time series obtained from the Advanced Scatterometer (ASCAT) and the Advanced Microwave Scanning Radiometer (AMSR-E; using the Land Parameter Retrieval Model) are estimated over a continental scale domain centered on North America, using two methods: triple colocation (RMSETC ) and error propagation through the soil moisture retrieval models (RMSEEP ). In the absence of an established consensus for the climatology of soil moisture over large domains, presenting a RMSE in soil moisture units requires that it be specified relative to a selected reference data set. To avoid the complications that arise from the use of a reference, the RMSE is presented as a fraction of the time series standard deviation (fRMSE). For both sensors, the fRMSETC and fRMSEEP show similar spatial patterns of relatively highlow errors, and the mean fRMSE for each land cover class is consistent with expectations. Triple colocation is also shown to be surprisingly robust to representativity differences between the soil moisture data sets used, and it is believed to accurately estimate the fRMSE in the remotely sensed soil moisture anomaly time series. Comparing the ASCAT and AMSR-E fRMSETC shows that both data sets have very similar accuracy across a range of land cover classes, although the AMSR-E accuracy is more directly related to vegetation cover. In general, both data sets have good skill up to moderate vegetation conditions.

Investigation of adaptive filtering and MDL mitigation based on space-time block-coding for spatial division multiplexed coherent receivers

NASA Astrophysics Data System (ADS)

Weng, Yi; He, Xuan; Yao, Wang; Pacheco, Michelle C.; Wang, Junyi; Pan, Zhongqi

2017-07-01

In this paper, we explored the performance of space-time block-coding (STBC) assisted multiple-input multiple-output (MIMO) scheme for modal dispersion and mode-dependent loss (MDL) mitigation in spatial-division multiplexed optical communication systems, whereas the weight matrices of frequency-domain equalization (FDE) were updated heuristically using decision-directed recursive least squares (RLS) algorithm for convergence and channel estimation. The proposed STBC-RLS algorithm can achieve 43.6% enhancement on convergence rate over conventional least mean squares (LMS) for quadrature phase-shift keying (QPSK) signals with merely 16.2% increase in hardware complexity. The overall optical signal to noise ratio (OSNR) tolerance can be improved via STBC by approximately 3.1, 4.9, 7.8 dB for QPSK, 16-quadrature amplitude modulation (QAM) and 64-QAM with respective bit-error-rates (BER) and minimum-mean-square-error (MMSE).

Resimulation of noise: a precision estimator for least square error curve-fitting tested for axial strain time constant imaging

NASA Astrophysics Data System (ADS)

Nair, S. P.; Righetti, R.

2015-05-01

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.

The output least-squares approach to estimating Lamé moduli

NASA Astrophysics Data System (ADS)

Gockenbach, Mark S.

2007-12-01

The Lamé moduli of a heterogeneous, isotropic, planar membrane can be estimated by observing the displacement of the membrane under a known edge traction, and choosing estimates of the moduli that best predict the observed displacement under a finite-element simulation. This algorithm converges to the exact moduli given pointwise measurements of the displacement on an increasingly fine mesh. The error estimates that prove this convergence also show the instability of the inverse problem.

Synthesis of hover autopilots for rotary-wing VTOL aircraft

NASA Technical Reports Server (NTRS)

Hall, W. E.; Bryson, A. E., Jr.

1972-01-01

The practical situation is considered where imperfect information on only a few rotor and fuselage state variables is available. Filters are designed to estimate all the state variables from noisy measurements of fuselage pitch/roll angles and from noisy measurements of both fuselage and rotor pitch/roll angles. The mean square response of the vehicle to a very gusty, random wind is computed using various filter/controllers and is found to be quite satisfactory although, of course, not so good as when one has perfect information (idealized case). The second part of the report considers precision hover over a point on the ground. A vehicle model without rotor dynamics is used and feedback signals in position and integral of position error are added. The mean square response of the vehicle to a very gusty, random wind is computed, assuming perfect information feedback, and is found to be excellent. The integral error feedback gives zero position error for a steady wind, and smaller position error for a random wind.

Estimation of perceptible water vapor of atmosphere using artificial neural network, support vector machine and multiple linear regression algorithm and their comparative study

NASA Astrophysics Data System (ADS)

Shastri, Niket; Pathak, Kamlesh

2018-05-01

The water vapor content in atmosphere plays very important role in climate. In this paper the application of GPS signal in meteorology is discussed, which is useful technique that is used to estimate the perceptible water vapor of atmosphere. In this paper various algorithms like artificial neural network, support vector machine and multiple linear regression are use to predict perceptible water vapor. The comparative studies in terms of root mean square error and mean absolute errors are also carried out for all the algorithms.

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2009-01-01

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling under Conditions of Misspecification and Nonnormality.

ERIC Educational Resources Information Center

Olsson, Ulf Henning; Foss, Tron; Troye, Sigurd V.; Howell, Roy D.

2000-01-01

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

Sampling plantations to determine white-pine weevil injury

Treesearch

Robert L. Talerico; Robert W., Jr. Wilson

1973-01-01

Use of 1/10-acre square plots to obtain estimates of the proportion of never-weeviled trees necessary for evaluating and scheduling white-pine weevil control is described. The optimum number of trees to observe per plot is estimated from data obtained from sample plantations in the Northeast and a table is given. Of sample size required to achieve a standard error of...

Inverting Image Data For Optical Testing And Alignment

NASA Technical Reports Server (NTRS)

Shao, Michael; Redding, David; Yu, Jeffrey W.; Dumont, Philip J.

1993-01-01

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Multi-Gaussian fitting for pulse waveform using Weighted Least Squares and multi-criteria decision making method.

PubMed

Wang, Lu; Xu, Lisheng; Feng, Shuting; Meng, Max Q-H; Wang, Kuanquan

2013-11-01

Analysis of pulse waveform is a low cost, non-invasive method for obtaining vital information related to the conditions of the cardiovascular system. In recent years, different Pulse Decomposition Analysis (PDA) methods have been applied to disclose the pathological mechanisms of the pulse waveform. All these methods decompose single-period pulse waveform into a constant number (such as 3, 4 or 5) of individual waves. Furthermore, those methods do not pay much attention to the estimation error of the key points in the pulse waveform. The estimation of human vascular conditions depends on the key points' positions of pulse wave. In this paper, we propose a Multi-Gaussian (MG) model to fit real pulse waveforms using an adaptive number (4 or 5 in our study) of Gaussian waves. The unknown parameters in the MG model are estimated by the Weighted Least Squares (WLS) method and the optimized weight values corresponding to different sampling points are selected by using the Multi-Criteria Decision Making (MCDM) method. Performance of the MG model and the WLS method has been evaluated by fitting 150 real pulse waveforms of five different types. The resulting Normalized Root Mean Square Error (NRMSE) was less than 2.0% and the estimation accuracy for the key points was satisfactory, demonstrating that our proposed method is effective in compressing, synthesizing and analyzing pulse waveforms. Copyright © 2013 Elsevier Ltd. All rights reserved.

Water quality management using statistical analysis and time-series prediction model

NASA Astrophysics Data System (ADS)

Parmar, Kulwinder Singh; Bhardwaj, Rashmi

2014-12-01

This paper deals with water quality management using statistical analysis and time-series prediction model. The monthly variation of water quality standards has been used to compare statistical mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation at Yamuna River. Model validated using R-squared, root mean square error, mean absolute percentage error, maximum absolute percentage error, mean absolute error, maximum absolute error, normalized Bayesian information criterion, Ljung-Box analysis, predicted value and confidence limits. Using auto regressive integrated moving average model, future water quality parameters values have been estimated. It is observed that predictive model is useful at 95 % confidence limits and curve is platykurtic for potential of hydrogen (pH), free ammonia, total Kjeldahl nitrogen, dissolved oxygen, water temperature (WT); leptokurtic for chemical oxygen demand, biochemical oxygen demand. Also, it is observed that predicted series is close to the original series which provides a perfect fit. All parameters except pH and WT cross the prescribed limits of the World Health Organization /United States Environmental Protection Agency, and thus water is not fit for drinking, agriculture and industrial use.

Estimating errors in least-squares fitting

NASA Technical Reports Server (NTRS)

Richter, P. H.

1995-01-01

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data.

PubMed

Lim, Changwon

2015-03-30

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program. Copyright © 2014 John Wiley & Sons, Ltd.

Ultrasonic tracking of shear waves using a particle filter.

PubMed

Ingle, Atul N; Ma, Chi; Varghese, Tomy

2015-11-01

This paper discusses an application of particle filtering for estimating shear wave velocity in tissue using ultrasound elastography data. Shear wave velocity estimates are of significant clinical value as they help differentiate stiffer areas from softer areas which is an indicator of potential pathology. Radio-frequency ultrasound echo signals are used for tracking axial displacements and obtaining the time-to-peak displacement at different lateral locations. These time-to-peak data are usually very noisy and cannot be used directly for computing velocity. In this paper, the denoising problem is tackled using a hidden Markov model with the hidden states being the unknown (noiseless) time-to-peak values. A particle filter is then used for smoothing out the time-to-peak curve to obtain a fit that is optimal in a minimum mean squared error sense. Simulation results from synthetic data and finite element modeling suggest that the particle filter provides lower mean squared reconstruction error with smaller variance as compared to standard filtering methods, while preserving sharp boundary detail. Results from phantom experiments show that the shear wave velocity estimates in the stiff regions of the phantoms were within 20% of those obtained from a commercial ultrasound scanner and agree with estimates obtained using a standard method using least-squares fit. Estimates of area obtained from the particle filtered shear wave velocity maps were within 10% of those obtained from B-mode ultrasound images. The particle filtering approach can be used for producing visually appealing SWV reconstructions by effectively delineating various areas of the phantom with good image quality properties comparable to existing techniques.

Comparing least-squares and quantile regression approaches to analyzing median hospital charges.

PubMed

Olsen, Cody S; Clark, Amy E; Thomas, Andrea M; Cook, Lawrence J

2012-07-01

Emergency department (ED) and hospital charges obtained from administrative data sets are useful descriptors of injury severity and the burden to EDs and the health care system. However, charges are typically positively skewed due to costly procedures, long hospital stays, and complicated or prolonged treatment for few patients. The median is not affected by extreme observations and is useful in describing and comparing distributions of hospital charges. A least-squares analysis employing a log transformation is one approach for estimating median hospital charges, corresponding confidence intervals (CIs), and differences between groups; however, this method requires certain distributional properties. An alternate method is quantile regression, which allows estimation and inference related to the median without making distributional assumptions. The objective was to compare the log-transformation least-squares method to the quantile regression approach for estimating median hospital charges, differences in median charges between groups, and associated CIs. The authors performed simulations using repeated sampling of observed statewide ED and hospital charges and charges randomly generated from a hypothetical lognormal distribution. The median and 95% CI and the multiplicative difference between the median charges of two groups were estimated using both least-squares and quantile regression methods. Performance of the two methods was evaluated. In contrast to least squares, quantile regression produced estimates that were unbiased and had smaller mean square errors in simulations of observed ED and hospital charges. Both methods performed well in simulations of hypothetical charges that met least-squares method assumptions. When the data did not follow the assumed distribution, least-squares estimates were often biased, and the associated CIs had lower than expected coverage as sample size increased. Quantile regression analyses of hospital charges provide unbiased estimates even when lognormal and equal variance assumptions are violated. These methods may be particularly useful in describing and analyzing hospital charges from administrative data sets. © 2012 by the Society for Academic Emergency Medicine.

Local Linear Regression for Data with AR Errors.

PubMed

Li, Runze; Li, Yan

2009-07-01

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

A study of GPS measurement errors due to noise and multipath interference for CGADS

NASA Technical Reports Server (NTRS)

Axelrad, Penina; MacDoran, Peter F.; Comp, Christopher J.

1996-01-01

This report describes a study performed by the Colorado Center for Astrodynamics Research (CCAR) on GPS measurement errors in the Codeless GPS Attitude Determination System (CGADS) due to noise and multipath interference. Preliminary simulation models fo the CGADS receiver and orbital multipath are described. The standard FFT algorithms for processing the codeless data is described and two alternative algorithms - an auto-regressive/least squares (AR-LS) method, and a combined adaptive notch filter/least squares (ANF-ALS) method, are also presented. Effects of system noise, quantization, baseband frequency selection, and Doppler rates on the accuracy of phase estimates with each of the processing methods are shown. Typical electrical phase errors for the AR-LS method are 0.2 degrees, compared to 0.3 and 0.5 degrees for the FFT and ANF-ALS algorithms, respectively. Doppler rate was found to have the largest effect on the performance.

Application of Adaptive Neuro-Fuzzy Inference System for Prediction of Neutron Yield of IR-IECF Facility in High Voltages

NASA Astrophysics Data System (ADS)

Adineh-Vand, A.; Torabi, M.; Roshani, G. H.; Taghipour, M.; Feghhi, S. A. H.; Rezaei, M.; Sadati, S. M.

2013-09-01

This paper presents a soft computing based artificial intelligent technique, adaptive neuro-fuzzy inference system (ANFIS) to predict the neutron production rate (NPR) of IR-IECF device in wide discharge current and voltage ranges. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS model. The performance of the proposed ANFIS model is tested using the experimental data using four performance measures: correlation coefficient, mean absolute error, mean relative error percentage (MRE%) and root mean square error. The obtained results show that the proposed ANFIS model has achieved good agreement with the experimental results. In comparison to the experimental data the proposed ANFIS model has MRE% <1.53 and 2.85 % for training and testing data respectively. Therefore, this model can be used as an efficient tool to predict the NPR in the IR-IECF device.

Estimating current and future streamflow characteristics at ungaged sites, central and eastern Montana, with application to evaluating effects of climate change on fish populations

USGS Publications Warehouse

Sando, Roy; Chase, Katherine J.

2017-03-23

A common statistical procedure for estimating streamflow statistics at ungaged locations is to develop a relational model between streamflow and drainage basin characteristics at gaged locations using least squares regression analysis; however, least squares regression methods are parametric and make constraining assumptions about the data distribution. The random forest regression method provides an alternative nonparametric method for estimating streamflow characteristics at ungaged sites and requires that the data meet fewer statistical conditions than least squares regression methods.Random forest regression analysis was used to develop predictive models for 89 streamflow characteristics using Precipitation-Runoff Modeling System simulated streamflow data and drainage basin characteristics at 179 sites in central and eastern Montana. The predictive models were developed from streamflow data simulated for current (baseline, water years 1982–99) conditions and three future periods (water years 2021–38, 2046–63, and 2071–88) under three different climate-change scenarios. These predictive models were then used to predict streamflow characteristics for baseline conditions and three future periods at 1,707 fish sampling sites in central and eastern Montana. The average root mean square error for all predictive models was about 50 percent. When streamflow predictions at 23 fish sampling sites were compared to nearby locations with simulated data, the mean relative percent difference was about 43 percent. When predictions were compared to streamflow data recorded at 21 U.S. Geological Survey streamflow-gaging stations outside of the calibration basins, the average mean absolute percent error was about 73 percent.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Mixed effects versus fixed effects modelling of binary data with inter-subject variability.

PubMed

Murphy, Valda; Dunne, Adrian

2005-04-01

The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389-412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.

Optimum data weighting and error calibration for estimation of gravitational parameters

NASA Technical Reports Server (NTRS)

Lerch, Francis J.

1989-01-01

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Covariance analysis for evaluating head trackers

NASA Astrophysics Data System (ADS)

Kang, Donghoon

2017-10-01

Existing methods for evaluating the performance of head trackers usually rely on publicly available face databases, which contain facial images and the ground truths of their corresponding head orientations. However, most of the existing publicly available face databases are constructed by assuming that a frontal head orientation can be determined by compelling the person under examination to look straight ahead at the camera on the first video frame. Since nobody can accurately direct one's head toward the camera, this assumption may be unrealistic. Rather than obtaining estimation errors, we present a method for computing the covariance of estimation error rotations to evaluate the reliability of head trackers. As an uncertainty measure of estimators, the Schatten 2-norm of a square root of error covariance (or the algebraic average of relative error angles) can be used. The merit of the proposed method is that it does not disturb the person under examination by asking him to direct his head toward certain directions. Experimental results using real data validate the usefulness of our method.

Estimate of procession and polar motion errors from planetary encounter station location solutions

NASA Technical Reports Server (NTRS)

Pease, G. E.

1978-01-01

Jet Propulsion Laboratory Deep Space Station (DSS) location solutions based on two JPL planetary ephemerides, DE 84 and DE 96, at eight planetary encounters were used to obtain weighted least squares estimates of precession and polar motion errors. The solution for precession error in right ascension yields a value of 0.3 X 10 to the minus 5 power plus or minus 0.8 X 10 to the minus 6 power deg/year. This maps to a right ascension error of 1.3 X 10 to the minus 5 power plus or minus 0.4 X 10 to the minus 5 power deg at the first Voyager 1979 Jupiter encounter if the current JPL DSS location set is used. Solutions for precession and polar motion using station locations based on DE 84 agree well with the solution using station locations referenced to DE 96. The precession solution removes the apparent drift in station longitude and spin axis distance estimates, while the encounter polar motion solutions consistently decrease the scatter in station spin axis distance estimates.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 2. Numerical experiments

NASA Astrophysics Data System (ADS)

Akmaev, R. a.

1999-04-01

In Part 1 of this work ([Akmaev, 1999]), an overview of the theory of optimal interpolation (OI) ([Gandin, 1963]) and related techniques of data assimilation based on linear optimal estimation ([Liebelt, 1967]; [Catlin, 1989]; [Mendel, 1995]) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., [Liebelt, 1967]; [Weisberg, 1985]; [Press et al., 1992]; [Mendel, 1995]).

Legitimate Techniques for Improving the R-Square and Related Statistics of a Multiple Regression Model

DTIC Science & Technology

1981-01-01

explanatory variable has been ommitted. Ramsey (1974) has developed a rather interesting test for detecting specification errors using estimates of the...Peter. (1979) A Guide to Econometrics , Cambridge, MA: The MIT Press. Ramsey , J.B. (1974), "Classical Model Selection Through Specification Error... Tests ," in P. Zarembka, Ed. Frontiers in Econometrics , New York: Academia Press. Theil, Henri. (1971), Principles of Econometrics , New York: John Wiley

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

PubMed

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Reconstruction of regional mean temperature for East Asia since 1900s and its uncertainties

NASA Astrophysics Data System (ADS)

Hua, W.

2017-12-01

Regional average surface air temperature (SAT) is one of the key variables often used to investigate climate change. Unfortunately, because of the limited observations over East Asia, there were also some gaps in the observation data sampling for regional mean SAT analysis, which was important to estimate past climate change. In this study, the regional average temperature of East Asia since 1900s is calculated by the Empirical Orthogonal Function (EOF)-based optimal interpolation (OA) method with considering the data errors. The results show that our estimate is more precise and robust than the results from simple average, which provides a better way for past climate reconstruction. In addition to the reconstructed regional average SAT anomaly time series, we also estimated uncertainties of reconstruction. The root mean square error (RMSE) results show that the the error decreases with respect to time, and are not sufficiently large to alter the conclusions on the persist warming in East Asia during twenty-first century. Moreover, the test of influence of data error on reconstruction clearly shows the sensitivity of reconstruction to the size of the data error.

Analysis of the Magnitude and Frequency of Peak Discharge and Maximum Observed Peak Discharge in New Mexico and Surrounding Areas

USGS Publications Warehouse

Waltemeyer, Scott D.

2008-01-01

Estimates of the magnitude and frequency of peak discharges are necessary for the reliable design of bridges, culverts, and open-channel hydraulic analysis, and for flood-hazard mapping in New Mexico and surrounding areas. The U.S. Geological Survey, in cooperation with the New Mexico Department of Transportation, updated estimates of peak-discharge magnitude for gaging stations in the region and updated regional equations for estimation of peak discharge and frequency at ungaged sites. Equations were developed for estimating the magnitude of peak discharges for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years at ungaged sites by use of data collected through 2004 for 293 gaging stations on unregulated streams that have 10 or more years of record. Peak discharges for selected recurrence intervals were determined at gaging stations by fitting observed data to a log-Pearson Type III distribution with adjustments for a low-discharge threshold and a zero skew coefficient. A low-discharge threshold was applied to frequency analysis of 140 of the 293 gaging stations. This application provides an improved fit of the log-Pearson Type III frequency distribution. Use of the low-discharge threshold generally eliminated the peak discharge by having a recurrence interval of less than 1.4 years in the probability-density function. Within each of the nine regions, logarithms of the maximum peak discharges for selected recurrence intervals were related to logarithms of basin and climatic characteristics by using stepwise ordinary least-squares regression techniques for exploratory data analysis. Generalized least-squares regression techniques, an improved regression procedure that accounts for time and spatial sampling errors, then were applied to the same data used in the ordinary least-squares regression analyses. The average standard error of prediction, which includes average sampling error and average standard error of regression, ranged from 38 to 93 percent (mean value is 62, and median value is 59) for the 100-year flood. The 1996 investigation standard error of prediction for the flood regions ranged from 41 to 96 percent (mean value is 67, and median value is 68) for the 100-year flood that was analyzed by using generalized least-squares regression analysis. Overall, the equations based on generalized least-squares regression techniques are more reliable than those in the 1996 report because of the increased length of record and improved geographic information system (GIS) method to determine basin and climatic characteristics. Flood-frequency estimates can be made for ungaged sites upstream or downstream from gaging stations by using a method that transfers flood-frequency data at the gaging station to the ungaged site by using a drainage-area ratio adjustment equation. The peak discharge for a given recurrence interval at the gaging station, drainage-area ratio, and the drainage-area exponent from the regional regression equation of the respective region is used to transfer the peak discharge for the recurrence interval to the ungaged site. Maximum observed peak discharge as related to drainage area was determined for New Mexico. Extreme events are commonly used in the design and appraisal of bridge crossings and other structures. Bridge-scour evaluations are commonly made by using the 500-year peak discharge for these appraisals. Peak-discharge data collected at 293 gaging stations and 367 miscellaneous sites were used to develop a maximum peak-discharge relation as an alternative method of estimating peak discharge of an extreme event such as a maximum probable flood.

The augmented Lagrangian method for parameter estimation in elliptic systems

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Kunisch, Karl

1990-01-01

In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.

Data consistency criterion for selecting parameters for k-space-based reconstruction in parallel imaging.

PubMed

Nana, Roger; Hu, Xiaoping

2010-01-01

k-space-based reconstruction in parallel imaging depends on the reconstruction kernel setting, including its support. An optimal choice of the kernel depends on the calibration data, coil geometry and signal-to-noise ratio, as well as the criterion used. In this work, data consistency, imposed by the shift invariance requirement of the kernel, is introduced as a goodness measure of k-space-based reconstruction in parallel imaging and demonstrated. Data consistency error (DCE) is calculated as the sum of squared difference between the acquired signals and their estimates obtained based on the interpolation of the estimated missing data. A resemblance between DCE and the mean square error in the reconstructed image was found, demonstrating DCE's potential as a metric for comparing or choosing reconstructions. When used for selecting the kernel support for generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction and the set of frames for calibration as well as the kernel support in temporal GRAPPA reconstruction, DCE led to improved images over existing methods. Data consistency error is efficient to evaluate, robust for selecting reconstruction parameters and suitable for characterizing and optimizing k-space-based reconstruction in parallel imaging.

Analysis of the Magnitude and Frequency of Peak Discharges for the Navajo Nation in Arizona, Utah, Colorado, and New Mexico

USGS Publications Warehouse

Waltemeyer, Scott D.

2006-01-01

Estimates of the magnitude and frequency of peak discharges are necessary for the reliable flood-hazard mapping in the Navajo Nation in Arizona, Utah, Colorado, and New Mexico. The Bureau of Indian Affairs, U.S. Army Corps of Engineers, and Navajo Nation requested that the U.S. Geological Survey update estimates of peak discharge magnitude for gaging stations in the region and update regional equations for estimation of peak discharge and frequency at ungaged sites. Equations were developed for estimating the magnitude of peak discharges for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years at ungaged sites using data collected through 1999 at 146 gaging stations, an additional 13 years of peak-discharge data since a 1997 investigation, which used gaging-station data through 1986. The equations for estimation of peak discharges at ungaged sites were developed for flood regions 8, 11, high elevation, and 6 and are delineated on the basis of the hydrologic codes from the 1997 investigation. Peak discharges for selected recurrence intervals were determined at gaging stations by fitting observed data to a log-Pearson Type III distribution with adjustments for a low-discharge threshold and a zero skew coefficient. A low-discharge threshold was applied to frequency analysis of 82 of the 146 gaging stations. This application provides an improved fit of the log-Pearson Type III frequency distribution. Use of the low-discharge threshold generally eliminated the peak discharge having a recurrence interval of less than 1.4 years in the probability-density function. Within each region, logarithms of the peak discharges for selected recurrence intervals were related to logarithms of basin and climatic characteristics using stepwise ordinary least-squares regression techniques for exploratory data analysis. Generalized least-squares regression techniques, an improved regression procedure that accounts for time and spatial sampling errors, then was applied to the same data used in the ordinary least-squares regression analyses. The average standard error of prediction for a peak discharge have a recurrence interval of 100-years for region 8 was 53 percent (average) for the 100-year flood. The average standard of prediction, which includes average sampling error and average standard error of regression, ranged from 45 to 83 percent for the 100-year flood. Estimated standard error of prediction for a hybrid method for region 11 was large in the 1997 investigation. No distinction of floods produced from a high-elevation region was presented in the 1997 investigation. Overall, the equations based on generalized least-squares regression techniques are considered to be more reliable than those in the 1997 report because of the increased length of record and improved GIS method. Techniques for transferring flood-frequency relations to ungaged sites on the same stream can be estimated at an ungaged site by a direct application of the regional regression equation or at an ungaged site on a stream that has a gaging station upstream or downstream by using the drainage-area ratio and the drainage-area exponent from the regional regression equation of the respective region.

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Gui-Long

2001-01-01

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Adaptive control strategies for flexible robotic arm

NASA Technical Reports Server (NTRS)

Bialasiewicz, Jan T.

1993-01-01

The motivation of this research came about when a neural network direct adaptive control scheme was applied to control the tip position of a flexible robotic arm. Satisfactory control performance was not attainable due to the inherent non-minimum phase characteristics of the flexible robotic arm tip. Most of the existing neural network control algorithms are based on the direct method and exhibit very high sensitivity if not unstable closed-loop behavior. Therefore a neural self-tuning control (NSTC) algorithm is developed and applied to this problem and showed promising results. Simulation results of the NSTC scheme and the conventional self-tuning (STR) control scheme are used to examine performance factors such as control tracking mean square error, estimation mean square error, transient response, and steady state response.

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System.

PubMed

Tang, Jinjun; Zou, Yajie; Ash, John; Zhang, Shen; Liu, Fang; Wang, Yinhai

2016-01-01

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP).

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System

PubMed Central

Tang, Jinjun; Zou, Yajie; Ash, John; Zhang, Shen; Liu, Fang; Wang, Yinhai

2016-01-01

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP). PMID:26829639

Methods for estimating selected low-flow frequency statistics and harmonic mean flows for streams in Iowa

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.

2017-01-01

A statewide study was conducted to develop regression equations for estimating six selected low-flow frequency statistics and harmonic mean flows for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include: the annual 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years, the annual 30-day mean low flow for a recurrence interval of 5 years, and the seasonal (October 1 through December 31) 1- and 7-day mean low flows for a recurrence interval of 10 years. Estimation equations also were developed for the harmonic-mean-flow statistic. Estimates of these seven selected statistics are provided for 208 U.S. Geological Survey continuous-record streamgages using data through September 30, 2006. The study area comprises streamgages located within Iowa and 50 miles beyond the State's borders. Because trend analyses indicated statistically significant positive trends when considering the entire period of record for the majority of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. The median number of years of record used to compute each of these seven selected statistics was 35. Geographic information system software was used to measure 54 selected basin characteristics for each streamgage. Following the removal of two streamgages from the initial data set, data collected for 206 streamgages were compiled to investigate three approaches for regionalization of the seven selected statistics. Regionalization, a process using statistical regression analysis, provides a relation for efficiently transferring information from a group of streamgages in a region to ungaged sites in the region. The three regionalization approaches tested included statewide, regional, and region-of-influence regressions. For the regional regression, the study area was divided into three low-flow regions on the basis of hydrologic characteristics, landform regions, and soil regions. A comparison of root mean square errors and average standard errors of prediction for the statewide, regional, and region-of-influence regressions determined that the regional regression provided the best estimates of the seven selected statistics at ungaged sites in Iowa. Because a significant number of streams in Iowa reach zero flow as their minimum flow during low-flow years, four different types of regression analyses were used: left-censored, logistic, generalized-least-squares, and weighted-least-squares regression. A total of 192 streamgages were included in the development of 27 regression equations for the three low-flow regions. For the northeast and northwest regions, a censoring threshold was used to develop 12 left-censored regression equations to estimate the 6 low-flow frequency statistics for each region. For the southern region a total of 12 regression equations were developed; 6 logistic regression equations were developed to estimate the probability of zero flow for the 6 low-flow frequency statistics and 6 generalized least-squares regression equations were developed to estimate the 6 low-flow frequency statistics, if nonzero flow is estimated first by use of the logistic equations. A weighted-least-squares regression equation was developed for each region to estimate the harmonic-mean-flow statistic. Average standard errors of estimate for the left-censored equations for the northeast region range from 64.7 to 88.1 percent and for the northwest region range from 85.8 to 111.8 percent. Misclassification percentages for the logistic equations for the southern region range from 5.6 to 14.0 percent. Average standard errors of prediction for generalized least-squares equations for the southern region range from 71.7 to 98.9 percent and pseudo coefficients of determination for the generalized-least-squares equations range from 87.7 to 91.8 percent. Average standard errors of prediction for weighted-least-squares equations developed for estimating the harmonic-mean-flow statistic for each of the three regions range from 66.4 to 80.4 percent. The regression equations are applicable only to stream sites in Iowa with low flows not significantly affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. If the equations are used at ungaged sites on regulated streams, or on streams affected by water-supply and agricultural withdrawals, then the estimates will need to be adjusted by the amount of regulation or withdrawal to estimate the actual flow conditions if that is of interest. Caution is advised when applying the equations for basins with characteristics near the applicable limits of the equations and for basins located in karst topography. A test of two drainage-area ratio methods using 31 pairs of streamgages, for the annual 7-day mean low-flow statistic for a recurrence interval of 10 years, indicates a weighted drainage-area ratio method provides better estimates than regional regression equations for an ungaged site on a gaged stream in Iowa when the drainage-area ratio is between 0.5 and 1.4. These regression equations will be implemented within the U.S. Geological Survey StreamStats web-based geographic-information-system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the seven selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these seven selected statistics are provided for the streamgage.

A Novel Four-Node Quadrilateral Smoothing Element for Stress Enhancement and Error Estimation

NASA Technical Reports Server (NTRS)

Tessler, A.; Riggs, H. R.; Dambach, M.

1998-01-01

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five-node macro-element configuration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very efficient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component.

Stress Recovery and Error Estimation for Shell Structures

NASA Technical Reports Server (NTRS)

Yazdani, A. A.; Riggs, H. R.; Tessler, A.

2000-01-01

The Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for two dimensional linear elliptic problems is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces. The proposed strategy involves mapping the finite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smoothing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA/PDLS for these problems. The recovered stresses are used in the Zienkiewicz-Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh refinement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary.

TLE uncertainty estimation using robust weighted differencing

NASA Astrophysics Data System (ADS)

Geul, Jacco; Mooij, Erwin; Noomen, Ron

2017-05-01

Accurate knowledge of satellite orbit errors is essential for many types of analyses. Unfortunately, for two-line elements (TLEs) this is not available. This paper presents a weighted differencing method using robust least-squares regression for estimating many important error characteristics. The method is applied to both classic and enhanced TLEs, compared to previous implementations, and validated using Global Positioning System (GPS) solutions for the GOCE satellite in Low-Earth Orbit (LEO), prior to its re-entry. The method is found to be more accurate than previous TLE differencing efforts in estimating initial uncertainty, as well as error growth. The method also proves more reliable and requires no data filtering (such as outlier removal). Sensitivity analysis shows a strong relationship between argument of latitude and covariance (standard deviations and correlations), which the method is able to approximate. Overall, the method proves accurate, computationally fast, and robust, and is applicable to any object in the satellite catalogue (SATCAT).

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

NASA Technical Reports Server (NTRS)

Melbourne, William G.

1986-01-01

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

A theoretical framework to predict the most likely ion path in particle imaging.

PubMed

Collins-Fekete, Charles-Antoine; Volz, Lennart; Portillo, Stephen K N; Beaulieu, Luc; Seco, Joao

2017-03-07

In this work, a generic rigorous Bayesian formalism is introduced to predict the most likely path of any ion crossing a medium between two detection points. The path is predicted based on a combination of the particle scattering in the material and measurements of its initial and final position, direction and energy. The path estimate's precision is compared to the Monte Carlo simulated path. Every ion from hydrogen to carbon is simulated in two scenarios, (1) where the range is fixed and (2) where the initial velocity is fixed. In the scenario where the range is kept constant, the maximal root-mean-square error between the estimated path and the Monte Carlo path drops significantly between the proton path estimate (0.50 mm) and the helium path estimate (0.18 mm), but less so up to the carbon path estimate (0.09 mm). However, this scenario is identified as the configuration that maximizes the dose while minimizing the path resolution. In the scenario where the initial velocity is fixed, the maximal root-mean-square error between the estimated path and the Monte Carlo path drops significantly between the proton path estimate (0.29 mm) and the helium path estimate (0.09 mm) but increases for heavier ions up to carbon (0.12 mm). As a result, helium is found to be the particle with the most accurate path estimate for the lowest dose, potentially leading to tomographic images of higher spatial resolution.

Optimal estimation of suspended-sediment concentrations in streams

USGS Publications Warehouse

Holtschlag, D.J.

2001-01-01

Optimal estimators are developed for computation of suspended-sediment concentrations in streams. The estimators are a function of parameters, computed by use of generalized least squares, which simultaneously account for effects of streamflow, seasonal variations in average sediment concentrations, a dynamic error component, and the uncertainty in concentration measurements. The parameters are used in a Kalman filter for on-line estimation and an associated smoother for off-line estimation of suspended-sediment concentrations. The accuracies of the optimal estimators are compared with alternative time-averaging interpolators and flow-weighting regression estimators by use of long-term daily-mean suspended-sediment concentration and streamflow data from 10 sites within the United States. For sampling intervals from 3 to 48 days, the standard errors of on-line and off-line optimal estimators ranged from 52.7 to 107%, and from 39.5 to 93.0%, respectively. The corresponding standard errors of linear and cubic-spline interpolators ranged from 48.8 to 158%, and from 50.6 to 176%, respectively. The standard errors of simple and multiple regression estimators, which did not vary with the sampling interval, were 124 and 105%, respectively. Thus, the optimal off-line estimator (Kalman smoother) had the lowest error characteristics of those evaluated. Because suspended-sediment concentrations are typically measured at less than 3-day intervals, use of optimal estimators will likely result in significant improvements in the accuracy of continuous suspended-sediment concentration records. Additional research on the integration of direct suspended-sediment concentration measurements and optimal estimators applied at hourly or shorter intervals is needed.

A comparison of methods for DPLL loop filter design

NASA Technical Reports Server (NTRS)

Aguirre, S.; Hurd, W. J.; Kumar, R.; Statman, J.

1986-01-01

Four design methodologies for loop filters for a class of digital phase-locked loops (DPLLs) are presented. The first design maps an optimum analog filter into the digital domain; the second approach designs a filter that minimizes in discrete time weighted combination of the variance of the phase error due to noise and the sum square of the deterministic phase error component; the third method uses Kalman filter estimation theory to design a filter composed of a least squares fading memory estimator and a predictor. The last design relies on classical theory, including rules for the design of compensators. Linear analysis is used throughout the article to compare different designs, and includes stability, steady state performance and transient behavior of the loops. Design methodology is not critical when the loop update rate can be made high relative to loop bandwidth, as the performance approaches that of continuous time. For low update rates, however, the miminization method is significantly superior to the other methods.

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

SMAP Level 4 Surface and Root Zone Soil Moisture

NASA Technical Reports Server (NTRS)

Reichle, R.; De Lannoy, G.; Liu, Q.; Ardizzone, J.; Kimball, J.; Koster, R.

2017-01-01

The SMAP Level 4 soil moisture (L4_SM) product provides global estimates of surface and root zone soil moisture, along with other land surface variables and their error estimates. These estimates are obtained through assimilation of SMAP brightness temperature observations into the Goddard Earth Observing System (GEOS-5) land surface model. The L4_SM product is provided at 9 km spatial and 3-hourly temporal resolution and with about 2.5 day latency. The soil moisture and temperature estimates in the L4_SM product are validated against in situ observations. The L4_SM product meets the required target uncertainty of 0.04 m(exp. 3)m(exp. -3), measured in terms of unbiased root-mean-square-error, for both surface and root zone soil moisture.

Methods for estimating flood frequency in Montana based on data through water year 1998

USGS Publications Warehouse

Parrett, Charles; Johnson, Dave R.

2004-01-01

Annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (T-year floods) were determined for 660 gaged sites in Montana and in adjacent areas of Idaho, Wyoming, and Canada, based on data through water year 1998. The updated flood-frequency information was subsequently used in regression analyses, either ordinary or generalized least squares, to develop equations relating T-year floods to various basin and climatic characteristics, equations relating T-year floods to active-channel width, and equations relating T-year floods to bankfull width. The equations can be used to estimate flood frequency at ungaged sites. Montana was divided into eight regions, within which flood characteristics were considered to be reasonably homogeneous, and the three sets of regression equations were developed for each region. A measure of the overall reliability of the regression equations is the average standard error of prediction. The average standard errors of prediction for the equations based on basin and climatic characteristics ranged from 37.4 percent to 134.1 percent. Average standard errors of prediction for the equations based on active-channel width ranged from 57.2 percent to 141.3 percent. Average standard errors of prediction for the equations based on bankfull width ranged from 63.1 percent to 155.5 percent. In most regions, the equations based on basin and climatic characteristics generally had smaller average standard errors of prediction than equations based on active-channel or bankfull width. An exception was the Southeast Plains Region, where all equations based on active-channel width had smaller average standard errors of prediction than equations based on basin and climatic characteristics or bankfull width. Methods for weighting estimates derived from the basin- and climatic-characteristic equations and the channel-width equations also were developed. The weights were based on the cross correlation of residuals from the different methods and the average standard errors of prediction. When all three methods were combined, the average standard errors of prediction ranged from 37.4 percent to 120.2 percent. Weighting of estimates reduced the standard errors of prediction for all T-year flood estimates in four regions, reduced the standard errors of prediction for some T-year flood estimates in two regions, and provided no reduction in average standard error of prediction in two regions. A computer program for solving the regression equations, weighting estimates, and determining reliability of individual estimates was developed and placed on the USGS Montana District World Wide Web page. A new regression method, termed Region of Influence regression, also was tested. Test results indicated that the Region of Influence method was not as reliable as the regional equations based on generalized least squares regression. Two additional methods for estimating flood frequency at ungaged sites located on the same streams as gaged sites also are described. The first method, based on a drainage-area-ratio adjustment, is intended for use on streams where the ungaged site of interest is located near a gaged site. The second method, based on interpolation between gaged sites, is intended for use on streams that have two or more streamflow-gaging stations.

Nondestructive evaluation of soluble solid content in strawberry by near infrared spectroscopy

NASA Astrophysics Data System (ADS)

Guo, Zhiming; Huang, Wenqian; Chen, Liping; Wang, Xiu; Peng, Yankun

This paper indicates the feasibility to use near infrared (NIR) spectroscopy combined with synergy interval partial least squares (siPLS) algorithms as a rapid nondestructive method to estimate the soluble solid content (SSC) in strawberry. Spectral preprocessing methods were optimized selected by cross-validation in the model calibration. Partial least squares (PLS) algorithm was conducted on the calibration of regression model. The performance of the final model was back-evaluated according to root mean square error of calibration (RMSEC) and correlation coefficient (R2 c) in calibration set, and tested by mean square error of prediction (RMSEP) and correlation coefficient (R2 p) in prediction set. The optimal siPLS model was obtained with after first derivation spectra preprocessing. The measurement results of best model were achieved as follow: RMSEC = 0.2259, R2 c = 0.9590 in the calibration set; and RMSEP = 0.2892, R2 p = 0.9390 in the prediction set. This work demonstrated that NIR spectroscopy and siPLS with efficient spectral preprocessing is a useful tool for nondestructively evaluation SSC in strawberry.

Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space.

PubMed

Dawes, Richard; Passalacqua, Alessio; Wagner, Albert F; Sewell, Thomas D; Minkoff, Michael; Thompson, Donald L

2009-04-14

We develop two approaches for growing a fitted potential energy surface (PES) by the interpolating moving least-squares (IMLS) technique using classical trajectories. We illustrate both approaches by calculating nitrous acid (HONO) cis-->trans isomerization trajectories under the control of ab initio forces from low-level HF/cc-pVDZ electronic structure calculations. In this illustrative example, as few as 300 ab initio energy/gradient calculations are required to converge the isomerization rate constant at a fixed energy to approximately 10%. Neither approach requires any preliminary electronic structure calculations or initial approximate representation of the PES (beyond information required for trajectory initial conditions). Hessians are not required. Both approaches rely on the fitting error estimation properties of IMLS fits. The first approach, called IMLS-accelerated direct dynamics, propagates individual trajectories directly with no preliminary exploratory trajectories. The PES is grown "on the fly" with the computation of new ab initio data only when a fitting error estimate exceeds a prescribed tight tolerance. The second approach, called dynamics-driven IMLS fitting, uses relatively inexpensive exploratory trajectories to both determine and fit the dynamically accessible configuration space. Once exploratory trajectories no longer find configurations with fitting error estimates higher than the designated accuracy, the IMLS fit is considered to be complete and usable in classical trajectory calculations or other applications.

Nonlinear least squares regression for single image scanning electron microscope signal-to-noise ratio estimation.

PubMed

Sim, K S; Norhisham, S

2016-11-01

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Bayesian estimation of the discrete coefficient of determination.

PubMed

Chen, Ting; Braga-Neto, Ulisses M

2016-12-01

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.

A new approach for modeling patient overall radiosensitivity and predicting multiple toxicity endpoints for breast cancer patients.

PubMed

Mbah, Chamberlain; De Ruyck, Kim; De Schrijver, Silke; De Sutter, Charlotte; Schiettecatte, Kimberly; Monten, Chris; Paelinck, Leen; De Neve, Wilfried; Thierens, Hubert; West, Catharine; Amorim, Gustavo; Thas, Olivier; Veldeman, Liv

2018-05-01

Evaluation of patient characteristics inducing toxicity in breast radiotherapy, using simultaneous modeling of multiple endpoints. In 269 early-stage breast cancer patients treated with whole-breast irradiation (WBI) after breast-conserving surgery, toxicity was scored, based on five dichotomized endpoints. Five logistic regression models were fitted, one for each endpoint and the effect sizes of all variables were estimated using maximum likelihood (MLE). The MLEs are improved with James-Stein estimates (JSEs). The method combines all the MLEs, obtained for the same variable but from different endpoints. Misclassification errors were computed using MLE- and JSE-based prediction models. For associations, p-values from the sum of squares of MLEs were compared with p-values from the Standardized Total Average Toxicity (STAT) Score. With JSEs, 19 highest ranked variables were predictive of the five different endpoints. Important variables increasing radiation-induced toxicity were chemotherapy, age, SATB2 rs2881208 SNP and nodal irradiation. Treatment position (prone position) was most protective and ranked eighth. Overall, the misclassification errors were 45% and 34% for the MLE- and JSE-based models, respectively. p-Values from the sum of squares of MLEs and p-values from STAT score led to very similar conclusions, except for the variables nodal irradiation and treatment position, for which STAT p-values suggested an association with radiosensitivity, whereas p-values from the sum of squares indicated no association. Breast volume was ranked as the most significant variable in both strategies. The James-Stein estimator was used for selecting variables that are predictive for multiple toxicity endpoints. With this estimator, 19 variables were predictive for all toxicities of which four were significantly associated with overall radiosensitivity. JSEs led to almost 25% reduction in the misclassification error rate compared to conventional MLEs. Finally, patient characteristics that are associated with radiosensitivity were identified without explicitly quantifying radiosensitivity.

Statistical models for estimating daily streamflow in Michigan

USGS Publications Warehouse

Holtschlag, D.J.; Salehi, Habib

1992-01-01

Statistical models for estimating daily streamflow were analyzed for 25 pairs of streamflow-gaging stations in Michigan. Stations were paired by randomly choosing a station operated in 1989 at which 10 or more years of continuous flow data had been collected and at which flow is virtually unregulated; a nearby station was chosen where flow characteristics are similar. Streamflow data from the 25 randomly selected stations were used as the response variables; streamflow data at the nearby stations were used to generate a set of explanatory variables. Ordinary-least squares regression (OLSR) equations, autoregressive integrated moving-average (ARIMA) equations, and transfer function-noise (TFN) equations were developed to estimate the log transform of flow for the 25 randomly selected stations. The precision of each type of equation was evaluated on the basis of the standard deviation of the estimation errors. OLSR equations produce one set of estimation errors; ARIMA and TFN models each produce l sets of estimation errors corresponding to the forecast lead. The lead-l forecast is the estimate of flow l days ahead of the most recent streamflow used as a response variable in the estimation. In this analysis, the standard deviation of lead l ARIMA and TFN forecast errors were generally lower than the standard deviation of OLSR errors for l < 2 days and l < 9 days, respectively. Composite estimates were computed as a weighted average of forecasts based on TFN equations and backcasts (forecasts of the reverse-ordered series) based on ARIMA equations. The standard deviation of composite errors varied throughout the length of the estimation interval and generally was at maximum near the center of the interval. For comparison with OLSR errors, the mean standard deviation of composite errors were computed for intervals of length 1 to 40 days. The mean standard deviation of length-l composite errors were generally less than the standard deviation of the OLSR errors for l < 32 days. In addition, the composite estimates ensure a gradual transition between periods of estimated and measured flows. Model performance among stations of differing model error magnitudes were compared by computing ratios of the mean standard deviation of the length l composite errors to the standard deviation of OLSR errors. The mean error ratio for the set of 25 selected stations was less than 1 for intervals l < 32 days. Considering the frequency characteristics of the length of intervals of estimated record in Michigan, the effective mean error ratio for intervals < 30 days was 0.52. Thus, for intervals of estimation of 1 month or less, the error of the composite estimate is substantially lower than error of the OLSR estimate.

Three-dimensional ultrasound strain imaging of skeletal muscles

NASA Astrophysics Data System (ADS)

Gijsbertse, K.; Sprengers, A. M. J.; Nillesen, M. M.; Hansen, H. H. G.; Lopata, R. G. P.; Verdonschot, N.; de Korte, C. L.

2017-01-01

In this study, a multi-dimensional strain estimation method is presented to assess local relative deformation in three orthogonal directions in 3D space of skeletal muscles during voluntary contractions. A rigid translation and compressive deformation of a block phantom, that mimics muscle contraction, is used as experimental validation of the 3D technique and to compare its performance with respect to a 2D based technique. Axial, lateral and (in case of 3D) elevational displacements are estimated using a cross-correlation based displacement estimation algorithm. After transformation of the displacements to a Cartesian coordinate system, strain is derived using a least-squares strain estimator. The performance of both methods is compared by calculating the root-mean-squared error of the estimated displacements with the calculated theoretical displacements of the phantom experiments. We observe that the 3D technique delivers more accurate displacement estimations compared to the 2D technique, especially in the translation experiment where out-of-plane motion hampers the 2D technique. In vivo application of the 3D technique in the musculus vastus intermedius shows good resemblance between measured strain and the force pattern. Similarity of the strain curves of repetitive measurements indicates the reproducibility of voluntary contractions. These results indicate that 3D ultrasound is a valuable imaging tool to quantify complex tissue motion, especially when there is motion in three directions, which results in out-of-plane errors for 2D techniques.

Modeling Water Temperature in the Yakima River, Washington, from Roza Diversion Dam to Prosser Dam, 2005-06

USGS Publications Warehouse

Voss, Frank D.; Curran, Christopher A.; Mastin, Mark C.

2008-01-01

A mechanistic water-temperature model was constructed by the U.S. Geological Survey for use by the Bureau of Reclamation for studying the effect of potential water management decisions on water temperature in the Yakima River between Roza and Prosser, Washington. Flow and water temperature data for model input were obtained from the Bureau of Reclamation Hydromet database and from measurements collected by the U.S. Geological Survey during field trips in autumn 2005. Shading data for the model were collected by the U.S. Geological Survey in autumn 2006. The model was calibrated with data collected from April 1 through October 31, 2005, and tested with data collected from April 1 through October 31, 2006. Sensitivity analysis results showed that for the parameters tested, daily maximum water temperature was most sensitive to changes in air temperature and solar radiation. Root mean squared error for the five sites used for model calibration ranged from 1.3 to 1.9 degrees Celsius (?C) and mean error ranged from ?1.3 to 1.6?C. The root mean squared error for the five sites used for testing simulation ranged from 1.6 to 2.2?C and mean error ranged from 0.1 to 1.3?C. The accuracy of the stream temperatures estimated by the model is limited by four errors (model error, data error, parameter error, and user error).

Gompertzian stochastic model with delay effect to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

2-Step Maximum Likelihood Channel Estimation for Multicode DS-CDMA with Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Kojima, Yohei; Takeda, Kazuaki; Adachi, Fumiyuki

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can provide better downlink bit error rate (BER) performance of direct sequence code division multiple access (DS-CDMA) than the conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. In this paper, we propose a new 2-step maximum likelihood channel estimation (MLCE) for DS-CDMA with FDE in a very slow frequency-selective fading environment. The 1st step uses the conventional pilot-assisted MMSE-CE and the 2nd step carries out the MLCE using decision feedback from the 1st step. The BER performance improvement achieved by 2-step MLCE over pilot assisted MMSE-CE is confirmed by computer simulation.

Submillimeter, millimeter, and microwave spectral line catalogue

NASA Technical Reports Server (NTRS)

Poynter, R. L.; Pickett, H. M.

1980-01-01

A computer accessible catalogue of submillimeter, millimeter, and microwave spectral lines in the frequency range between O and 3000 GHz (such as; wavelengths longer than 100 m) is discussed. The catalogue was used as a planning guide and as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, lower state energy, and quantum number assignment. The catalogue was constructed by using theoretical least squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances.

Optimized System Identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Longman, Richard W.

1999-01-01

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

M-estimator for the 3D symmetric Helmert coordinate transformation

NASA Astrophysics Data System (ADS)

Chang, Guobin; Xu, Tianhe; Wang, Qianxin

2018-01-01

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3 × 1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method's statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.

MRI-based intelligence quotient (IQ) estimation with sparse learning.

PubMed

Wang, Liye; Wee, Chong-Yaw; Suk, Heung-Il; Tang, Xiaoying; Shen, Dinggang

2015-01-01

In this paper, we propose a novel framework for IQ estimation using Magnetic Resonance Imaging (MRI) data. In particular, we devise a new feature selection method based on an extended dirty model for jointly considering both element-wise sparsity and group-wise sparsity. Meanwhile, due to the absence of large dataset with consistent scanning protocols for the IQ estimation, we integrate multiple datasets scanned from different sites with different scanning parameters and protocols. In this way, there is large variability in these different datasets. To address this issue, we design a two-step procedure for 1) first identifying the possible scanning site for each testing subject and 2) then estimating the testing subject's IQ by using a specific estimator designed for that scanning site. We perform two experiments to test the performance of our method by using the MRI data collected from 164 typically developing children between 6 and 15 years old. In the first experiment, we use a multi-kernel Support Vector Regression (SVR) for estimating IQ values, and obtain an average correlation coefficient of 0.718 and also an average root mean square error of 8.695 between the true IQs and the estimated ones. In the second experiment, we use a single-kernel SVR for IQ estimation, and achieve an average correlation coefficient of 0.684 and an average root mean square error of 9.166. All these results show the effectiveness of using imaging data for IQ prediction, which is rarely done in the field according to our knowledge.

Missing value imputation in DNA microarrays based on conjugate gradient method.

PubMed

Dorri, Fatemeh; Azmi, Paeiz; Dorri, Faezeh

2012-02-01

Analysis of gene expression profiles needs a complete matrix of gene array values; consequently, imputation methods have been suggested. In this paper, an algorithm that is based on conjugate gradient (CG) method is proposed to estimate missing values. k-nearest neighbors of the missed entry are first selected based on absolute values of their Pearson correlation coefficient. Then a subset of genes among the k-nearest neighbors is labeled as the best similar ones. CG algorithm with this subset as its input is then used to estimate the missing values. Our proposed CG based algorithm (CGimpute) is evaluated on different data sets. The results are compared with sequential local least squares (SLLSimpute), Bayesian principle component analysis (BPCAimpute), local least squares imputation (LLSimpute), iterated local least squares imputation (ILLSimpute) and adaptive k-nearest neighbors imputation (KNNKimpute) methods. The average of normalized root mean squares error (NRMSE) and relative NRMSE in different data sets with various missing rates shows CGimpute outperforms other methods. Copyright © 2011 Elsevier Ltd. All rights reserved.

Measurement uncertainty and feasibility study of a flush airdata system for a hypersonic flight experiment

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Moes, Timothy R.

1994-01-01

Presented is a feasibility and error analysis for a hypersonic flush airdata system on a hypersonic flight experiment (HYFLITE). HYFLITE heating loads make intrusive airdata measurement impractical. Although this analysis is specifically for the HYFLITE vehicle and trajectory, the problems analyzed are generally applicable to hypersonic vehicles. A layout of the flush-port matrix is shown. Surface pressures are related airdata parameters using a simple aerodynamic model. The model is linearized using small perturbations and inverted using nonlinear least-squares. Effects of various error sources on the overall uncertainty are evaluated using an error simulation. Error sources modeled include boundarylayer/viscous interactions, pneumatic lag, thermal transpiration in the sensor pressure tubing, misalignment in the matrix layout, thermal warping of the vehicle nose, sampling resolution, and transducer error. Using simulated pressure data for input to the estimation algorithm, effects caused by various error sources are analyzed by comparing estimator outputs with the original trajectory. To obtain ensemble averages the simulation is run repeatedly and output statistics are compiled. Output errors resulting from the various error sources are presented as a function of Mach number. Final uncertainties with all modeled error sources included are presented as a function of Mach number.

Ultrasonic tracking of shear waves using a particle filter

PubMed Central

Ingle, Atul N.; Ma, Chi; Varghese, Tomy

2015-01-01

Purpose: This paper discusses an application of particle filtering for estimating shear wave velocity in tissue using ultrasound elastography data. Shear wave velocity estimates are of significant clinical value as they help differentiate stiffer areas from softer areas which is an indicator of potential pathology. Methods: Radio-frequency ultrasound echo signals are used for tracking axial displacements and obtaining the time-to-peak displacement at different lateral locations. These time-to-peak data are usually very noisy and cannot be used directly for computing velocity. In this paper, the denoising problem is tackled using a hidden Markov model with the hidden states being the unknown (noiseless) time-to-peak values. A particle filter is then used for smoothing out the time-to-peak curve to obtain a fit that is optimal in a minimum mean squared error sense. Results: Simulation results from synthetic data and finite element modeling suggest that the particle filter provides lower mean squared reconstruction error with smaller variance as compared to standard filtering methods, while preserving sharp boundary detail. Results from phantom experiments show that the shear wave velocity estimates in the stiff regions of the phantoms were within 20% of those obtained from a commercial ultrasound scanner and agree with estimates obtained using a standard method using least-squares fit. Estimates of area obtained from the particle filtered shear wave velocity maps were within 10% of those obtained from B-mode ultrasound images. Conclusions: The particle filtering approach can be used for producing visually appealing SWV reconstructions by effectively delineating various areas of the phantom with good image quality properties comparable to existing techniques. PMID:26520761

MSE-impact of PPP-RTK ZTD estimation strategies

NASA Astrophysics Data System (ADS)

Wang, K.; Khodabandeh, A.; Teunissen, P. J. G.

2018-06-01

In PPP-RTK network processing, the wet component of the zenith tropospheric delay (ZTD) cannot be precisely modelled and thus remains unknown in the observation equations. For small networks, the tropospheric mapping functions of different stations to a given satellite are almost equal to each other, thereby causing a near rank-deficiency between the ZTDs and satellite clocks. The stated near rank-deficiency can be solved by estimating the wet ZTD components relatively to that of the reference receiver, while the wet ZTD component of the reference receiver is constrained to zero. However, by increasing network scale and humidity around the reference receiver, enlarged mismodelled effects could bias the network and the user solutions. To consider both the influences of the noise and the biases, the mean-squared errors (MSEs) of different network and user parameters are studied analytically employing both the ZTD estimation strategies. We conclude that for a certain set of parameters, the difference in their MSE structures using both strategies is only driven by the square of the reference wet ZTD component and the formal variance of its solution. Depending on the network scale and the humidity condition around the reference receiver, the ZTD estimation strategy that delivers more accurate solutions might be different. Simulations are performed to illustrate the conclusions made by analytical studies. We find that estimating the ZTDs relatively in large networks and humid regions (for the reference receiver) could significantly degrade the network ambiguity success rates. Using ambiguity-fixed network-derived PPP-RTK corrections, for networks with an inter-station distance within 100 km, the choices of the ZTD estimation strategy is not crucial for single-epoch ambiguity-fixed user positioning. Using ambiguity-float network corrections, for networks with inter-station distances of 100, 300 and 500 km in humid regions (for the reference receiver), the root-mean-squared errors (RMSEs) of the estimated user coordinates using relative ZTD estimation could be higher than those under the absolute case with differences up to millimetres, centimetres and decimetres, respectively.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Joint inversion of regional and teleseismic earthquake waveforms

NASA Astrophysics Data System (ADS)

Baker, Mark R.; Doser, Diane I.

1988-03-01

A least squares joint inversion technique for regional and teleseismic waveforms is presented. The mean square error between seismograms and synthetics is minimized using true amplitudes. Matching true amplitudes in modeling requires meaningful estimates of modeling uncertainties and of seismogram signal-to-noise ratios. This also permits calculating linearized uncertainties on the solution based on accuracy and resolution. We use a priori estimates of earthquake parameters to stabilize unresolved parameters, and for comparison with a posteriori uncertainties. We verify the technique on synthetic data, and on the 1983 Borah Peak, Idaho (M = 7.3), earthquake. We demonstrate the inversion on the August 1954 Rainbow Mountain, Nevada (M = 6.8), earthquake and find parameters consistent with previous studies.

Red Wine Age Estimation by the Alteration of Its Color Parameters: Fourier Transform Infrared Spectroscopy as a Tool to Monitor Wine Maturation Time

PubMed Central

Basalekou, M.; Pappas, C.; Kotseridis, Y.; Tarantilis, P. A.; Kontaxakis, E.

2017-01-01

Color, phenolic content, and chemical age values of red wines made from Cretan grape varieties (Kotsifali, Mandilari) were evaluated over nine months of maturation in different containers for two vintages. The wines differed greatly on their anthocyanin profiles. Mid-IR spectra were also recorded with the use of a Fourier Transform Infrared Spectrophotometer in ZnSe disk mode. Analysis of Variance was used to explore the parameter's dependency on time. Determination models were developed for the chemical age indexes using Partial Least Squares (PLS) (TQ Analyst software) considering the spectral region 1830–1500 cm−1. The correlation coefficients (r) for chemical age index i were 0.86 for Kotsifali (Root Mean Square Error of Calibration (RMSEC) = 0.067, Root Mean Square Error of Prediction (RMSEP) = 0,115, and Root Mean Square Error of Validation (RMSECV) = 0.164) and 0.90 for Mandilari (RMSEC = 0.050, RMSEP = 0.040, and RMSECV = 0.089). For chemical age index ii the correlation coefficients (r) were 0.86 and 0.97 for Kotsifali (RMSEC 0.044, RMSEP = 0.087, and RMSECV = 0.214) and Mandilari (RMSEC = 0.024, RMSEP = 0.033, and RMSECV = 0.078), respectively. The proposed method is simpler, less time consuming, and more economical and does not require chemical reagents. PMID:29225994

Constrained inference in mixed-effects models for longitudinal data with application to hearing loss.

PubMed

Davidov, Ori; Rosen, Sophia

2011-04-01

In medical studies, endpoints are often measured for each patient longitudinally. The mixed-effects model has been a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, in hearing loss studies, we expect hearing to deteriorate with time. This means that hearing thresholds which reflect hearing acuity will, on average, increase over time. Therefore, the regression coefficients associated with the mean effect of time on hearing ability will be constrained. Such constraints should be accounted for in the analysis. We propose maximum likelihood estimation procedures, based on the expectation-conditional maximization either algorithm, to estimate the parameters of the model while accounting for the constraints on them. The proposed methods improve, in terms of mean square error, on the unconstrained estimators. In some settings, the improvement may be substantial. Hypotheses testing procedures that incorporate the constraints are developed. Specifically, likelihood ratio, Wald, and score tests are proposed and investigated. Their empirical significance levels and power are studied using simulations. It is shown that incorporating the constraints improves the mean squared error of the estimates and the power of the tests. These improvements may be substantial. The methodology is used to analyze a hearing loss study.

Mapping from disease-specific measures to health-state utility values in individuals with migraine.

PubMed

Gillard, Patrick J; Devine, Beth; Varon, Sepideh F; Liu, Lei; Sullivan, Sean D

2012-05-01

The objective of this study was to develop empirical algorithms that estimate health-state utility values from disease-specific quality-of-life scores in individuals with migraine. Data from a cross-sectional, multicountry study were used. Individuals with episodic and chronic migraine were randomly assigned to training or validation samples. Spearman's correlation coefficients between paired EuroQol five-dimensional (EQ-5D) questionnaire utility values and both Headache Impact Test (HIT-6) scores and Migraine-Specific Quality-of-Life Questionnaire version 2.1 (MSQ) domain scores (role restrictive, role preventive, and emotional function) were examined. Regression models were constructed to estimate EQ-5D questionnaire utility values from the HIT-6 score or the MSQ domain scores. Preferred algorithms were confirmed in the validation samples. In episodic migraine, the preferred HIT-6 and MSQ algorithms explained 22% and 25% of the variance (R(2)) in the training samples, respectively, and had similar prediction errors (root mean square errors of 0.30). In chronic migraine, the preferred HIT-6 and MSQ algorithms explained 36% and 45% of the variance in the training samples, respectively, and had similar prediction errors (root mean square errors 0.31 and 0.29). In episodic and chronic migraine, no statistically significant differences were observed between the mean observed and the mean estimated EQ-5D questionnaire utility values for the preferred HIT-6 and MSQ algorithms in the validation samples. The relationship between the EQ-5D questionnaire and the HIT-6 or the MSQ is adequate to use regression equations to estimate EQ-5D questionnaire utility values. The preferred HIT-6 and MSQ algorithms will be useful in estimating health-state utilities in migraine trials in which no preference-based measure is present. Copyright © 2012 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Results and Error Estimates from GRACE Forward Modeling over Antarctica

NASA Astrophysics Data System (ADS)

Bonin, Jennifer; Chambers, Don

2013-04-01

Forward modeling using a weighted least squares technique allows GRACE information to be projected onto a pre-determined collection of local basins. This decreases the impact of spatial leakage, allowing estimates of mass change to be better localized. The technique is especially valuable where models of current-day mass change are poor, such as over Antarctica. However when tested previously, the least squares technique has required constraints in the form of added process noise in order to be reliable. Poor choice of local basin layout has also adversely affected results, as has the choice of spatial smoothing used with GRACE. To develop design parameters which will result in correct high-resolution mass detection and to estimate the systematic errors of the method over Antarctica, we use a "truth" simulation of the Antarctic signal. We apply the optimal parameters found from the simulation to RL05 GRACE data across Antarctica and the surrounding ocean. We particularly focus on separating the Antarctic peninsula's mass signal from that of the rest of western Antarctica. Additionally, we characterize how well the technique works for removing land leakage signal from the nearby ocean, particularly that near the Drake Passage.

Solar Irradiance from GOES Albedo performance in a Hydrologic Model Simulation of Snowmelt Runoff

NASA Astrophysics Data System (ADS)

Sumargo, E.; Cayan, D. R.; McGurk, B. J.

2015-12-01

In many hydrologic modeling applications, solar radiation has been parameterized using commonly available measures, such as the daily temperature range, due to scarce in situ solar radiation measurement network. However, these parameterized estimates often produce significant biases. Here we test hourly solar irradiance derived from the Geostationary Operational Environmental Satellite (GOES) visible albedo product, using several established algorithms. Focusing on the Sierra Nevada and White Mountain in California, we compared the GOES irradiance and that from a traditional temperature-based algorithm with incoming irradiance from pyranometers at 19 stations. The GOES based estimates yielded 21-27% reduction in root-mean-squared error (average over 19 sites). The derived irradiance is then prescribed as an input to Precipitation-Runoff Modeling System (PRMS). We constrain our experiment to the Tuolumne River watershed and focus our attention on the winter and spring of 1996-2014. A root-mean-squared error reduction of 2-6% in daily inflow to Hetch Hetchy at the lower end of the Tuolumne catchment was achieved by incorporating the insolation estimates at only 8 out of 280 Hydrologic Response Units (HRUs) within the basin. Our ongoing work endeavors to apply satellite-derived irradiance at each individual HRU.

Estimating School Efficiency: A Comparison of Methods Using Simulated Data.

ERIC Educational Resources Information Center

Bifulco, Robert; Bretschneider, Stuart

2001-01-01

Uses simulated data to assess the adequacy of two econometric and linear-programming techniques (data-envelopment analysis and corrected ordinary least squares) for measuring performance-based school reform. In complex data sets (simulated to contain measurement error and endogeneity), these methods are inadequate efficiency measures. (Contains 40…

Synchronous front-face fluorescence spectroscopy for authentication of the adulteration of edible vegetable oil with refined used frying oil.

PubMed

Tan, Jin; Li, Rong; Jiang, Zi-Tao; Tang, Shu-Hua; Wang, Ying; Shi, Meng; Xiao, Yi-Qian; Jia, Bin; Lu, Tian-Xiang; Wang, Hao

2017-02-15

Synchronous front-face fluorescence spectroscopy has been developed for the discrimination of used frying oil (UFO) from edible vegetable oil (EVO), the estimation of the using time of UFO, and the determination of the adulteration of EVO with UFO. Both the heating time of laboratory prepared UFO and the adulteration of EVO with UFO could be determined by partial least squares regression (PLSR). To simulate the EVO adulteration with UFO, for each kind of oil, fifty adulterated samples at the adulterant amounts range of 1-50% were prepared. PLSR was then adopted to build the model and both full (leave-one-out) cross-validation and external validation were performed to evaluate the predictive ability. Under the optimum condition, the plots of observed versus predicted values exhibited high linearity (R(2)>0.96). The root mean square error of cross-validation (RMSECV) and root mean square error of prediction (RMSEP) were both lower than 3%. Copyright © 2016 Elsevier Ltd. All rights reserved.

The effect of constraints on the analytical figures of merit achieved by extended multivariate curve resolution-alternating least-squares.

PubMed

Pellegrino Vidal, Rocío B; Allegrini, Franco; Olivieri, Alejandro C

2018-03-20

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with some non-trilinear arrays, specifically when the data are of chromatographic origin. To drive the iterative procedure to chemically interpretable solutions, the use of constraints becomes essential. In this work, both simulated and experimental data have been analyzed by MCR-ALS, applying chemically reasonable constraints, and investigating the relationship between selectivity, analytical sensitivity (γ) and root mean square error of prediction (RMSEP). As the selectivity in the instrumental modes decreases, the estimated values for γ did not fully represent the predictive model capabilities, judged from the obtained RMSEP values. Since the available sensitivity expressions have been developed by error propagation theory in unconstrained systems, there is a need of developing new expressions or analytical indicators. They should not only consider the specific profiles retrieved by MCR-ALS, but also the constraints under which the latter ones have been obtained. Copyright © 2017 Elsevier B.V. All rights reserved.

Determination of main fruits in adulterated nectars by ATR-FTIR spectroscopy combined with multivariate calibration and variable selection methods.

PubMed

Miaw, Carolina Sheng Whei; Assis, Camila; Silva, Alessandro Rangel Carolino Sales; Cunha, Maria Luísa; Sena, Marcelo Martins; de Souza, Scheilla Vitorino Carvalho

2018-07-15

Grape, orange, peach and passion fruit nectars were formulated and adulterated by dilution with syrup, apple and cashew juices at 10 levels for each adulterant. Attenuated total reflectance Fourier transform mid infrared (ATR-FTIR) spectra were obtained. Partial least squares (PLS) multivariate calibration models allied to different variable selection methods, such as interval partial least squares (iPLS), ordered predictors selection (OPS) and genetic algorithm (GA), were used to quantify the main fruits. PLS improved by iPLS-OPS variable selection showed the highest predictive capacity to quantify the main fruit contents. The selected variables in the final models varied from 72 to 100; the root mean square errors of prediction were estimated from 0.5 to 2.6%; the correlation coefficients of prediction ranged from 0.948 to 0.990; and, the mean relative errors of prediction varied from 3.0 to 6.7%. All of the developed models were validated. Copyright © 2018 Elsevier Ltd. All rights reserved.

Neural self-tuning adaptive control of non-minimum phase system

NASA Technical Reports Server (NTRS)

Ho, Long T.; Bialasiewicz, Jan T.; Ho, Hai T.

1993-01-01

The motivation of this research came about when a neural network direct adaptive control scheme was applied to control the tip position of a flexible robotic arm. Satisfactory control performance was not attainable due to the inherent non-minimum phase characteristics of the flexible robotic arm tip. Most of the existing neural network control algorithms are based on the direct method and exhibit very high sensitivity, if not unstable, closed-loop behavior. Therefore, a neural self-tuning control (NSTC) algorithm is developed and applied to this problem and showed promising results. Simulation results of the NSTC scheme and the conventional self-tuning (STR) control scheme are used to examine performance factors such as control tracking mean square error, estimation mean square error, transient response, and steady state response.

The multicategory case of the sequential Bayesian pixel selection and estimation procedure

NASA Technical Reports Server (NTRS)

Pore, M. D.; Dennis, T. B. (Principal Investigator)

1980-01-01

A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.

Transmuted of Rayleigh Distribution with Estimation and Application on Noise Signal

NASA Astrophysics Data System (ADS)

Ahmed, Suhad; Qasim, Zainab

2018-05-01

This paper deals with transforming one parameter Rayleigh distribution, into transmuted probability distribution through introducing a new parameter (λ), since this studied distribution is necessary in representing signal data distribution and failure data model the value of this transmuted parameter |λ| ≤ 1, is also estimated as well as the original parameter (⊖) by methods of moments and maximum likelihood using different sample size (n=25, 50, 75, 100) and comparing the results of estimation by statistical measure (mean square error, MSE).

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

Robust Tracking of Small Displacements with a Bayesian Estimator

PubMed Central

Dumont, Douglas M.; Byram, Brett C.

2016-01-01

Radiation-force-based elasticity imaging describes a group of techniques that use acoustic radiation force (ARF) to displace tissue in order to obtain qualitative or quantitative measurements of tissue properties. Because ARF-induced displacements are on the order of micrometers, tracking these displacements in vivo can be challenging. Previously, it has been shown that Bayesian-based estimation can overcome some of the limitations of a traditional displacement estimator like normalized cross-correlation (NCC). In this work, we describe a Bayesian framework that combines a generalized Gaussian-Markov random field (GGMRF) prior with an automated method for selecting the prior’s width. We then evaluate its performance in the context of tracking the micrometer-order displacements encountered in an ARF-based method like acoustic radiation force impulse (ARFI) imaging. The results show that bias, variance, and mean-square error performance vary with prior shape and width, and that an almost one order-of-magnitude reduction in mean-square error can be achieved by the estimator at the automatically-selected prior width. Lesion simulations show that the proposed estimator has a higher contrast-to-noise ratio but lower contrast than NCC, median-filtered NCC, and the previous Bayesian estimator, with a non-Gaussian prior shape having better lesion-edge resolution than a Gaussian prior. In vivo results from a cardiac, radiofrequency ablation ARFI imaging dataset show quantitative improvements in lesion contrast-to-noise ratio over NCC as well as the previous Bayesian estimator. PMID:26529761

Pilot-Assisted Channel Estimation for Orthogonal Multi-Carrier DS-CDMA with Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Shima, Tomoyuki; Tomeba, Hiromichi; Adachi, Fumiyuki

Orthogonal multi-carrier direct sequence code division multiple access (orthogonal MC DS-CDMA) is a combination of time-domain spreading and orthogonal frequency division multiplexing (OFDM). In orthogonal MC DS-CDMA, the frequency diversity gain can be obtained by applying frequency-domain equalization (FDE) based on minimum mean square error (MMSE) criterion to a block of OFDM symbols and can improve the bit error rate (BER) performance in a severe frequency-selective fading channel. FDE requires an accurate estimate of the channel gain. The channel gain can be estimated by removing the pilot modulation in the frequency domain. In this paper, we propose a pilot-assisted channel estimation suitable for orthogonal MC DS-CDMA with FDE and evaluate, by computer simulation, the BER performance in a frequency-selective Rayleigh fading channel.

Instrumental variables vs. grouping approach for reducing bias due to measurement error.

PubMed

Batistatou, Evridiki; McNamee, Roseanne

2008-01-01

Attenuation of the exposure-response relationship due to exposure measurement error is often encountered in epidemiology. Given that error cannot be totally eliminated, bias correction methods of analysis are needed. Many methods require more than one exposure measurement per person to be made, but the `group mean OLS method,' in which subjects are grouped into several a priori defined groups followed by ordinary least squares (OLS) regression on the group means, can be applied with one measurement. An alternative approach is to use an instrumental variable (IV) method in which both the single error-prone measure and an IV are used in IV analysis. In this paper we show that the `group mean OLS' estimator is equal to an IV estimator with the group mean used as IV, but that the variance estimators for the two methods are different. We derive a simple expression for the bias in the common estimator which is a simple function of group size, reliability and contrast of exposure between groups, and show that the bias can be very small when group size is large. We compare this method with a new proposal (group mean ranking method), also applicable with a single exposure measurement, in which the IV is the rank of the group means. When there are two independent exposure measurements per subject, we propose a new IV method (EVROS IV) and compare it with Carroll and Stefanski's (CS IV) proposal in which the second measure is used as an IV; the new IV estimator combines aspects of the `group mean' and `CS' strategies. All methods are evaluated in terms of bias, precision and root mean square error via simulations and a dataset from occupational epidemiology. The `group mean ranking method' does not offer much improvement over the `group mean method.' Compared with the `CS' method, the `EVROS' method is less affected by low reliability of exposure. We conclude that the group IV methods we propose may provide a useful way to handle mismeasured exposures in epidemiology with or without replicate measurements. Our finding may also have implications for the use of aggregate variables in epidemiology to control for unmeasured confounding.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Maximum-Likelihood Estimation for Frequency-Modulated Continuous-Wave Laser Ranging Using Photon-Counting Detectors

DTIC Science & Technology

2013-01-01

are calculated from coherently -detected fields, e.g., coherent Doppler lidar . Our CRB results reveal that the best-case mean-square error scales as 1...1088 (2001). 7. K. Asaka, Y. Hirano, K. Tatsumi, K. Kasahara, and T. Tajime, “A pseudo-random frequency modulation continuous wave coherent lidar using...multiple returns,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 2170–2180 (2007). 11. T. J. Karr, “Atmospheric phase error in coherent laser radar

Estimation of Rice Crop Yields Using Random Forests in Taiwan

NASA Astrophysics Data System (ADS)

Chen, C. F.; Lin, H. S.; Nguyen, S. T.; Chen, C. R.

2017-12-01

Rice is globally one of the most important food crops, directly feeding more people than any other crops. Rice is not only the most important commodity, but also plays a critical role in the economy of Taiwan because it provides employment and income for large rural populations. The rice harvested area and production are thus monitored yearly due to the government's initiatives. Agronomic planners need such information for more precise assessment of food production to tackle issues of national food security and policymaking. This study aimed to develop a machine-learning approach using physical parameters to estimate rice crop yields in Taiwan. We processed the data for 2014 cropping seasons, following three main steps: (1) data pre-processing to construct input layers, including soil types and weather parameters (e.g., maxima and minima air temperature, precipitation, and solar radiation) obtained from meteorological stations across the country; (2) crop yield estimation using the random forests owing to its merits as it can process thousands of variables, estimate missing data, maintain the accuracy level when a large proportion of the data is missing, overcome most of over-fitting problems, and run fast and efficiently when handling large datasets; and (3) error verification. To execute the model, we separated the datasets into two groups of pixels: group-1 (70% of pixels) for training the model and group-2 (30% of pixels) for testing the model. Once the model is trained to produce small and stable out-of-bag error (i.e., the mean squared error between predicted and actual values), it can be used for estimating rice yields of cropping seasons. The results obtained from the random forests-based regression were compared with the actual yield statistics indicated the values of root mean square error (RMSE) and mean absolute error (MAE) achieved for the first rice crop were respectively 6.2% and 2.7%, while those for the second rice crop were 5.3% and 2.9%, respectively. Although there are several uncertainties attributed to the data quality of input layers, our study demonstrates the promising application of random forests for estimating rice crop yields at the national level in Taiwan. This approach could be transferable to other regions of the world for improving large-scale estimation of rice crop yields.

Estimating the Mechanical Behavior of the Knee Joint during Crouch Gait: Implications for Real-Time Motor Control of Robotic Knee Orthoses

PubMed Central

Damiano, Diane L.; Bulea, Thomas C.

2016-01-01

Individuals with cerebral palsy frequently exhibit crouch gait, a pathological walking pattern characterized by excessive knee flexion. Knowledge of the knee joint moment during crouch gait is necessary for the design and control of assistive devices used for treatment. Our goal was to 1) develop statistical models to estimate knee joint moment extrema and dynamic stiffness during crouch gait, and 2) use the models to estimate the instantaneous joint moment during weight-acceptance. We retrospectively computed knee moments from 10 children with crouch gait and used stepwise linear regression to develop statistical models describing the knee moment features. The models explained at least 90% of the response value variability: peak moment in early (99%) and late (90%) stance, and dynamic stiffness of weight-acceptance flexion (94%) and extension (98%). We estimated knee extensor moment profiles from the predicted dynamic stiffness and instantaneous knee angle. This approach captured the timing and shape of the computed moment (root-mean-squared error: 2.64 Nm); including the predicted early-stance peak moment as a correction factor improved model performance (root-mean-squared error: 1.37 Nm). Our strategy provides a practical, accurate method to estimate the knee moment during crouch gait, and could be used for real-time, adaptive control of robotic orthoses. PMID:27101612

Assessing sequential data assimilation techniques for integrating GRACE data into a hydrological model

NASA Astrophysics Data System (ADS)

Khaki, M.; Hoteit, I.; Kuhn, M.; Awange, J.; Forootan, E.; van Dijk, A. I. J. M.; Schumacher, M.; Pattiaratchi, C.

2017-09-01

The time-variable terrestrial water storage (TWS) products from the Gravity Recovery And Climate Experiment (GRACE) have been increasingly used in recent years to improve the simulation of hydrological models by applying data assimilation techniques. In this study, for the first time, we assess the performance of the most popular data assimilation sequential techniques for integrating GRACE TWS into the World-Wide Water Resources Assessment (W3RA) model. We implement and test stochastic and deterministic ensemble-based Kalman filters (EnKF), as well as Particle filters (PF) using two different resampling approaches of Multinomial Resampling and Systematic Resampling. These choices provide various opportunities for weighting observations and model simulations during the assimilation and also accounting for error distributions. Particularly, the deterministic EnKF is tested to avoid perturbing observations before assimilation (that is the case in an ordinary EnKF). Gaussian-based random updates in the EnKF approaches likely do not fully represent the statistical properties of the model simulations and TWS observations. Therefore, the fully non-Gaussian PF is also applied to estimate more realistic updates. Monthly GRACE TWS are assimilated into W3RA covering the entire Australia. To evaluate the filters performances and analyze their impact on model simulations, their estimates are validated by independent in-situ measurements. Our results indicate that all implemented filters improve the estimation of water storage simulations of W3RA. The best results are obtained using two versions of deterministic EnKF, i.e. the Square Root Analysis (SQRA) scheme and the Ensemble Square Root Filter (EnSRF), respectively, improving the model groundwater estimations errors by 34% and 31% compared to a model run without assimilation. Applying the PF along with Systematic Resampling successfully decreases the model estimation error by 23%.

Thickness distribution of a cooling pyroclastic flow deposit on Augustine Volcano, Alaska: Optimization using InSAR, FEMs, and an adaptive mesh algorithm

USGS Publications Warehouse

Masterlark, Timothy; Lu, Zhong; Rykhus, Russell P.

2006-01-01

Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992–1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 °C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE = 2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE = 0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 × 107m3) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500–800 °C.

Estimation of flood-frequency characteristics of small urban streams in North Carolina

USGS Publications Warehouse

Robbins, J.C.; Pope, B.F.

1996-01-01

A statewide study was conducted to develop methods for estimating the magnitude and frequency of floods of small urban streams in North Carolina. This type of information is critical in the design of bridges, culverts and water-control structures, establishment of flood-insurance rates and flood-plain regulation, and for other uses by urban planners and engineers. Concurrent records of rainfall and runoff data collected in small urban basins were used to calibrate rainfall-runoff models. Historic rain- fall records were used with the calibrated models to synthesize a long- term record of annual peak discharges. The synthesized record of annual peak discharges were used in a statistical analysis to determine flood- frequency distributions. These frequency distributions were used with distributions from previous investigations to develop a database for 32 small urban basins in the Blue Ridge-Piedmont, Sand Hills, and Coastal Plain hydrologic areas. The study basins ranged in size from 0.04 to 41.0 square miles. Data describing the size and shape of the basin, level of urban development, and climate and rural flood charac- teristics also were included in the database. Estimation equations were developed by relating flood-frequency char- acteristics to basin characteristics in a generalized least-squares regression analysis. The most significant basin characteristics are drainage area, impervious area, and rural flood discharge. The model error and prediction errors for the estimating equations were less than those for the national flood-frequency equations previously reported. Resulting equations, which have prediction errors generally less than 40 percent, can be used to estimate flood-peak discharges for 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals for small urban basins across the State assuming negligible, sustainable, in- channel detention or basin storage.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Bridge, Thomas M.; Amaya, Max A.

2014-01-01

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

An affordable cuff-less blood pressure estimation solution.

PubMed

Jain, Monika; Kumar, Niranjan; Deb, Sujay

2016-08-01

This paper presents a cuff-less hypertension pre-screening device that non-invasively monitors the Blood Pressure (BP) and Heart Rate (HR) continuously. The proposed device simultaneously records two clinically significant and highly correlated biomedical signals, viz., Electrocardiogram (ECG) and Photoplethysmogram (PPG). The device provides a common data acquisition platform that can interface with PC/laptop, Smart phone/tablet and Raspberry-pi etc. The hardware stores and processes the recorded ECG and PPG in order to extract the real-time BP and HR using kernel regression approach. The BP and HR estimation error is measured in terms of normalized mean square error, Error Standard Deviation (ESD) and Mean Absolute Error (MAE), with respect to a clinically proven digital BP monitor (OMRON HBP1300). The computed error falls under the maximum standard allowable error mentioned by Association for the Advancement of Medical Instrumentation; MAE <; 5 mmHg and ESD <; 8mmHg. The results are validated using two-tailed dependent sample t-test also. The proposed device is a portable low-cost home and clinic bases solution for continuous health monitoring.

Signal-to-noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky-Golay filters and weighted least squares error.

PubMed

Kiani, M A; Sim, K S; Nia, M E; Tso, C P

2015-05-01

A new technique based on cubic spline interpolation with Savitzky-Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real-time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky-Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal-to-noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation-based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.

As-built design specification for proportion estimate software subsystem

NASA Technical Reports Server (NTRS)

Obrien, S. (Principal Investigator)

1980-01-01

The Proportion Estimate Processor evaluates four estimation techniques in order to get an improved estimate of the proportion of a scene that is planted in a selected crop. The four techniques to be evaluated were provided by the techniques development section and are: (1) random sampling; (2) proportional allocation, relative count estimate; (3) proportional allocation, Bayesian estimate; and (4) sequential Bayesian allocation. The user is given two options for computation of the estimated mean square error. These are referred to as the cluster calculation option and the segment calculation option. The software for the Proportion Estimate Processor is operational on the IBM 3031 computer.

Comparison of ArcGIS and SAS Geostatistical Analyst to Estimate Population-Weighted Monthly Temperature for US Counties.

PubMed

Xiaopeng, Q I; Liang, Wei; Barker, Laurie; Lekiachvili, Akaki; Xingyou, Zhang

Temperature changes are known to have significant impacts on human health. Accurate estimates of population-weighted average monthly air temperature for US counties are needed to evaluate temperature's association with health behaviours and disease, which are sampled or reported at the county level and measured on a monthly-or 30-day-basis. Most reported temperature estimates were calculated using ArcGIS, relatively few used SAS. We compared the performance of geostatistical models to estimate population-weighted average temperature in each month for counties in 48 states using ArcGIS v9.3 and SAS v 9.2 on a CITGO platform. Monthly average temperature for Jan-Dec 2007 and elevation from 5435 weather stations were used to estimate the temperature at county population centroids. County estimates were produced with elevation as a covariate. Performance of models was assessed by comparing adjusted R 2 , mean squared error, root mean squared error, and processing time. Prediction accuracy for split validation was above 90% for 11 months in ArcGIS and all 12 months in SAS. Cokriging in SAS achieved higher prediction accuracy and lower estimation bias as compared to cokriging in ArcGIS. County-level estimates produced by both packages were positively correlated (adjusted R 2 range=0.95 to 0.99); accuracy and precision improved with elevation as a covariate. Both methods from ArcGIS and SAS are reliable for U.S. county-level temperature estimates; However, ArcGIS's merits in spatial data pre-processing and processing time may be important considerations for software selection, especially for multi-year or multi-state projects.

Application of an Optimal Tuner Selection Approach for On-Board Self-Tuning Engine Models

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Armstrong, Jeffrey B.; Garg, Sanjay

2012-01-01

An enhanced design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented in this paper. It specific-ally addresses the under-determined estimation problem, in which there are more unknown parameters than available sensor measurements. This work builds upon an existing technique for systematically selecting a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. While the existing technique was optimized for open-loop engine operation at a fixed design point, in this paper an alternative formulation is presented that enables the technique to be optimized for an engine operating under closed-loop control throughout the flight envelope. The theoretical Kalman filter mean squared estimation error at a steady-state closed-loop operating point is derived, and the tuner selection approach applied to minimize this error is discussed. A technique for constructing a globally optimal tuning parameter vector, which enables full-envelope application of the technology, is also presented, along with design steps for adjusting the dynamic response of the Kalman filter state estimates. Results from the application of the technique to linear and nonlinear aircraft engine simulations are presented and compared to the conventional approach of tuner selection. The new methodology is shown to yield a significant improvement in on-line Kalman filter estimation accuracy.

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

NASA Astrophysics Data System (ADS)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

On-board adaptive model for state of charge estimation of lithium-ion batteries based on Kalman filter with proportional integral-based error adjustment

NASA Astrophysics Data System (ADS)

Wei, Jingwen; Dong, Guangzhong; Chen, Zonghai

2017-10-01

With the rapid development of battery-powered electric vehicles, the lithium-ion battery plays a critical role in the reliability of vehicle system. In order to provide timely management and protection for battery systems, it is necessary to develop a reliable battery model and accurate battery parameters estimation to describe battery dynamic behaviors. Therefore, this paper focuses on an on-board adaptive model for state-of-charge (SOC) estimation of lithium-ion batteries. Firstly, a first-order equivalent circuit battery model is employed to describe battery dynamic characteristics. Then, the recursive least square algorithm and the off-line identification method are used to provide good initial values of model parameters to ensure filter stability and reduce the convergence time. Thirdly, an extended-Kalman-filter (EKF) is applied to on-line estimate battery SOC and model parameters. Considering that the EKF is essentially a first-order Taylor approximation of battery model, which contains inevitable model errors, thus, a proportional integral-based error adjustment technique is employed to improve the performance of EKF method and correct model parameters. Finally, the experimental results on lithium-ion batteries indicate that the proposed EKF with proportional integral-based error adjustment method can provide robust and accurate battery model and on-line parameter estimation.

Vehicle longitudinal velocity estimation during the braking process using unknown input Kalman filter

NASA Astrophysics Data System (ADS)

Moaveni, Bijan; Khosravi Roqaye Abad, Mahdi; Nasiri, Sayyad

2015-10-01

In this paper, vehicle longitudinal velocity during the braking process is estimated by measuring the wheels speed. Here, a new algorithm based on the unknown input Kalman filter is developed to estimate the vehicle longitudinal velocity with a minimum mean square error and without using the value of braking torque in the estimation procedure. The stability and convergence of the filter are analysed and proved. Effectiveness of the method is shown by designing a real experiment and comparing the estimation result with actual longitudinal velocity computing from a three-axis accelerometer output.

A Comparison of Energy Expenditure Estimation of Several Physical Activity Monitors

PubMed Central

Dannecker, Kathryn L.; Sazonova, Nadezhda A.; Melanson, Edward L.; Sazonov, Edward S.; Browning, Raymond C.

2013-01-01

Accurately and precisely estimating free-living energy expenditure (EE) is important for monitoring energy balance and quantifying physical activity. Recently, single and multi-sensor devices have been developed that can classify physical activities, potentially resulting in improved estimates of EE. PURPOSE To determine the validity of EE estimation of a footwear-based physical activity monitor and to compare this validity against a variety of research and consumer physical activity monitors. METHODS Nineteen healthy young adults (10 male, 9 female), completed a four-hour stay in a room calorimeter. Participants wore a footwear-based physical activity monitor, as well as Actical, Actigraph, IDEEA, DirectLife and Fitbit devices. Each individual performed a series of postures/activities. We developed models to estimate EE from the footwear-based device, and we used the manufacturer's software to estimate EE for all other devices. RESULTS Estimated EE using the shoe-based device was not significantly different than measured EE (476(20) vs. 478(18) kcal) (Mean (SE)), respectively, and had a root mean square error (RMSE) of (29.6 kcal (6.2%)). The IDEEA and DirectLlife estimates of EE were not significantly different than the measured EE but the Actigraph and Fitbit devices significantly underestimated EE. Root mean square errors were 93.5 (19%), 62.1 kcal (14%), 88.2 kcal (18%), 136.6 kcal (27%), 130.1 kcal (26%), and 143.2 kcal (28%) for Actical, DirectLife, IDEEA, Actigraph and Fitbit respectively. CONCLUSIONS The shoe based physical activity monitor provides a valid estimate of EE while the other physical activity monitors tested have a wide range of validity when estimating EE. Our results also demonstrate that estimating EE based on classification of physical activities can be more accurate and precise than estimating EE based on total physical activity. PMID:23669877

Breast Tissue Characterization with Photon-counting Spectral CT Imaging: A Postmortem Breast Study

PubMed Central

Ding, Huanjun; Klopfer, Michael J.; Ducote, Justin L.; Masaki, Fumitaro

2014-01-01

Purpose To investigate the feasibility of breast tissue characterization in terms of water, lipid, and protein contents with a spectral computed tomographic (CT) system based on a cadmium zinc telluride (CZT) photon-counting detector by using postmortem breasts. Materials and Methods Nineteen pairs of postmortem breasts were imaged with a CZT-based photon-counting spectral CT system with beam energy of 100 kVp. The mean glandular dose was estimated to be in the range of 1.8–2.2 mGy. The images were corrected for pulse pile-up and other artifacts by using spectral distortion corrections. Dual-energy decomposition was then applied to characterize each breast into water, lipid, and protein contents. The precision of the three-compartment characterization was evaluated by comparing the composition of right and left breasts, where the standard error of the estimations was determined. The results of dual-energy decomposition were compared by using averaged root mean square to chemical analysis, which was used as the reference standard. Results The standard errors of the estimations of the right-left correlations obtained from spectral CT were 7.4%, 6.7%, and 3.2% for water, lipid, and protein contents, respectively. Compared with the reference standard, the average root mean square error in breast tissue composition was 2.8%. Conclusion Spectral CT can be used to accurately quantify the water, lipid, and protein contents in breast tissue in a laboratory study by using postmortem specimens. © RSNA, 2014 PMID:24814180

Skin movement artefact assessment and compensation in the estimation of knee-joint kinematics.

PubMed

Lucchetti, L; Cappozzo, A; Cappello, A; Della Croce, U

1998-11-01

In three dimensional (3-D) human movement analysis using close-range photogrammetry, surface marker clusters deform and rigidly move relative to the underlying bone. This introduces an important artefact (skin movement artefact) which propagates to bone position and orientation and joint kinematics estimates. This occurs to the extent that those joint attitude components that undergo small variations result in totally unreliable values. This paper presents an experimental and analytical procedure, to be included in a subject-specific movement analysis protocol, which allows for the assessment of skin movement artefacts and, based on this knowledge, for their compensation. The effectiveness of this procedure was verified with reference to knee-joint kinematics and to the artefacts caused by the hip movements on markers located on the thigh surface. Quantitative validation was achieved through experimental paradigms whereby prior reliable information on the target joint kinematics was available. When position and orientation of bones were determined during the execution of a motor task, using a least-squares optimal estimator, but the rigid artefactual marker cluster movement was not dealt with, then knee joint translations and rotations were affected by root mean square errors (r.m.s.) up to 14 mm and 6 degrees, respectively. When the rigid artefactual movement was also compensated for, then r.m.s errors were reduced to less than 4 mm and 3 degrees, respectively. In addition, errors originally strongly correlated with hip rotations, after compensation, lost this correlation.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting.

PubMed

Wear, Keith A

2013-04-01

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Best estimate of luminal cross-sectional area of coronary arteries from angiograms

NASA Technical Reports Server (NTRS)

Lee, P. L.; Selzer, R. H.

1988-01-01

We have reexamined the problem of estimating the luminal area of an elliptically-shaped coronary artery cross section from two or more radiographic diameter measurements. The expected error is found to be much smaller than the maximum potential error. In the cae of two orthogonal views, closed form expressions have been derived for calculating the area and the uncertainty. Assuming that the underlying ellipse has limited ellipticity (major/minor axis ratio less than five), it is shown that the average uncertainty in the area is less than 14 percent. When more than two views are available, we suggest using a least-squares fit method to extract all available information from the data.

About an adaptively weighted Kaplan-Meier estimate.

PubMed

Plante, Jean-François

2009-09-01

The minimum averaged mean squared error nonparametric adaptive weights use data from m possibly different populations to infer about one population of interest. The definition of these weights is based on the properties of the empirical distribution function. We use the Kaplan-Meier estimate to let the weights accommodate right-censored data and use them to define the weighted Kaplan-Meier estimate. The proposed estimate is smoother than the usual Kaplan-Meier estimate and converges uniformly in probability to the target distribution. Simulations show that the performances of the weighted Kaplan-Meier estimate on finite samples exceed that of the usual Kaplan-Meier estimate. A case study is also presented.

Simple Form of MMSE Estimator for Super-Gaussian Prior Densities

NASA Astrophysics Data System (ADS)

Kittisuwan, Pichid

2015-04-01

The denoising method that become popular in recent years for additive white Gaussian noise (AWGN) are Bayesian estimation techniques e.g., maximum a posteriori (MAP) and minimum mean square error (MMSE). In super-Gaussian prior densities, it is well known that the MMSE estimator in such a case has a complicated form. In this work, we derive the MMSE estimation with Taylor series. We show that the proposed estimator also leads to a simple formula. An extension of this estimator to Pearson type VII prior density is also offered. The experimental result shows that the proposed estimator to the original MMSE nonlinearity is reasonably good.

Optimum data analysis procedures for Titan 4 and Space Shuttle payload acoustic measurements during lift-off

NASA Technical Reports Server (NTRS)

Piersol, Allan G.

1991-01-01

Analytical expressions have been derived to describe the mean square error in the estimation of the maximum rms value computed from a step-wise (or running) time average of a nonstationary random signal. These analytical expressions have been applied to the problem of selecting the optimum averaging times that will minimize the total mean square errors in estimates of the maximum sound pressure levels measured inside the Titan IV payload fairing (PLF) and the Space Shuttle payload bay (PLB) during lift-off. Based on evaluations of typical Titan IV and Space Shuttle launch data, it has been determined that the optimum averaging times for computing the maximum levels are (1) T (sub o) = 1.14 sec for the maximum overall level, and T(sub oi) = 4.88 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Titan IV PLF, and (2) T (sub o) = 1.65 sec for the maximum overall level, and T (sub oi) = 7.10 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Space Shuttle PLB, where f (sub i) is the 1/3 octave band center frequency. However, the results for both vehicles indicate that the total rms error in the maximum level estimates will be within 25 percent the minimum error for all averaging times within plus or minus 50 percent of the optimum averaging time, so a precise selection of the exact optimum averaging time is not critical. Based on these results, linear averaging times (T) are recommended for computing the maximum sound pressure level during lift-off.

Estimating the settling velocity of bioclastic sediment using common grain-size analysis techniques

USGS Publications Warehouse

Cuttler, Michael V. W.; Lowe, Ryan J.; Falter, James L.; Buscombe, Daniel D.

2017-01-01

Most techniques for estimating settling velocities of natural particles have been developed for siliciclastic sediments. Therefore, to understand how these techniques apply to bioclastic environments, measured settling velocities of bioclastic sedimentary deposits sampled from a nearshore fringing reef in Western Australia were compared with settling velocities calculated using results from several common grain-size analysis techniques (sieve, laser diffraction and image analysis) and established models. The effects of sediment density and shape were also examined using a range of density values and three different models of settling velocity. Sediment density was found to have a significant effect on calculated settling velocity, causing a range in normalized root-mean-square error of up to 28%, depending upon settling velocity model and grain-size method. Accounting for particle shape reduced errors in predicted settling velocity by 3% to 6% and removed any velocity-dependent bias, which is particularly important for the fastest settling fractions. When shape was accounted for and measured density was used, normalized root-mean-square errors were 4%, 10% and 18% for laser diffraction, sieve and image analysis, respectively. The results of this study show that established models of settling velocity that account for particle shape can be used to estimate settling velocity of irregularly shaped, sand-sized bioclastic sediments from sieve, laser diffraction, or image analysis-derived measures of grain size with a limited amount of error. Collectively, these findings will allow for grain-size data measured with different methods to be accurately converted to settling velocity for comparison. This will facilitate greater understanding of the hydraulic properties of bioclastic sediment which can help to increase our general knowledge of sediment dynamics in these environments.

Using weighted power mean for equivalent square estimation.

PubMed

Zhou, Sumin; Wu, Qiuwen; Li, Xiaobo; Ma, Rongtao; Zheng, Dandan; Wang, Shuo; Zhang, Mutian; Li, Sicong; Lei, Yu; Fan, Qiyong; Hyun, Megan; Diener, Tyler; Enke, Charles

2017-11-01

Equivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula. The proposed WPM formula is ESWPMa,b=waα+1-wbα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (S cp ) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981-7018), and published S cp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125-148). For the BJR dataset, the best-fit parameter value α = -1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125-148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields. The WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling.

PubMed

Rodrigo, Marianito R

2016-01-01

The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10-15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand-held device for field use. © 2015 American Academy of Forensic Sciences.

Accurate position estimation methods based on electrical impedance tomography measurements

NASA Astrophysics Data System (ADS)

Vergara, Samuel; Sbarbaro, Daniel; Johansen, T. A.

2017-08-01

Electrical impedance tomography (EIT) is a technology that estimates the electrical properties of a body or a cross section. Its main advantages are its non-invasiveness, low cost and operation free of radiation. The estimation of the conductivity field leads to low resolution images compared with other technologies, and high computational cost. However, in many applications the target information lies in a low intrinsic dimensionality of the conductivity field. The estimation of this low-dimensional information is addressed in this work. It proposes optimization-based and data-driven approaches for estimating this low-dimensional information. The accuracy of the results obtained with these approaches depends on modelling and experimental conditions. Optimization approaches are sensitive to model discretization, type of cost function and searching algorithms. Data-driven methods are sensitive to the assumed model structure and the data set used for parameter estimation. The system configuration and experimental conditions, such as number of electrodes and signal-to-noise ratio (SNR), also have an impact on the results. In order to illustrate the effects of all these factors, the position estimation of a circular anomaly is addressed. Optimization methods based on weighted error cost functions and derivate-free optimization algorithms provided the best results. Data-driven approaches based on linear models provided, in this case, good estimates, but the use of nonlinear models enhanced the estimation accuracy. The results obtained by optimization-based algorithms were less sensitive to experimental conditions, such as number of electrodes and SNR, than data-driven approaches. Position estimation mean squared errors for simulation and experimental conditions were more than twice for the optimization-based approaches compared with the data-driven ones. The experimental position estimation mean squared error of the data-driven models using a 16-electrode setup was less than 0.05% of the tomograph radius value. These results demonstrate that the proposed approaches can estimate an object’s position accurately based on EIT measurements if enough process information is available for training or modelling. Since they do not require complex calculations it is possible to use them in real-time applications without requiring high-performance computers.

A Method for Estimating Zero-Flow Pressure and Intracranial Pressure

PubMed Central

Caren, Marzban; Paul, Raymond Illian; David, Morison; Anne, Moore; Michel, Kliot; Marek, Czosnyka; Pierre, Mourad

2012-01-01

Background It has been hypothesized that critical closing pressure of cerebral circulation, or zero-flow pressure (ZFP), can estimate intracranial pressure (ICP). One ZFP estimation method employs extrapolation of arterial blood pressure versus blood-flow velocity. The aim of this study is to improve ICP predictions. Methods Two revisions are considered: 1) The linear model employed for extrapolation is extended to a nonlinear equation, and 2) the parameters of the model are estimated by an alternative criterion (not least-squares). The method is applied to data on transcranial Doppler measurements of blood-flow velocity, arterial blood pressure, and ICP, from 104 patients suffering from closed traumatic brain injury, sampled across the United States and England. Results The revisions lead to qualitative (e.g., precluding negative ICP) and quantitative improvements in ICP prediction. In going from the original to the revised method, the ±2 standard deviation of error is reduced from 33 to 24 mm Hg; the root-mean-squared error (RMSE) is reduced from 11 to 8.2 mm Hg. The distribution of RMSE is tighter as well; for the revised method the 25th and 75th percentiles are 4.1 and 13.7 mm Hg, respectively, as compared to 5.1 and 18.8 mm Hg for the original method. Conclusions Proposed alterations to a procedure for estimating ZFP lead to more accurate and more precise estimates of ICP, thereby offering improved means of estimating it noninvasively. The quality of the estimates is inadequate for many applications, but further work is proposed which may lead to clinically useful results. PMID:22824923

MRI-Based Intelligence Quotient (IQ) Estimation with Sparse Learning

PubMed Central

Wang, Liye; Wee, Chong-Yaw; Suk, Heung-Il; Tang, Xiaoying; Shen, Dinggang

2015-01-01

In this paper, we propose a novel framework for IQ estimation using Magnetic Resonance Imaging (MRI) data. In particular, we devise a new feature selection method based on an extended dirty model for jointly considering both element-wise sparsity and group-wise sparsity. Meanwhile, due to the absence of large dataset with consistent scanning protocols for the IQ estimation, we integrate multiple datasets scanned from different sites with different scanning parameters and protocols. In this way, there is large variability in these different datasets. To address this issue, we design a two-step procedure for 1) first identifying the possible scanning site for each testing subject and 2) then estimating the testing subject’s IQ by using a specific estimator designed for that scanning site. We perform two experiments to test the performance of our method by using the MRI data collected from 164 typically developing children between 6 and 15 years old. In the first experiment, we use a multi-kernel Support Vector Regression (SVR) for estimating IQ values, and obtain an average correlation coefficient of 0.718 and also an average root mean square error of 8.695 between the true IQs and the estimated ones. In the second experiment, we use a single-kernel SVR for IQ estimation, and achieve an average correlation coefficient of 0.684 and an average root mean square error of 9.166. All these results show the effectiveness of using imaging data for IQ prediction, which is rarely done in the field according to our knowledge. PMID:25822851

Demand Forecasting: An Evaluation of DODs Accuracy Metric and Navys Procedures

DTIC Science & Technology

2016-06-01

inventory management improvement plan, mean of absolute scaled error, lead time adjusted squared error, forecast accuracy, benchmarking, naïve method...Manager JASA Journal of the American Statistical Association LASE Lead-time Adjusted Squared Error LCI Life Cycle Indicator MA Moving Average MAE...Mean Squared Error xvi NAVSUP Naval Supply Systems Command NDAA National Defense Authorization Act NIIN National Individual Identification Number

Application of artificial intelligence to estimate the reference evapotranspiration in sub-humid Doon valley

NASA Astrophysics Data System (ADS)

Nema, Manish K.; Khare, Deepak; Chandniha, Surendra K.

2017-11-01

Estimation of evapotranspiration (ET) is an essential component of the hydrologic cycle, which is also requisite for efficient irrigation water management planning and hydro-meteorological studies at both the basin and catchment scales. There are about twenty well-established methods available for ET estimation which depends upon various meteorological parameters and assumptions. Most of these methods are physically based and need a variety of input data. The FAO-56 Penman-Monteith method (PM) for estimating reference evapotranspiration (ET0) is recommend for irrigation scheduling worldwide, because PM generally yields the best results under various climatic conditions. This study investigates the abilities of artificial neural networks (ANN) to improve the accuracy of monthly evaporation estimation in sub-humid climatic region of Dehradun. In the first part of the study, different ANN models, comprising various combinations of training function and number of neutrons were developed to estimate the ET0 and it has been compared with the Penman-Monteith (PM) ET0 as the ideal (observed) ET0. Various statistical approaches were considered to estimate the model performance, i.e. Coefficient of Correlation ( r), Sum of Squared Errors, Root Mean Square Error, Nash-Sutcliffe Efficiency Index (NSE) and Mean Absolute Error. The ANN model with Levenberg-Marquardt training algorithm, single hidden layer and nine number of neutron schema was found the best predicting capabilities for the study station with Coefficient of Correlation ( r) and NSE value of 0.996 and 0.991 for calibration period and 0.990 and 0.980 for validation period, respectively. In the subsequent part of the study, the trend analysis of ET0 time series revealed a rising trend in the month of March, and a falling trend during June to November, except August, with more than 90% significance level and the annual declining rate was found to 1.49 mm per year.

Height and Biomass of Mangroves in Africa from ICEsat/GLAS and SRTM

NASA Technical Reports Server (NTRS)

Fatoyinbo, Temilola E.; Simard, Marc

2012-01-01

The accurate quantification of forest 3-D structure is of great importance for studies of the global carbon cycle and biodiversity. These studies are especially relevant in Africa, where deforestation rates are high and the lack of background data is great. Mangrove forests are ecologically significant and it is important to measure mangrove canopy heights and biomass. The objectives of this study are to estimate: 1. The total area, 2. Canopy height distributions and 3. Aboveground biomass of mangrove forests in Africa. To derive mangrove 3-D structure and biomass maps, we used a combination of mangrove maps derived from Landsat ETM+, LiDAR canopy height estimates from ICEsat/GLAS (Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System) and elevation data from SRTM (Shuttle Radar Topography Mission) for the African continent. More specifically, we extracted mangrove forest areas on the SRTM DEM using Landsat based landcover maps. The LiDAR (Light Detection and Ranging) measurements from the large footprint GLAS sensor were used to derive local estimates of canopy height and calibrate the Interferometric Synthetic Aperture Radar (InSAR) data from SRTM. We then applied allometric equations relating canopy height to biomass in order to estimate above ground biomass (AGB) from the canopy height product. The total mangrove area of Africa was estimated to be 25 960 square kilometers with 83% accuracy. The largest mangrove areas and greatest total biomass was 29 found in Nigeria covering 8 573 km2 with 132 x10(exp 6) Mg AGB. Canopy height across Africa was estimated with an overall root mean square error of 3.55 m. This error also includes the impact of using sensors with different resolutions and geolocation error which make comparison between measurements sensitive to canopy heterogeneities. This study provides the first systematic estimates of mangrove area, height and biomass in Africa. Our results showed that the combination of ICEsat/GLAS and SRTM data is well suited for vegetation 3-D mapping on a continental scale.

A Comparison of Latent Growth Models for Constructs Measured by Multiple Items

ERIC Educational Resources Information Center

Leite, Walter L.

2007-01-01

Univariate latent growth modeling (LGM) of composites of multiple items (e.g., item means or sums) has been frequently used to analyze the growth of latent constructs. This study evaluated whether LGM of composites yields unbiased parameter estimates, standard errors, chi-square statistics, and adequate fit indexes. Furthermore, LGM was compared…

A Strategy for Replacing Sum Scoring

ERIC Educational Resources Information Center

Ramsay, James O.; Wiberg, Marie

2017-01-01

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and…

Incorporating Quality Scores in Meta-Analysis

ERIC Educational Resources Information Center

Ahn, Soyeon; Becker, Betsy Jane

2011-01-01

This paper examines the impact of quality-score weights in meta-analysis. A simulation examines the roles of study characteristics such as population effect size (ES) and its variance on the bias and mean square errors (MSEs) of the estimators for several patterns of relationship between quality and ES, and for specific patterns of systematic…

Causal Models with Unmeasured Variables: An Introduction to LISREL.

ERIC Educational Resources Information Center

Wolfle, Lee M.

Whenever one uses ordinary least squares regression, one is making an implicit assumption that all of the independent variables have been measured without error. Such an assumption is obviously unrealistic for most social data. One approach for estimating such regression models is to measure implied coefficients between latent variables for which…

Analyzing Multivariate Repeated Measures Designs: A Comparison of Two Approximate Degrees of Freedom Procedures

ERIC Educational Resources Information Center

Lix, Lisa M.; Algina, James; Keselman, H. J.

2003-01-01

The approximate degrees of freedom Welch-James (WJ) and Brown-Forsythe (BF) procedures for testing within-subjects effects in multivariate groups by trials repeated measures designs were investigated under departures from covariance homogeneity and normality. Empirical Type I error and power rates were obtained for least-squares estimators and…

Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE

PubMed Central

Weller, Daniel S.; Nielsen, Jon-Fredrik; Fessler, Jeffrey A.

2013-01-01

Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate (based on the principle of Stein’s unbiased risk estimate—SURE) of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the ℓ1-norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error (MSE) optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction. PMID:23591478

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Landsat-4 (TDRSS-user) orbit determination using batch least-squares and sequential methods

NASA Technical Reports Server (NTRS)

Oza, D. H.; Jones, T. L.; Hakimi, M.; Samii, M. V.; Doll, C. E.; Mistretta, G. D.; Hart, R. C.

1992-01-01

TDRSS user orbit determination is analyzed using a batch least-squares method and a sequential estimation method. It was found that in the batch least-squares method analysis, the orbit determination consistency for Landsat-4, which was heavily tracked by TDRSS during January 1991, was about 4 meters in the rms overlap comparisons and about 6 meters in the maximum position differences in overlap comparisons. The consistency was about 10 to 30 meters in the 3 sigma state error covariance function in the sequential method analysis. As a measure of consistency, the first residual of each pass was within the 3 sigma bound in the residual space.

Least-Squares Self-Calibration of Imaging Array Data

NASA Technical Reports Server (NTRS)

Arendt, R. G.; Moseley, S. H.; Fixsen, D. J.

2004-01-01

When arrays are used to collect multiple appropriately-dithered images of the same region of sky, the resulting data set can be calibrated using a least-squares minimization procedure that determines the optimal fit between the data and a model of that data. The model parameters include the desired sky intensities as well as instrument parameters such as pixel-to-pixel gains and offsets. The least-squares solution simultaneously provides the formal error estimates for the model parameters. With a suitable observing strategy, the need for separate calibration observations is reduced or eliminated. We show examples of this calibration technique applied to HST NICMOS observations of the Hubble Deep Fields and simulated SIRTF IRAC observations.

Regression model development and computational procedures to support estimation of real-time concentrations and loads of selected constituents in two tributaries to Lake Houston near Houston, Texas, 2005-9

USGS Publications Warehouse

Lee, Michael T.; Asquith, William H.; Oden, Timothy D.

2012-01-01

In December 2005, the U.S. Geological Survey (USGS), in cooperation with the City of Houston, Texas, began collecting discrete water-quality samples for nutrients, total organic carbon, bacteria (Escherichia coli and total coliform), atrazine, and suspended sediment at two USGS streamflow-gaging stations that represent watersheds contributing to Lake Houston (08068500 Spring Creek near Spring, Tex., and 08070200 East Fork San Jacinto River near New Caney, Tex.). Data from the discrete water-quality samples collected during 2005–9, in conjunction with continuously monitored real-time data that included streamflow and other physical water-quality properties (specific conductance, pH, water temperature, turbidity, and dissolved oxygen), were used to develop regression models for the estimation of concentrations of water-quality constituents of substantial source watersheds to Lake Houston. The potential explanatory variables included discharge (streamflow), specific conductance, pH, water temperature, turbidity, dissolved oxygen, and time (to account for seasonal variations inherent in some water-quality data). The response variables (the selected constituents) at each site were nitrite plus nitrate nitrogen, total phosphorus, total organic carbon, E. coli, atrazine, and suspended sediment. The explanatory variables provide easily measured quantities to serve as potential surrogate variables to estimate concentrations of the selected constituents through statistical regression. Statistical regression also facilitates accompanying estimates of uncertainty in the form of prediction intervals. Each regression model potentially can be used to estimate concentrations of a given constituent in real time. Among other regression diagnostics, the diagnostics used as indicators of general model reliability and reported herein include the adjusted R-squared, the residual standard error, residual plots, and p-values. Adjusted R-squared values for the Spring Creek models ranged from .582–.922 (dimensionless). The residual standard errors ranged from .073–.447 (base-10 logarithm). Adjusted R-squared values for the East Fork San Jacinto River models ranged from .253–.853 (dimensionless). The residual standard errors ranged from .076–.388 (base-10 logarithm). In conjunction with estimated concentrations, constituent loads can be estimated by multiplying the estimated concentration by the corresponding streamflow and by applying the appropriate conversion factor. The regression models presented in this report are site specific, that is, they are specific to the Spring Creek and East Fork San Jacinto River streamflow-gaging stations; however, the general methods that were developed and documented could be applied to most perennial streams for the purpose of estimating real-time water quality data.

An attempt to bridge muscle architecture dynamics and its instantaneous rate of force development using ultrasonography.

PubMed

Li, Jizhou; Zhou, Yongjin; Zheng, Yong-Ping; Li, Guanglin

2015-08-01

Muscle force output is an essential index in rehabilitation assessment or physical exams, and could provide considerable insights for various applications such as load monitoring and muscle assessment in sports science or rehabilitation therapy. Besides direct measurement of force output using a dynamometer, electromyography has earlier been used in several studies to quantify muscle force as an indirect means. However, its spatial resolution is easily compromised as a summation of the action potentials from neighboring motor units of electrode site. To explore an alternative method to indirectly estimate the muscle force output, and with better muscle specificity, we started with an investigation on the relationship between architecture dynamics and force output of triceps surae. The muscular architecture dynamics is captured in ultrasonography sequences and estimated using a previously reported motion estimation method. Then an indicator named as the dorsoventrally averaged motion profile (DAMP) is employed. The performance of force output is represented by an instantaneous version of the rate of force development (RFD), namely I-RFD. From experimental results on ten normal subjects, there were significant correlations between the I-RFD and DAMP for triceps surae, both normalized between 0 and 1, with the sum of squares error at 0.0516±0.0224, R-square at 0.7929±0.0931 and root mean squared error at 0.0159±0.0033. The statistical significance results were less than 0.01. The present study suggested that muscle architecture dynamics extracted from ultrasonography during contraction is well correlated to the I-RFD and it can be a promising option for indirect estimation of muscle force output. Copyright © 2015 Elsevier B.V. All rights reserved.

Desert soil clay content estimation using reflectance spectroscopy preprocessed by fractional derivative

PubMed Central

Tiyip, Tashpolat; Ding, Jianli; Zhang, Dong; Liu, Wei; Wang, Fei; Tashpolat, Nigara

2017-01-01

Effective pretreatment of spectral reflectance is vital to model accuracy in soil parameter estimation. However, the classic integer derivative has some disadvantages, including spectral information loss and the introduction of high-frequency noise. In this paper, the fractional order derivative algorithm was applied to the pretreatment and partial least squares regression (PLSR) was used to assess the clay content of desert soils. Overall, 103 soil samples were collected from the Ebinur Lake basin in the Xinjiang Uighur Autonomous Region of China, and used as data sets for calibration and validation. Following laboratory measurements of spectral reflectance and clay content, the raw spectral reflectance and absorbance data were treated using the fractional derivative order from the 0.0 to the 2.0 order (order interval: 0.2). The ratio of performance to deviation (RPD), determinant coefficients of calibration (Rc2), root mean square errors of calibration (RMSEC), determinant coefficients of prediction (Rp2), and root mean square errors of prediction (RMSEP) were applied to assess the performance of predicting models. The results showed that models built on the fractional derivative order performed better than when using the classic integer derivative. Comparison of the predictive effects of 22 models for estimating clay content, calibrated by PLSR, showed that those models based on the fractional derivative 1.8 order of spectral reflectance (Rc2 = 0.907, RMSEC = 0.425%, Rp2 = 0.916, RMSEP = 0.364%, and RPD = 2.484 ≥ 2.000) and absorbance (Rc2 = 0.888, RMSEC = 0.446%, Rp2 = 0.918, RMSEP = 0.383% and RPD = 2.511 ≥ 2.000) were most effective. Furthermore, they performed well in quantitative estimations of the clay content of soils in the study area. PMID:28934274

Metameric MIMO-OOK transmission scheme using multiple RGB LEDs.

PubMed

Bui, Thai-Chien; Cusani, Roberto; Scarano, Gaetano; Biagi, Mauro

2018-05-28

In this work, we propose a novel visible light communication (VLC) scheme utilizing multiple different red green and blue triplets each with a different emission spectrum of red, green and blue for mitigating the effect of interference due to different colors using spatial multiplexing. On-off keying modulation is considered and its effect on light emission in terms of flickering, dimming and color rendering is discussed so as to demonstrate how metameric properties have been considered. At the receiver, multiple photodiodes with color filter-tuned on each transmit light emitting diode (LED) are employed. Three different detection mechanisms of color zero forcing, minimum mean square error estimation and minimum mean square error equalization are then proposed. The system performance of the proposed scheme is evaluated both with computer simulations and tests with an Arduino board implementation.

A comparative study of optimum and suboptimum direct-detection laser ranging receivers

NASA Technical Reports Server (NTRS)

Abshire, J. B.

1978-01-01

A summary of previously proposed receiver strategies for direct-detection laser ranging receivers is presented. Computer simulations are used to compare performance of candidate implementation strategies in the 1- to 100-photoelectron region. Under the condition of no background radiation, the maximum-likelihood and minimum mean-square error estimators were found to give the same performance for both bell-shaped and rectangular optical-pulse shapes. For signal energies greater than 100 photoelectrons, the root-mean-square range error is shown to decrease as Q to the -1/2 power for bell-shaped pulses and Q to the -1 power for rectangular pulses, where Q represents the average pulse energy. Of several receiver implementations presented, the matched-filter peak detector was found to be preferable. A similar configuration, using a constant-fraction discriminator, exhibited a signal-level dependent time bias.

Analysis of S-box in Image Encryption Using Root Mean Square Error Method

NASA Astrophysics Data System (ADS)

Hussain, Iqtadar; Shah, Tariq; Gondal, Muhammad Asif; Mahmood, Hasan

2012-07-01

The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes

Weather adjustment using seemingly unrelated regression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noll, T.A.

1995-05-01

Seemingly unrelated regression (SUR) is a system estimation technique that accounts for time-contemporaneous correlation between individual equations within a system of equations. SUR is suited to weather adjustment estimations when the estimation is: (1) composed of a system of equations and (2) the system of equations represents either different weather stations, different sales sectors or a combination of different weather stations and different sales sectors. SUR utilizes the cross-equation error values to develop more accurate estimates of the system coefficients than are obtained using ordinary least-squares (OLS) estimation. SUR estimates can be generated using a variety of statistical software packagesmore » including MicroTSP and SAS.« less

Optimal estimation of the optomechanical coupling strength

NASA Astrophysics Data System (ADS)

Bernád, József Zsolt; Sanavio, Claudio; Xuereb, André

2018-06-01

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cramér-Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely results in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times on the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

Simulation of rare events in quantum error correction

NASA Astrophysics Data System (ADS)

Bravyi, Sergey; Vargo, Alexander

2013-12-01

We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability PL for the two-dimensional surface code on a square lattice with a pair of holes for all code distances d≤20 and all error rates p below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay PL˜exp[-α(p)d] and provide a simple fitting formula for the decay rate α(p). Both noiseless and noisy syndrome readout circuits are considered.

Estimating Traffic Accidents in Turkey Using Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Akgüngör, Ali Payıdar; Korkmaz, Ersin

2017-06-01

Estimating traffic accidents play a vital role to apply road safety procedures. This study proposes Differential Evolution Algorithm (DEA) models to estimate the number of accidents in Turkey. In the model development, population (P) and the number of vehicles (N) are selected as model parameters. Three model forms, linear, exponential and semi-quadratic models, are developed using DEA with the data covering from 2000 to 2014. Developed models are statistically compared to select the best fit model. The results of the DE models show that the linear model form is suitable to estimate the number of accidents. The statistics of this form is better than other forms in terms of performance criteria which are the Mean Absolute Percentage Errors (MAPE) and the Root Mean Square Errors (RMSE). To investigate the performance of linear DE model for future estimations, a ten-year period from 2015 to 2024 is considered. The results obtained from future estimations reveal the suitability of DE method for road safety applications.

Quantized kernel least mean square algorithm.

PubMed

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

An Empirical State Error Covariance Matrix Orbit Determination Example

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Evaluation of the predicted error of the soil moisture retrieval from C-band SAR by comparison against modelled soil moisture estimates over Australia

PubMed Central

Doubková, Marcela; Van Dijk, Albert I.J.M.; Sabel, Daniel; Wagner, Wolfgang; Blöschl, Günter

2012-01-01

The Sentinel-1 will carry onboard a C-band radar instrument that will map the European continent once every four days and the global land surface at least once every twelve days with finest 5 × 20 m spatial resolution. The high temporal sampling rate and operational configuration make Sentinel-1 of interest for operational soil moisture monitoring. Currently, updated soil moisture data are made available at 1 km spatial resolution as a demonstration service using Global Mode (GM) measurements from the Advanced Synthetic Aperture Radar (ASAR) onboard ENVISAT. The service demonstrates the potential of the C-band observations to monitor variations in soil moisture. Importantly, a retrieval error estimate is also available; these are needed to assimilate observations into models. The retrieval error is estimated by propagating sensor errors through the retrieval model. In this work, the existing ASAR GM retrieval error product is evaluated using independent top soil moisture estimates produced by the grid-based landscape hydrological model (AWRA-L) developed within the Australian Water Resources Assessment system (AWRA). The ASAR GM retrieval error estimate, an assumed prior AWRA-L error estimate and the variance in the respective datasets were used to spatially predict the root mean square error (RMSE) and the Pearson's correlation coefficient R between the two datasets. These were compared with the RMSE calculated directly from the two datasets. The predicted and computed RMSE showed a very high level of agreement in spatial patterns as well as good quantitative agreement; the RMSE was predicted within accuracy of 4% of saturated soil moisture over 89% of the Australian land mass. Predicted and calculated R maps corresponded within accuracy of 10% over 61% of the continent. The strong correspondence between the predicted and calculated RMSE and R builds confidence in the retrieval error model and derived ASAR GM error estimates. The ASAR GM and Sentinel-1 have the same basic physical measurement characteristics, and therefore very similar retrieval error estimation method can be applied. Because of the expected improvements in radiometric resolution of the Sentinel-1 backscatter measurements, soil moisture estimation errors can be expected to be an order of magnitude less than those for ASAR GM. This opens the possibility for operationally available medium resolution soil moisture estimates with very well-specified errors that can be assimilated into hydrological or crop yield models, with potentially large benefits for land-atmosphere fluxes, crop growth, and water balance monitoring and modelling. PMID:23483015

Stereo pair design for cameras with a fovea

NASA Technical Reports Server (NTRS)

Chettri, Samir R.; Keefe, Michael; Zimmerman, John R.

1992-01-01

We describe the methodology for the design and selection of a stereo pair when the cameras have a greater concentration of sensing elements in the center of the image plane (fovea). Binocular vision is important for the purpose of depth estimation, which in turn is important in a variety of applications such as gaging and autonomous vehicle guidance. We assume that one camera has square pixels of size dv and the other has pixels of size rdv, where r is between 0 and 1. We then derive results for the average error, the maximum error, and the error distribution in the depth determination of a point. These results can be shown to be a general form of the results for the case when the cameras have equal sized pixels. We discuss the behavior of the depth estimation error as we vary r and the tradeoffs between the extra processing time and increased accuracy. Knowing these results makes it possible to study the case when we have a pair of cameras with a fovea.

Improved error estimates of a discharge algorithm for remotely sensed river measurements: Test cases on Sacramento and Garonne Rivers

NASA Astrophysics Data System (ADS)

Yoon, Yeosang; Garambois, Pierre-André; Paiva, Rodrigo C. D.; Durand, Michael; Roux, Hélène; Beighley, Edward

2016-01-01

We present an improvement to a previously presented algorithm that used a Bayesian Markov Chain Monte Carlo method for estimating river discharge from remotely sensed observations of river height, width, and slope. We also present an error budget for discharge calculations from the algorithm. The algorithm may be utilized by the upcoming Surface Water and Ocean Topography (SWOT) mission. We present a detailed evaluation of the method using synthetic SWOT-like observations (i.e., SWOT and AirSWOT, an airborne version of SWOT). The algorithm is evaluated using simulated AirSWOT observations over the Sacramento and Garonne Rivers that have differing hydraulic characteristics. The algorithm is also explored using SWOT observations over the Sacramento River. SWOT and AirSWOT height, width, and slope observations are simulated by corrupting the "true" hydraulic modeling results with instrument error. Algorithm discharge root mean square error (RMSE) was 9% for the Sacramento River and 15% for the Garonne River for the AirSWOT case using expected observation error. The discharge uncertainty calculated from Manning's equation was 16.2% and 17.1%, respectively. For the SWOT scenario, the RMSE and uncertainty of the discharge estimate for the Sacramento River were 15% and 16.2%, respectively. A method based on the Kalman filter to correct errors of discharge estimates was shown to improve algorithm performance. From the error budget, the primary source of uncertainty was the a priori uncertainty of bathymetry and roughness parameters. Sensitivity to measurement errors was found to be a function of river characteristics. For example, Steeper Garonne River is less sensitive to slope errors than the flatter Sacramento River.

Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons

DTIC Science & Technology

1989-03-25

error term. 1 For this model, the total sum of squares ( SSTO ), defined as n 2 SSTO = E (yi y) i=1 can be partitioned into error and regression sums...of the regression line around the mean value. Mathematically, for the model given by equation A.4, SSTO = SSE + SSR (A.6) A-4 where SSTO is the total...sum of squares (i.e., the variance of the yi’s), SSE is error sum of squares, and SSR is the regression sum of squares. SSTO , SSE, and SSR are given

Performance of statistical models to predict mental health and substance abuse cost.

PubMed

Montez-Rath, Maria; Christiansen, Cindy L; Ettner, Susan L; Loveland, Susan; Rosen, Amy K

2006-10-26

Providers use risk-adjustment systems to help manage healthcare costs. Typically, ordinary least squares (OLS) models on either untransformed or log-transformed cost are used. We examine the predictive ability of several statistical models, demonstrate how model choice depends on the goal for the predictive model, and examine whether building models on samples of the data affects model choice. Our sample consisted of 525,620 Veterans Health Administration patients with mental health (MH) or substance abuse (SA) diagnoses who incurred costs during fiscal year 1999. We tested two models on a transformation of cost: a Log Normal model and a Square-root Normal model, and three generalized linear models on untransformed cost, defined by distributional assumption and link function: Normal with identity link (OLS); Gamma with log link; and Gamma with square-root link. Risk-adjusters included age, sex, and 12 MH/SA categories. To determine the best model among the entire dataset, predictive ability was evaluated using root mean square error (RMSE), mean absolute prediction error (MAPE), and predictive ratios of predicted to observed cost (PR) among deciles of predicted cost, by comparing point estimates and 95% bias-corrected bootstrap confidence intervals. To study the effect of analyzing a random sample of the population on model choice, we re-computed these statistics using random samples beginning with 5,000 patients and ending with the entire sample. The Square-root Normal model had the lowest estimates of the RMSE and MAPE, with bootstrap confidence intervals that were always lower than those for the other models. The Gamma with square-root link was best as measured by the PRs. The choice of best model could vary if smaller samples were used and the Gamma with square-root link model had convergence problems with small samples. Models with square-root transformation or link fit the data best. This function (whether used as transformation or as a link) seems to help deal with the high comorbidity of this population by introducing a form of interaction. The Gamma distribution helps with the long tail of the distribution. However, the Normal distribution is suitable if the correct transformation of the outcome is used.

Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients

NASA Astrophysics Data System (ADS)

Gorgees, HazimMansoor; Mahdi, FatimahAssim

2018-05-01

This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.

A tight Cramér-Rao bound for joint parameter estimation with a pure two-mode squeezed probe

NASA Astrophysics Data System (ADS)

Bradshaw, Mark; Assad, Syed M.; Lam, Ping Koy

2017-08-01

We calculate the Holevo Cramér-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4 exp ⁡ (- 2 r). This equals the sum of the mean squared error obtained from a dual homodyne measurement, indicating that the bound is tight and that the dual homodyne measurement is optimal.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwon, Deukwoo; Little, Mark P.; Miller, Donald L.

Purpose: To determine more accurate regression formulas for estimating peak skin dose (PSD) from reference air kerma (RAK) or kerma-area product (KAP). Methods: After grouping of the data from 21 procedures into 13 clinically similar groups, assessments were made of optimal clustering using the Bayesian information criterion to obtain the optimal linear regressions of (log-transformed) PSD vs RAK, PSD vs KAP, and PSD vs RAK and KAP. Results: Three clusters of clinical groups were optimal in regression of PSD vs RAK, seven clusters of clinical groups were optimal in regression of PSD vs KAP, and six clusters of clinical groupsmore » were optimal in regression of PSD vs RAK and KAP. Prediction of PSD using both RAK and KAP is significantly better than prediction of PSD with either RAK or KAP alone. The regression of PSD vs RAK provided better predictions of PSD than the regression of PSD vs KAP. The partial-pooling (clustered) method yields smaller mean squared errors compared with the complete-pooling method.Conclusion: PSD distributions for interventional radiology procedures are log-normal. Estimates of PSD derived from RAK and KAP jointly are most accurate, followed closely by estimates derived from RAK alone. Estimates of PSD derived from KAP alone are the least accurate. Using a stochastic search approach, it is possible to cluster together certain dissimilar types of procedures to minimize the total error sum of squares.« less

A new mean estimator using auxiliary variables for randomized response models

NASA Astrophysics Data System (ADS)

Ozgul, Nilgun; Cingi, Hulya

2013-10-01

Randomized response models are commonly used in surveys dealing with sensitive questions such as abortion, alcoholism, sexual orientation, drug taking, annual income, tax evasion to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Starting from the pioneering work of Warner [7], many versions of RRM have been developed that can deal with quantitative responses. In this study, new mean estimator is suggested for RRM including quantitative responses. The mean square error is derived and a simulation study is performed to show the efficiency of the proposed estimator to other existing estimators in RRM.

Two-dimensional radial laser scanning for circular marker detection and external mobile robot tracking.

PubMed

Teixidó, Mercè; Pallejà, Tomàs; Font, Davinia; Tresanchez, Marcel; Moreno, Javier; Palacín, Jordi

2012-11-28

This paper presents the use of an external fixed two-dimensional laser scanner to detect cylindrical targets attached to moving devices, such as a mobile robot. This proposal is based on the detection of circular markers in the raw data provided by the laser scanner by applying an algorithm for outlier avoidance and a least-squares circular fitting. Some experiments have been developed to empirically validate the proposal with different cylindrical targets in order to estimate the location and tracking errors achieved, which are generally less than 20 mm in the area covered by the laser sensor. As a result of the validation experiments, several error maps have been obtained in order to give an estimate of the uncertainty of any location computed. This proposal has been validated with a medium-sized mobile robot with an attached cylindrical target (diameter 200 mm). The trajectory of the mobile robot was estimated with an average location error of less than 15 mm, and the real location error in each individual circular fitting was similar to the error estimated with the obtained error maps. The radial area covered in this validation experiment was up to 10 m, a value that depends on the radius of the cylindrical target and the radial density of the distance range points provided by the laser scanner but this area can be increased by combining the information of additional external laser scanners.

June and August median streamflows estimated for ungaged streams in southern Maine

USGS Publications Warehouse

Lombard, Pamela J.

2010-01-01

Methods for estimating June and August median streamflows were developed for ungaged, unregulated streams in southern Maine. The methods apply to streams with drainage areas ranging in size from 0.4 to 74 square miles, with percentage of basin underlain by a sand and gravel aquifer ranging from 0 to 84 percent, and with distance from the centroid of the basin to a Gulf of Maine line paralleling the coast ranging from 14 to 94 miles. Equations were developed with data from 4 long-term continuous-record streamgage stations and 27 partial-record streamgage stations. Estimates of median streamflows at the continuous-record and partial-record stations are presented. A mathematical technique for estimating standard low-flow statistics, such as June and August median streamflows, at partial-record streamgage stations was applied by relating base-flow measurements at these stations to concurrent daily streamflows at nearby long-term (at least 10 years of record) continuous-record streamgage stations (index stations). Weighted least-squares regression analysis (WLS) was used to relate estimates of June and August median streamflows at streamgage stations to basin characteristics at these same stations to develop equations that can be used to estimate June and August median streamflows on ungaged streams. WLS accounts for different periods of record at the gaging stations. Three basin characteristics-drainage area, percentage of basin underlain by a sand and gravel aquifer, and distance from the centroid of the basin to a Gulf of Maine line paralleling the coast-are used in the final regression equation to estimate June and August median streamflows for ungaged streams. The three-variable equation to estimate June median streamflow has an average standard error of prediction from -35 to 54 percent. The three-variable equation to estimate August median streamflow has an average standard error of prediction from -45 to 83 percent. Simpler one-variable equations that use only drainage area to estimate June and August median streamflows were developed for use when less accuracy is acceptable. These equations have average standard errors of prediction from -46 to 87 percent and from -57 to 133 percent, respectively.

Stochastic modeling for time series InSAR: with emphasis on atmospheric effects

NASA Astrophysics Data System (ADS)

Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai

2018-02-01

Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.

Motion estimation accuracy for visible-light/gamma-ray imaging fusion for portable portal monitoring

NASA Astrophysics Data System (ADS)

Karnowski, Thomas P.; Cunningham, Mark F.; Goddard, James S.; Cheriyadat, Anil M.; Hornback, Donald E.; Fabris, Lorenzo; Kerekes, Ryan A.; Ziock, Klaus-Peter; Gee, Timothy F.

2010-01-01

The use of radiation sensors as portal monitors is increasing due to heightened concerns over the smuggling of fissile material. Portable systems that can detect significant quantities of fissile material that might be present in vehicular traffic are of particular interest. We have constructed a prototype, rapid-deployment portal gamma-ray imaging portal monitor that uses machine vision and gamma-ray imaging to monitor multiple lanes of traffic. Vehicles are detected and tracked by using point detection and optical flow methods as implemented in the OpenCV software library. Points are clustered together but imperfections in the detected points and tracks cause errors in the accuracy of the vehicle position estimates. The resulting errors cause a "blurring" effect in the gamma image of the vehicle. To minimize these errors, we have compared a variety of motion estimation techniques including an estimate using the median of the clustered points, a "best-track" filtering algorithm, and a constant velocity motion estimation model. The accuracy of these methods are contrasted and compared to a manually verified ground-truth measurement by quantifying the rootmean- square differences in the times the vehicles cross the gamma-ray image pixel boundaries compared with a groundtruth manual measurement.

a New Method for Calculating the Fractal Dimension of Surface Topography

NASA Astrophysics Data System (ADS)

Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Li, Yan

2015-06-01

A new method termed as three-dimensional root-mean-square (3D-RMS) method, is proposed to calculate the fractal dimension (FD) of machined surfaces. The measure of this method is the root-mean-square value of surface data, and the scale is the side length of square in the projection plane. In order to evaluate the calculation accuracy of the proposed method, the isotropic surfaces with deterministic FD are generated based on the fractional Brownian function and Weierstrass-Mandelbrot (WM) fractal function, and two kinds of anisotropic surfaces are generated by stretching or rotating a WM fractal curve. Their FDs are estimated by the proposed method, as well as differential boxing-counting (DBC) method, triangular prism surface area (TPSA) method and variation method (VM). The results show that the 3D-RMS method performs better than the other methods with a lower relative error for both isotropic and anisotropic surfaces, especially for the surfaces with dimensions higher than 2.5, since the relative error between the estimated value and its theoretical value decreases with theoretical FD. Finally, the electrodeposited surface, end-turning surface and grinding surface are chosen as examples to illustrate the application of 3D-RMS method on the real machined surfaces. This method gives a new way to accurately calculate the FD from the surface topographic data.

A hybrid SVM-FFA method for prediction of monthly mean global solar radiation

NASA Astrophysics Data System (ADS)

Shamshirband, Shahaboddin; Mohammadi, Kasra; Tong, Chong Wen; Zamani, Mazdak; Motamedi, Shervin; Ch, Sudheer

2016-07-01

In this study, a hybrid support vector machine-firefly optimization algorithm (SVM-FFA) model is proposed to estimate monthly mean horizontal global solar radiation (HGSR). The merit of SVM-FFA is assessed statistically by comparing its performance with three previously used approaches. Using each approach and long-term measured HGSR, three models are calibrated by considering different sets of meteorological parameters measured for Bandar Abbass situated in Iran. It is found that the model (3) utilizing the combination of relative sunshine duration, difference between maximum and minimum temperatures, relative humidity, water vapor pressure, average temperature, and extraterrestrial solar radiation shows superior performance based upon all approaches. Moreover, the extraterrestrial radiation is introduced as a significant parameter to accurately estimate the global solar radiation. The survey results reveal that the developed SVM-FFA approach is greatly capable to provide favorable predictions with significantly higher precision than other examined techniques. For the SVM-FFA (3), the statistical indicators of mean absolute percentage error (MAPE), root mean square error (RMSE), relative root mean square error (RRMSE), and coefficient of determination ( R 2) are 3.3252 %, 0.1859 kWh/m2, 3.7350 %, and 0.9737, respectively which according to the RRMSE has an excellent performance. As a more evaluation of SVM-FFA (3), the ratio of estimated to measured values is computed and found that 47 out of 48 months considered as testing data fall between 0.90 and 1.10. Also, by performing a further verification, it is concluded that SVM-FFA (3) offers absolute superiority over the empirical models using relatively similar input parameters. In a nutshell, the hybrid SVM-FFA approach would be considered highly efficient to estimate the HGSR.

Building on crossvalidation for increasing the quality of geostatistical modeling

USGS Publications Warehouse

Olea, R.A.

2012-01-01

The random function is a mathematical model commonly used in the assessment of uncertainty associated with a spatially correlated attribute that has been partially sampled. There are multiple algorithms for modeling such random functions, all sharing the requirement of specifying various parameters that have critical influence on the results. The importance of finding ways to compare the methods and setting parameters to obtain results that better model uncertainty has increased as these algorithms have grown in number and complexity. Crossvalidation has been used in spatial statistics, mostly in kriging, for the analysis of mean square errors. An appeal of this approach is its ability to work with the same empirical sample available for running the algorithms. This paper goes beyond checking estimates by formulating a function sensitive to conditional bias. Under ideal conditions, such function turns into a straight line, which can be used as a reference for preparing measures of performance. Applied to kriging, deviations from the ideal line provide sensitivity to the semivariogram lacking in crossvalidation of kriging errors and are more sensitive to conditional bias than analyses of errors. In terms of stochastic simulation, in addition to finding better parameters, the deviations allow comparison of the realizations resulting from the applications of different methods. Examples show improvements of about 30% in the deviations and approximately 10% in the square root of mean square errors between reasonable starting modelling and the solutions according to the new criteria. ?? 2011 US Government.

A selective-update affine projection algorithm with selective input vectors

NASA Astrophysics Data System (ADS)

Kong, NamWoong; Shin, JaeWook; Park, PooGyeon

2011-10-01

This paper proposes an affine projection algorithm (APA) with selective input vectors, which based on the concept of selective-update in order to reduce estimation errors and computations. The algorithm consists of two procedures: input- vector-selection and state-decision. The input-vector-selection procedure determines the number of input vectors by checking with mean square error (MSE) whether the input vectors have enough information for update. The state-decision procedure determines the current state of the adaptive filter by using the state-decision criterion. As the adaptive filter is in transient state, the algorithm updates the filter coefficients with the selected input vectors. On the other hand, as soon as the adaptive filter reaches the steady state, the update procedure is not performed. Through these two procedures, the proposed algorithm achieves small steady-state estimation errors, low computational complexity and low update complexity for colored input signals.

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

PubMed

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Age estimation based on pulp chamber volume of first molars from cone-beam computed tomography images.

PubMed

Ge, Zhi-pu; Ma, Ruo-han; Li, Gang; Zhang, Ji-zong; Ma, Xu-chen

2015-08-01

To establish a method that can be used for human age estimation on the basis of pulp chamber volume of first molars and to identify whether the method is good enough for age estimation in real human cases. CBCT images of 373 maxillary first molars and 372 mandibular first molars were collected to establish the mathematical model from 190 female and 213 male patients whose age between 12 and 69 years old. The inclusion criteria of the first molars were: no caries, no excessive tooth wear, no dental restorations, no artifacts due to metal restorative materials present in adjacent teeth, and no pulpal calcification. All the CBCT images were acquired with a CBCT unit NewTom VG (Quantitative Radiology, Verona, Italy) and reconstructed with a voxel-size of 0.15mm. The images were subsequently exported as DICOM data sets and imported into an open source 3D image semi-automatic segmenting and voxel-counting software ITK-SNAP 2.4 for the calculation of pulp chamber volumes. A logarithmic regression analysis was conducted with age as dependent variable and pulp chamber volume as independent variables to establish a mathematical model for the human age estimation. To identify the precision and accuracy of the model for human age estimation, another 104 maxillary first molars and 103 mandibular first molars from 55 female and 57 male patients whose age between 12 and 67 years old were collected, too. Mean absolute error and root mean square error between the actual age and estimated age were used to determine the precision and accuracy of the mathematical model. The study was approved by the Institutional Review Board of Peking University School and Hospital of Stomatology. A mathematical model was suggested for: AGE=117.691-26.442×ln (pulp chamber volume). The regression was statistically significant (p=0.000<0.01). The coefficient of determination (R(2)) was 0.564. There is a mean absolute error of 8.122 and root mean square error of 5.603 between the actual age and estimated age for all the tested teeth. The pulp chamber volume of first molar is a useful index for the estimation of human age with reasonable precision and accuracy. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference.

PubMed

Breda, F C; Albuquerque, L G; Euclydes, R F; Bignardi, A B; Baldi, F; Torres, R A; Barbosa, L; Tonhati, H

2010-02-01

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Comparison of ArcGIS and SAS Geostatistical Analyst to Estimate Population-Weighted Monthly Temperature for US Counties

PubMed Central

Xiaopeng, QI; Liang, WEI; BARKER, Laurie; LEKIACHVILI, Akaki; Xingyou, ZHANG

2015-01-01

Temperature changes are known to have significant impacts on human health. Accurate estimates of population-weighted average monthly air temperature for US counties are needed to evaluate temperature’s association with health behaviours and disease, which are sampled or reported at the county level and measured on a monthly—or 30-day—basis. Most reported temperature estimates were calculated using ArcGIS, relatively few used SAS. We compared the performance of geostatistical models to estimate population-weighted average temperature in each month for counties in 48 states using ArcGIS v9.3 and SAS v 9.2 on a CITGO platform. Monthly average temperature for Jan-Dec 2007 and elevation from 5435 weather stations were used to estimate the temperature at county population centroids. County estimates were produced with elevation as a covariate. Performance of models was assessed by comparing adjusted R2, mean squared error, root mean squared error, and processing time. Prediction accuracy for split validation was above 90% for 11 months in ArcGIS and all 12 months in SAS. Cokriging in SAS achieved higher prediction accuracy and lower estimation bias as compared to cokriging in ArcGIS. County-level estimates produced by both packages were positively correlated (adjusted R2 range=0.95 to 0.99); accuracy and precision improved with elevation as a covariate. Both methods from ArcGIS and SAS are reliable for U.S. county-level temperature estimates; However, ArcGIS’s merits in spatial data pre-processing and processing time may be important considerations for software selection, especially for multi-year or multi-state projects. PMID:26167169

Quantifying Parkinson's disease finger-tapping severity by extracting and synthesizing finger motion properties.

PubMed

Sano, Yuko; Kandori, Akihiko; Shima, Keisuke; Yamaguchi, Yuki; Tsuji, Toshio; Noda, Masafumi; Higashikawa, Fumiko; Yokoe, Masaru; Sakoda, Saburo

2016-06-01

We propose a novel index of Parkinson's disease (PD) finger-tapping severity, called "PDFTsi," for quantifying the severity of symptoms related to the finger tapping of PD patients with high accuracy. To validate the efficacy of PDFTsi, the finger-tapping movements of normal controls and PD patients were measured by using magnetic sensors, and 21 characteristics were extracted from the finger-tapping waveforms. To distinguish motor deterioration due to PD from that due to aging, the aging effect on finger tapping was removed from these characteristics. Principal component analysis (PCA) was applied to the age-normalized characteristics, and principal components that represented the motion properties of finger tapping were calculated. Multiple linear regression (MLR) with stepwise variable selection was applied to the principal components, and PDFTsi was calculated. The calculated PDFTsi indicates that PDFTsi has a high estimation ability, namely a mean square error of 0.45. The estimation ability of PDFTsi is higher than that of the alternative method, MLR with stepwise regression selection without PCA, namely a mean square error of 1.30. This result suggests that PDFTsi can quantify PD finger-tapping severity accurately. Furthermore, the result of interpreting a model for calculating PDFTsi indicated that motion wideness and rhythm disorder are important for estimating PD finger-tapping severity.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Documentation of a spreadsheet for time-series analysis and drawdown estimation

USGS Publications Warehouse

Halford, Keith J.

2006-01-01

Drawdowns during aquifer tests can be obscured by barometric pressure changes, earth tides, regional pumping, and recharge events in the water-level record. These stresses can create water-level fluctuations that should be removed from observed water levels prior to estimating drawdowns. Simple models have been developed for estimating unpumped water levels during aquifer tests that are referred to as synthetic water levels. These models sum multiple time series such as barometric pressure, tidal potential, and background water levels to simulate non-pumping water levels. The amplitude and phase of each time series are adjusted so that synthetic water levels match measured water levels during periods unaffected by an aquifer test. Differences between synthetic and measured water levels are minimized with a sum-of-squares objective function. Root-mean-square errors during fitting and prediction periods were compared multiple times at four geographically diverse sites. Prediction error equaled fitting error when fitting periods were greater than or equal to four times prediction periods. The proposed drawdown estimation approach has been implemented in a spreadsheet application. Measured time series are independent so that collection frequencies can differ and sampling times can be asynchronous. Time series can be viewed selectively and magnified easily. Fitting and prediction periods can be defined graphically or entered directly. Synthetic water levels for each observation well are created with earth tides, measured time series, moving averages of time series, and differences between measured and moving averages of time series. Selected series and fitting parameters for synthetic water levels are stored and drawdowns are estimated for prediction periods. Drawdowns can be viewed independently and adjusted visually if an anomaly skews initial drawdowns away from 0. The number of observations in a drawdown time series can be reduced by averaging across user-defined periods. Raw or reduced drawdown estimates can be copied from the spreadsheet application or written to tab-delimited ASCII files.

Linking Field and Satellite Observations to Reveal Differences in Single vs. Double-Cropped Soybean Yields in Central Brazil

NASA Astrophysics Data System (ADS)

Jeffries, G. R.; Cohn, A.

2016-12-01

Soy-corn double cropping (DC) has been widely adopted in Central Brazil alongside single cropped (SC) soybean production. DC involves different cropping calendars, soy varieties, and may be associated with different crop yield patterns and volatility than SC. Study of the performance of the region's agriculture in a changing climate depends on tracking differences in the productivity of SC vs. DC, but has been limited by crop yield data that conflate the two systems. We predicted SC and DC yields across Central Brazil, drawing on field observations and remotely sensed data. We first modeled field yield estimates as a function of remotely sensed DC status and vegetation index (VI) metrics, and other management and biophysical factors. We then used the statistical model estimated to predict SC and DC soybean yields at each 500 m2 grid cell of Central Brazil for harvest years 2001 - 2015. The yield estimation model was constructed using 1) a repeated cross-sectional survey of soybean yields and management factors for years 2007-2015, 2) a custom agricultural land cover classification dataset which assimilates earlier datasets for the region, and 3) 500m 8-day MODIS image composites used to calculate the wide dynamic range vegetation index (WDRVI) and derivative metrics such as area under the curve for WDRVI values in critical crop development periods. A statistical yield estimation model which primarily entails WDRVI metrics, DC status, and spatial fixed effects was developed on a subset of the yield dataset. Model validation was conducted by predicting previously withheld yield records, and then assessing error and goodness-of-fit for predicted values with metrics including root mean squared error (RMSE), mean squared error (MSE), and R2. We found a statistical yield estimation model which incorporates WDRVI and DC status to be way to estimate crop yields over the region. Statistical properties of the resulting gridded yield dataset may be valuable for understanding linkages between crop yields, farm management factors, and climate.

Development of a transformation model to derive general population-based utility: Mapping the pruritus-visual analog scale (VAS) to the EQ-5D utility.

PubMed

Park, Sun-Young; Park, Eun-Ja; Suh, Hae Sun; Ha, Dongmun; Lee, Eui-Kyung

2017-08-01

Although nonpreference-based disease-specific measures are widely used in clinical studies, they cannot generate utilities for economic evaluation. A solution to this problem is to estimate utilities from disease-specific instruments using the mapping function. This study aimed to develop a transformation model for mapping the pruritus-visual analog scale (VAS) to the EuroQol 5-Dimension 3-Level (EQ-5D-3L) utility index in pruritus. A cross-sectional survey was conducted with a sample (n = 268) drawn from the general population of South Korea. Data were randomly divided into 2 groups, one for estimating and the other for validating mapping models. To select the best model, we developed and compared 3 separate models using demographic information and the pruritus-VAS as independent variables. The predictive performance was assessed using the mean absolute deviation and root mean square error in a separate dataset. Among the 3 models, model 2 using age, age squared, sex, and the pruritus-VAS as independent variables had the best performance based on the goodness of fit and model simplicity, with a log likelihood of 187.13. The 3 models had similar precision errors based on mean absolute deviation and root mean square error in the validation dataset. No statistically significant difference was observed between the mean observed and predicted values in all models. In conclusion, model 2 was chosen as the preferred mapping model. Outcomes measured as the pruritus-VAS can be transformed into the EQ-5D-3L utility index using this mapping model, which makes an economic evaluation possible when only pruritus-VAS data are available. © 2017 John Wiley & Sons, Ltd.

The GEOS Ozone Data Assimilation System: Specification of Error Statistics

NASA Technical Reports Server (NTRS)

Stajner, Ivanka; Riishojgaard, Lars Peter; Rood, Richard B.

2000-01-01

A global three-dimensional ozone data assimilation system has been developed at the Data Assimilation Office of the NASA/Goddard Space Flight Center. The Total Ozone Mapping Spectrometer (TOMS) total ozone and the Solar Backscatter Ultraviolet (SBUV) or (SBUV/2) partial ozone profile observations are assimilated. The assimilation, into an off-line ozone transport model, is done using the global Physical-space Statistical Analysis Scheme (PSAS). This system became operational in December 1999. A detailed description of the statistical analysis scheme, and in particular, the forecast and observation error covariance models is given. A new global anisotropic horizontal forecast error correlation model accounts for a varying distribution of observations with latitude. Correlations are largest in the zonal direction in the tropics where data is sparse. Forecast error variance model is proportional to the ozone field. The forecast error covariance parameters were determined by maximum likelihood estimation. The error covariance models are validated using x squared statistics. The analyzed ozone fields in the winter 1992 are validated against independent observations from ozone sondes and HALOE. There is better than 10% agreement between mean Halogen Occultation Experiment (HALOE) and analysis fields between 70 and 0.2 hPa. The global root-mean-square (RMS) difference between TOMS observed and forecast values is less than 4%. The global RMS difference between SBUV observed and analyzed ozone between 50 and 3 hPa is less than 15%.

Estimation of sensible and latent heat flux from natural sparse vegetation surfaces using surface renewal

NASA Astrophysics Data System (ADS)

Zapata, N.; Martínez-Cob, A.

2001-12-01

This paper reports a study undertaken to evaluate the feasibility of the surface renewal method to accurately estimate long-term evaporation from the playa and margins of an endorreic salty lagoon (Gallocanta lagoon, Spain) under semiarid conditions. High-frequency temperature readings were taken for two time lags ( r) and three measurement heights ( z) in order to get surface renewal sensible heat flux ( HSR) values. These values were compared against eddy covariance sensible heat flux ( HEC) values for a calibration period (25-30 July 2000). Error analysis statistics (index of agreement, IA; root mean square error, RMSE; and systematic mean square error, MSEs) showed that the agreement between HSR and HEC improved as measurement height decreased and time lag increased. Calibration factors α were obtained for all analyzed cases. The best results were obtained for the z=0.9 m ( r=0.75 s) case for which α=1.0 was observed. In this case, uncertainty was about 10% in terms of relative error ( RE). Latent heat flux values were obtained by solving the energy balance equation for both the surface renewal ( LESR) and the eddy covariance ( LEEC) methods, using HSR and HEC, respectively, and measurements of net radiation and soil heat flux. For the calibration period, error analysis statistics for LESR were quite similar to those for HSR, although errors were mostly at random. LESR uncertainty was less than 9%. Calibration factors were applied for a validation data subset (30 July-4 August 2000) for which meteorological conditions were somewhat different (higher temperatures and wind speed and lower solar and net radiation). Error analysis statistics for both HSR and LESR were quite good for all cases showing the goodness of the calibration factors. Nevertheless, the results obtained for the z=0.9 m ( r=0.75 s) case were still the best ones.

Estimation of color filter array data from JPEG images for improved demosaicking

NASA Astrophysics Data System (ADS)

Feng, Wei; Reeves, Stanley J.

2006-02-01

On-camera demosaicking algorithms are necessarily simple and therefore do not yield the best possible images. However, off-camera demosaicking algorithms face the additional challenge that the data has been compressed and therefore corrupted by quantization noise. We propose a method to estimate the original color filter array (CFA) data from JPEG-compressed images so that more sophisticated (and better) demosaicking schemes can be applied to get higher-quality images. The JPEG image formation process, including simple demosaicking, color space transformation, chrominance channel decimation and DCT, is modeled as a series of matrix operations followed by quantization on the CFA data, which is estimated by least squares. An iterative method is used to conserve memory and speed computation. Our experiments show that the mean square error (MSE) with respect to the original CFA data is reduced significantly using our algorithm, compared to that of unprocessed JPEG and deblocked JPEG data.

Triple collocation-based estimation of spatially correlated observation error covariance in remote sensing soil moisture data assimilation

NASA Astrophysics Data System (ADS)

Wu, Kai; Shu, Hong; Nie, Lei; Jiao, Zhenhang

2018-01-01

Spatially correlated errors are typically ignored in data assimilation, thus degenerating the observation error covariance R to a diagonal matrix. We argue that a nondiagonal R carries more observation information making assimilation results more accurate. A method, denoted TC_Cov, was proposed for soil moisture data assimilation to estimate spatially correlated observation error covariance based on triple collocation (TC). Assimilation experiments were carried out to test the performance of TC_Cov. AMSR-E soil moisture was assimilated with a diagonal R matrix computed using the TC and assimilated using a nondiagonal R matrix, as estimated by proposed TC_Cov. The ensemble Kalman filter was considered as the assimilation method. Our assimilation results were validated against climate change initiative data and ground-based soil moisture measurements using the Pearson correlation coefficient and unbiased root mean square difference metrics. These experiments confirmed that deterioration of diagonal R assimilation results occurred when model simulation is more accurate than observation data. Furthermore, nondiagonal R achieved higher correlation coefficient and lower ubRMSD values over diagonal R in experiments and demonstrated the effectiveness of TC_Cov to estimate richly structuralized R in data assimilation. In sum, compared with diagonal R, nondiagonal R may relieve the detrimental effects of assimilation when simulated model results outperform observation data.

Efficient estimation of Pareto model: Some modified percentile estimators.

PubMed

Bhatti, Sajjad Haider; Hussain, Shahzad; Ahmad, Tanvir; Aslam, Muhammad; Aftab, Muhammad; Raza, Muhammad Ali

2018-01-01

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

Prediction of Soil Organic Carbon at the European Scale by Visible and Near InfraRed Reflectance Spectroscopy.

PubMed

Stevens, Antoine; Nocita, Marco; Tóth, Gergely; Montanarella, Luca; van Wesemael, Bas

2013-01-01

Soil organic carbon is a key soil property related to soil fertility, aggregate stability and the exchange of CO2 with the atmosphere. Existing soil maps and inventories can rarely be used to monitor the state and evolution in soil organic carbon content due to their poor spatial resolution, lack of consistency and high updating costs. Visible and Near Infrared diffuse reflectance spectroscopy is an alternative method to provide cheap and high-density soil data. However, there are still some uncertainties on its capacity to produce reliable predictions for areas characterized by large soil diversity. Using a large-scale EU soil survey of about 20,000 samples and covering 23 countries, we assessed the performance of reflectance spectroscopy for the prediction of soil organic carbon content. The best calibrations achieved a root mean square error ranging from 4 to 15 g C kg(-1) for mineral soils and a root mean square error of 50 g C kg(-1) for organic soil materials. Model errors are shown to be related to the levels of soil organic carbon and variations in other soil properties such as sand and clay content. Although errors are ∼5 times larger than the reproducibility error of the laboratory method, reflectance spectroscopy provides unbiased predictions of the soil organic carbon content. Such estimates could be used for assessing the mean soil organic carbon content of large geographical entities or countries. This study is a first step towards providing uniform continental-scale spectroscopic estimations of soil organic carbon, meeting an increasing demand for information on the state of the soil that can be used in biogeochemical models and the monitoring of soil degradation.

A passive microwave technique for estimating rainfall and vertical structure information from space. Part 2: Applications to SSM/I data

NASA Technical Reports Server (NTRS)

Kummerow, Christian; Giglio, Louis

1994-01-01

A multi channel physical approach for retrieving rainfall and its vertical structure from Special Sensor Microwave/Imager (SSM/I) observations is examined. While a companion paper was devoted exclusively to the description of the algorithm, its strengths, and its limitations, the main focus of this paper is to report on the results, applicability, and expected accuraciesfrom this algorithm. Some examples are given that compare retrieved results with ground-based radar data from different geographical regions to illustrate the performance and utility of the algorithm under distinct rainfall conditions. More quantitative validation is accomplished using two months of radar data from Darwin, Australia, and the radar network over Japan. Instantaneous comparisons at Darwin indicate that root-mean-square errors for 1.25 deg areas over water are 0.09 mm/h compared to the mean rainfall value of 0.224 mm/h while the correlation exceeds 0.9. Similar results are obtained over the Japanese validation site with rms errors of 0.615 mm/h compared to the mean of 0.0880 mm/h and a correlation of 0.9. Results are less encouraging over land with root-mean-square errors somewhat larger than the mean rain rates and correlations of only 0.71 and 0.62 for Darwin and Japan, respectively. These validation studies are further used in combination with the theoretical treatment of expected accuracies developed in the companion paper to define error estimates on a broader scale than individual radar sites from which the errors may be analyzed. Comparisons with simpler techniques that are based on either emission or scattering measurements are used to illustrate the fact that the current algorithm, while better correlated with the emission methods over water, cannot be reduced to either of these simpler methods.

Prediction of Soil Organic Carbon at the European Scale by Visible and Near InfraRed Reflectance Spectroscopy

PubMed Central

Stevens, Antoine; Nocita, Marco; Tóth, Gergely; Montanarella, Luca; van Wesemael, Bas

2013-01-01

Soil organic carbon is a key soil property related to soil fertility, aggregate stability and the exchange of CO2 with the atmosphere. Existing soil maps and inventories can rarely be used to monitor the state and evolution in soil organic carbon content due to their poor spatial resolution, lack of consistency and high updating costs. Visible and Near Infrared diffuse reflectance spectroscopy is an alternative method to provide cheap and high-density soil data. However, there are still some uncertainties on its capacity to produce reliable predictions for areas characterized by large soil diversity. Using a large-scale EU soil survey of about 20,000 samples and covering 23 countries, we assessed the performance of reflectance spectroscopy for the prediction of soil organic carbon content. The best calibrations achieved a root mean square error ranging from 4 to 15 g C kg−1 for mineral soils and a root mean square error of 50 g C kg−1 for organic soil materials. Model errors are shown to be related to the levels of soil organic carbon and variations in other soil properties such as sand and clay content. Although errors are ∼5 times larger than the reproducibility error of the laboratory method, reflectance spectroscopy provides unbiased predictions of the soil organic carbon content. Such estimates could be used for assessing the mean soil organic carbon content of large geographical entities or countries. This study is a first step towards providing uniform continental-scale spectroscopic estimations of soil organic carbon, meeting an increasing demand for information on the state of the soil that can be used in biogeochemical models and the monitoring of soil degradation. PMID:23840459

A deep proper motion catalog within the Sloan digital sky survey footprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munn, Jeffrey A.; Harris, Hugh C.; Tilleman, Trudy M.

2014-12-01

A new proper motion catalog is presented, combining the Sloan Digital Sky Survey (SDSS) with second epoch observations in the r band within a portion of the SDSS imaging footprint. The new observations were obtained with the 90prime camera on the Steward Observatory Bok 90 inch telescope, and the Array Camera on the U.S. Naval Observatory, Flagstaff Station, 1.3 m telescope. The catalog covers 1098 square degrees to r = 22.0, an additional 1521 square degrees to r = 20.9, plus a further 488 square degrees of lesser quality data. Statistical errors in the proper motions range from 5 masmore » year{sup −1} at the bright end to 15 mas year{sup −1} at the faint end, for a typical epoch difference of six years. Systematic errors are estimated to be roughly 1 mas year{sup −1} for the Array Camera data, and as much as 2–4 mas year{sup −1} for the 90prime data (though typically less). The catalog also includes a second epoch of r band photometry.« less

Acidity measurement of iron ore powders using laser-induced breakdown spectroscopy with partial least squares regression.

PubMed

Hao, Z Q; Li, C M; Shen, M; Yang, X Y; Li, K H; Guo, L B; Li, X Y; Lu, Y F; Zeng, X Y

2015-03-23

Laser-induced breakdown spectroscopy (LIBS) with partial least squares regression (PLSR) has been applied to measuring the acidity of iron ore, which can be defined by the concentrations of oxides: CaO, MgO, Al₂O₃, and SiO₂. With the conventional internal standard calibration, it is difficult to establish the calibration curves of CaO, MgO, Al₂O₃, and SiO₂ in iron ore due to the serious matrix effects. PLSR is effective to address this problem due to its excellent performance in compensating the matrix effects. In this work, fifty samples were used to construct the PLSR calibration models for the above-mentioned oxides. These calibration models were validated by the 10-fold cross-validation method with the minimum root-mean-square errors (RMSE). Another ten samples were used as a test set. The acidities were calculated according to the estimated concentrations of CaO, MgO, Al₂O₃, and SiO₂ using the PLSR models. The average relative error (ARE) and RMSE of the acidity achieved 3.65% and 0.0048, respectively, for the test samples.

More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares.

PubMed

Yuan, Ke-Hai; Jiang, Ge; Cheng, Ying

2017-11-01

Data in psychology are often collected using Likert-type scales, and it has been shown that factor analysis of Likert-type data is better performed on the polychoric correlation matrix than on the product-moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real-data example indicates that estimates by ridge GLS are 9-20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich-type standard errors following the ridge GLS methods also perform reasonably well. © 2017 The British Psychological Society.

Phase and Pupil Amplitude Recovery for JWST Space-Optics Control

NASA Technical Reports Server (NTRS)

Dean, B. H.; Zielinski, T. P.; Smith, J. S.; Bolcar, M. R.; Aronstein, D. L.; Fienup, J. R.

2010-01-01

This slide presentation reviews the phase and pupil amplitude recovery for the James Webb Space Telescope (JWST) Near Infrared Camera (NIRCam). It includes views of the Integrated Science Instrument Module (ISIM), the NIRCam, examples of Phase Retrieval Data, Ghost Irradiance, Pupil Amplitude Estimation, Amplitude Retrieval, Initial Plate Scale Estimation using the Modulation Transfer Function (MTF), Pupil Amplitude Estimation vs lambda, Pupil Amplitude Estimation vs. number of Images, Pupil Amplitude Estimation vs Rotation (clocking), and Typical Phase Retrieval Results Also included is information about the phase retrieval approach, Non-Linear Optimization (NLO) Optimized Diversity Functions, and Least Square Error vs. Starting Pupil Amplitude.

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems.

PubMed

Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng

2018-05-31

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A Generally Robust Approach for Testing Hypotheses and Setting Confidence Intervals for Effect Sizes

ERIC Educational Resources Information Center

Keselman, H. J.; Algina, James; Lix, Lisa M.; Wilcox, Rand R.; Deering, Kathleen N.

2008-01-01

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of…

An Investigation of the Sample Performance of Two Nonnormality Corrections for RMSEA

ERIC Educational Resources Information Center

Brosseau-Liard, Patricia E.; Savalei, Victoria; Li, Libo

2012-01-01

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

Annual updating of plantation inventory estimates using hybrid models

Treesearch

Peter Snowdon

2000-01-01

Data for Pinus radiata D. Don grown in the Australian Capital Territory (ACT) are used to show that annual indices of growth potential can be successfully incorporated into Schumacher projection models of stand basal area growth. Significant reductions in the error mean squares of the models can be obtained by including an annual growth index derived...

Estimation of distributional parameters for censored trace level water quality data: 1. Estimation techniques

USGS Publications Warehouse

Gilliom, Robert J.; Helsel, Dennis R.

1986-01-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.

Estimation of distributional parameters for censored trace level water quality data. 1. Estimation Techniques

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilliom, R.J.; Helsel, D.R.

1986-02-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensoredmore » observations, for determining the best performing parameter estimation method for any particular data det. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.« less

Optimum data weighting and error calibration for estimation of gravitational parameters

NASA Technical Reports Server (NTRS)

Lerch, F. J.

1989-01-01

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Mapping CHU9D Utility Scores from the PedsQLTM 4.0 SF-15.

PubMed

Mpundu-Kaambwa, Christine; Chen, Gang; Russo, Remo; Stevens, Katherine; Petersen, Karin Dam; Ratcliffe, Julie

2017-04-01

The Pediatric Quality of Life Inventory™ 4.0 Short Form 15 Generic Core Scales (hereafter the PedsQL) and the Child Health Utility-9 Dimensions (CHU9D) are two generic instruments designed to measure health-related quality of life in children and adolescents in the general population and paediatric patient groups living with specific health conditions. Although the PedsQL is widely used among paediatric patient populations, presently it is not possible to directly use the scores from the instrument to calculate quality-adjusted life-years (QALYs) for application in economic evaluation because it produces summary scores which are not preference-based. This paper examines different econometric mapping techniques for estimating CHU9D utility scores from the PedsQL for the purpose of calculating QALYs for cost-utility analysis. The PedsQL and the CHU9D were completed by a community sample of 755 Australian adolescents aged 15-17 years. Seven regression models were estimated: ordinary least squares estimator, generalised linear model, robust MM estimator, multivariate factorial polynomial estimator, beta-binomial estimator, finite mixture model and multinomial logistic model. The mean absolute error (MAE) and the mean squared error (MSE) were used to assess predictive ability of the models. The MM estimator with stepwise-selected PedsQL dimension scores as explanatory variables had the best predictive accuracy using MAE and the equivalent beta-binomial model had the best predictive accuracy using MSE. Our mapping algorithm facilitates the estimation of health-state utilities for use within economic evaluations where only PedsQL data is available and is suitable for use in community-based adolescents aged 15-17 years. Applicability of the algorithm in younger populations should be assessed in further research.

Direct Regularized Estimation of Retinal Vascular Oxygen Tension Based on an Experimental Model

PubMed Central

Yildirim, Isa; Ansari, Rashid; Yetik, I. Samil; Shahidi, Mahnaz

2014-01-01

Phosphorescence lifetime imaging is commonly used to generate oxygen tension maps of retinal blood vessels by classical least squares (LS) estimation method. A spatial regularization method was later proposed and provided improved results. However, both methods obtain oxygen tension values from the estimates of intermediate variables, and do not yield an optimum estimate of oxygen tension values, due to their nonlinear dependence on the ratio of intermediate variables. In this paper, we provide an improved solution by devising a regularized direct least squares (RDLS) method that exploits available knowledge in studies that provide models of oxygen tension in retinal arteries and veins, unlike the earlier regularized LS approach where knowledge about intermediate variables is limited. The performance of the proposed RDLS method is evaluated by investigating and comparing the bias, variance, oxygen tension maps, 1-D profiles of arterial oxygen tension, and mean absolute error with those of earlier methods, and its superior performance both quantitatively and qualitatively is demonstrated. PMID:23732915

Analysis of the low-flow characteristics of streams in Louisiana

USGS Publications Warehouse

Lee, Fred N.

1985-01-01

The U.S. Geological Survey, in cooperation with the Louisiana Department of Transportation and Development, Office of Public Works, used geologic maps, soils maps, precipitation data, and low-flow data to define four hydrographic regions in Louisiana having distinct low-flow characteristics. Equations were derived, using regression analyses, to estimate the 7Q2, 7Q10, and 7Q20 flow rates for basically unaltered stream basins smaller than 525 square miles. Independent variables in the equations include drainage area (square miles), mean annual precipitation index (inches), and main channel slope (feet per mile). Average standard errors of regression ranged from +44 to +61 percent. Graphs are given for estimating the 7Q2, 7Q10, and 7Q20 for stream basins for which the drainage area of the most downstream data-collection site is larger than 525 square miles. Detailed examples are given in this report for the use of the equations and graphs.

Reduced-rank technique for joint channel estimation in TD-SCDMA systems

NASA Astrophysics Data System (ADS)

Kamil Marzook, Ali; Ismail, Alyani; Mohd Ali, Borhanuddin; Sali, Adawati; Khatun, Sabira

2013-02-01

In time division-synchronous code division multiple access systems, increasing the system capacity by exploiting the inserting of the largest number of users in one time slot (TS) requires adding more estimation processes to estimate the joint channel matrix for the whole system. The increase in the number of channel parameters due the increase in the number of users in one TS directly affects the precision of the estimator's performance. This article presents a novel channel estimation with low complexity, which relies on reducing the rank order of the total channel matrix H. The proposed method exploits the rank deficiency of H to reduce the number of parameters that characterise this matrix. The adopted reduced-rank technique is based on truncated singular value decomposition algorithm. The algorithms for reduced-rank joint channel estimation (JCE) are derived and compared against traditional full-rank JCEs: least squares (LS) or Steiner and enhanced (LS or MMSE) algorithms. Simulation results of the normalised mean square error showed the superiority of reduced-rank estimators. In addition, the channel impulse responses founded by reduced-rank estimator for all active users offers considerable performance improvement over the conventional estimator along the channel window length.

On the Mean Squared Error of Nonparametric Quantile Estimators under Random Right-Censorship.

DTIC Science & Technology

1986-09-01

SECURITY CI.ASSIFICATION lb. RESTRICTIVE MARKINGS UNCLASSIFIED 2a, SECURITY CLASSIFICATION AUTHORITY 3 . OISTRIBUTIONIAVAILASIL.ITY OF REPORT P16e 2b...UNCLASSIPIEO/UNLIMITEO 3 SAME AS RPT". 0 OTIC USERS 1 UNCLASSIFIED p." " 22. NAME OP RESPONSIBLE INOIVIOUAL 22b. TELEPHONE NUMBER 22c. OFFICE SYMBOL...in Section 3 , and the result for the kernel estimator Qn is derived in Section 4. It should be k. mentioned that the order statistic methods used by

A Gompertzian model with random effects to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

2015-05-15

In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

An analysis of the least-squares problem for the DSN systematic pointing error model

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

Orbit Determination of KOMPSAT-1 and Cryosat-2 Satellites Using Optical Wide-field Patrol Network (OWL-Net) Data with Batch Least Squares Filter

NASA Astrophysics Data System (ADS)

Lee, Eunji; Park, Sang-Young; Shin, Bumjoon; Cho, Sungki; Choi, Eun-Jung; Jo, Junghyun; Park, Jang-Hyun

2017-03-01

The optical wide-field patrol network (OWL-Net) is a Korean optical surveillance system that tracks and monitors domestic satellites. In this study, a batch least squares algorithm was developed for optical measurements and verified by Monte Carlo simulation and covariance analysis. Potential error sources of OWL-Net, such as noise, bias, and clock errors, were analyzed. There is a linear relation between the estimation accuracy and the noise level, and the accuracy significantly depends on the declination bias. In addition, the time-tagging error significantly degrades the observation accuracy, while the time-synchronization offset corresponds to the orbital motion. The Cartesian state vector and measurement bias were determined using the OWL-Net tracking data of the KOMPSAT-1 and Cryosat-2 satellites. The comparison with known orbital information based on two-line elements (TLE) and the consolidated prediction format (CPF) shows that the orbit determination accuracy is similar to that of TLE. Furthermore, the precision and accuracy of OWL-Net observation data were determined to be tens of arcsec and sub-degree level, respectively.

Estimation of distributional parameters for censored trace-level water-quality data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilliom, R.J.; Helsel, D.R.

1984-01-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water-sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations,more » for determining the best-performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least-squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification. 6 figs., 6 tabs.« less

Estimation of Soil Moisture Profile using a Simple Hydrology Model and Passive Microwave Remote Sensing

NASA Technical Reports Server (NTRS)

Soman, Vishwas V.; Crosson, William L.; Laymon, Charles; Tsegaye, Teferi

1998-01-01

Soil moisture is an important component of analysis in many Earth science disciplines. Soil moisture information can be obtained either by using microwave remote sensing or by using a hydrologic model. In this study, we combined these two approaches to increase the accuracy of profile soil moisture estimation. A hydrologic model was used to analyze the errors in the estimation of soil moisture using the data collected during Huntsville '96 microwave remote sensing experiment in Huntsville, Alabama. Root mean square errors (RMSE) in soil moisture estimation increase by 22% with increase in the model input interval from 6 hr to 12 hr for the grass-covered plot. RMSEs were reduced for given model time step by 20-50% when model soil moisture estimates were updated using remotely-sensed data. This methodology has a potential to be employed in soil moisture estimation using rainfall data collected by a space-borne sensor, such as the Tropical Rainfall Measuring Mission (TRMM) satellite, if remotely-sensed data are available to update the model estimates.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Bandwidth efficient channel estimation method for airborne hyperspectral data transmission in sparse doubly selective communication channels

NASA Astrophysics Data System (ADS)

Vahidi, Vahid; Saberinia, Ebrahim; Regentova, Emma E.

2017-10-01

A channel estimation (CE) method based on compressed sensing (CS) is proposed to estimate the sparse and doubly selective (DS) channel for hyperspectral image transmission from unmanned aircraft vehicles to ground stations. The proposed method contains three steps: (1) the priori estimate of the channel by orthogonal matching pursuit (OMP), (2) calculation of the linear minimum mean square error (LMMSE) estimate of the received pilots given the estimated channel, and (3) estimate of the complex amplitudes and Doppler shifts of the channel using the enhanced received pilot data applying a second round of a CS algorithm. The proposed method is named DS-LMMSE-OMP, and its performance is evaluated by simulating transmission of AVIRIS hyperspectral data via the communication channel and assessing their fidelity for the automated analysis after demodulation. The performance of the DS-LMMSE-OMP approach is compared with that of two other state-of-the-art CE methods. The simulation results exhibit up to 8-dB figure of merit in the bit error rate and 50% improvement in the hyperspectral image classification accuracy.

A technique for estimating ground-water levels at sites in Rhode Island from observation-well data

USGS Publications Warehouse

Socolow, Roy S.; Frimpter, Michael H.; Turtora, Michael; Bell, Richard W.

1994-01-01

Estimates of future high, median, and low ground- water levels are needed for engineering and architectural design decisions and for appropriate selection of land uses. For example, the failure of individual underground sewage-disposal systems due to high ground-water levels can be prevented if accurate water-level estimates are available. Estimates of extreme or average conditions are needed because short duration preconstruction obser- vations are unlikely to be adequately represen- tative. Water-level records for 40 U.S. Geological Survey observation wells in Rhode Island were used to describe and interpret water-level fluctuations. The maximum annual range of water levels average about 6 feet in sand and gravel and 11 feet in till. These data were used to develop equations for estimating future high, median, and low water levels on the basis of any one measurement at a site and records of water levels at observation wells used as indexes. The estimating technique relies on several assumptions about temporal and spatial variations: (1) Water levels will vary in the future as they have in the past, (2) Water levels fluctuate seasonally (3) Ground-water fluctuations are dependent on site geology, and (4) Water levels throughout Rhode Island are subject to similar precipitation and climate. Comparison of 6,697 estimates of high, median, and low water levels (depth to water level exceeded 95, 50, and 5 percent of the time, respectively) with the actual measured levels exceeded 95, 50, and 5 percent of the time at 14 sites unaffected by pumping and unknown reasons, yielded mean squared errors ranging from 0.34 to 1.53 square feet, 0.30 to 1.22 square feet, and 0.32 to 2.55 square feet, respectively. (USGS)

GDF v2.0, an enhanced version of GDF

NASA Astrophysics Data System (ADS)

Tsoulos, Ioannis G.; Gavrilis, Dimitris; Dermatas, Evangelos

2007-12-01

An improved version of the function estimation program GDF is presented. The main enhancements of the new version include: multi-output function estimation, capability of defining custom functions in the grammar and selection of the error function. The new version has been evaluated on a series of classification and regression datasets, that are widely used for the evaluation of such methods. It is compared to two known neural networks and outperforms them in 5 (out of 10) datasets. Program summaryTitle of program: GDF v2.0 Catalogue identifier: ADXC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 98 147 No. of bytes in distributed program, including test data, etc.: 2 040 684 Distribution format: tar.gz Programming language: GNU C++ Computer: The program is designed to be portable in all systems running the GNU C++ compiler Operating system: Linux, Solaris, FreeBSD RAM: 200000 bytes Classification: 4.9 Does the new version supersede the previous version?: Yes Nature of problem: The technique of function estimation tries to discover from a series of input data a functional form that best describes them. This can be performed with the use of parametric models, whose parameters can adapt according to the input data. Solution method: Functional forms are being created by genetic programming which are approximations for the symbolic regression problem. Reasons for new version: The GDF package was extended in order to be more flexible and user customizable than the old package. The user can extend the package by defining his own error functions and he can extend the grammar of the package by adding new functions to the function repertoire. Also, the new version can perform function estimation of multi-output functions and it can be used for classification problems. Summary of revisions: The following features have been added to the package GDF: Multi-output function approximation. The package can now approximate any function f:R→R. This feature gives also to the package the capability of performing classification and not only regression. User defined function can be added to the repertoire of the grammar, extending the regression capabilities of the package. This feature is limited to 3 functions, but easily this number can be increased. Capability of selecting the error function. The package offers now to the user apart from the mean square error other error functions such as: mean absolute square error, maximum square error. Also, user defined error functions can be added to the set of error functions. More verbose output. The main program displays more information to the user as well as the default values for the parameters. Also, the package gives to the user the capability to define an output file, where the output of the gdf program for the testing set will be stored after the termination of the process. Additional comments: A technical report describing the revisions, experiments and test runs is packaged with the source code. Running time: Depending on the train data.

Fuzzy-Estimation Control for Improvement Microwave Connection for Iraq Electrical Grid

NASA Astrophysics Data System (ADS)

Hoomod, Haider K.; Radi, Mohammed

2018-05-01

The demand for broadband wireless services is increasing day by day (as internet or radio broadcast and TV etc.) for this reason and optimal exploiting for this bandwidth may be other reasons indeed be there is problem in the communication channels. it’s necessary that exploiting the good part form this bandwidth. In this paper, we propose to use estimation technique for estimate channel availability in that moment and next one to know the error in the bandwidth channel for controlling the possibility data transferring through the channel. The proposed estimation based on the combination of the least Minimum square (LMS), Standard Kalman filter, and Modified Kalman filter. The error estimation in channel use as control parameter in fuzzy rules to adjusted the rate and size sending data through the network channel, and rearrangement the priorities of the buffered data (workstation control parameters, Texts, phone call, images, and camera video) for the worst cases of error in channel. The propose system is designed to management data communications through the channels connect among the Iraqi electrical grid stations. The proposed results show that the modified Kalman filter have a best result in time and noise estimation (0.1109 for 5% noise estimation to 0.3211 for 90% noise estimation) and the packets loss rate is reduced with ratio from (35% to 385%).

Assessment of the global monthly mean surface insolation estimated from satellite measurements using global energy balance archive data

NASA Technical Reports Server (NTRS)

Li, Zhanqing; Whitlock, Charles H.; Charlock, Thomas P.

1995-01-01

Global sets of surface radiation budget (SRB) have been obtained from satellite programs. These satellite-based estimates need validation with ground-truth observations. This study validates the estimates of monthly mean surface insolation contained in two satellite-based SRB datasets with the surface measurements made at worldwide radiation stations from the Global Energy Balance Archive (GEBA). One dataset was developed from the Earth Radiation Budget Experiment (ERBE) using the algorithm of Li et al. (ERBE/SRB), and the other from the International Satellite Cloud Climatology Project (ISCCP) using the algorithm of Pinker and Laszlo and that of Staylor (GEWEX/SRB). Since the ERBE/SRB data contain the surface net solar radiation only, the values of surface insolation were derived by making use of the surface albedo data contained GEWEX/SRB product. The resulting surface insolation has a bias error near zero and a root-mean-square error (RMSE) between 8 and 28 W/sq m. The RMSE is mainly associated with poor representation of surface observations within a grid cell. When the number of surface observations are sufficient, the random error is estimated to be about 5 W/sq m with present satellite-based estimates. In addition to demonstrating the strength of the retrieving method, the small random error demonstrates how well the ERBE derives from the monthly mean fluxes at the top of the atmosphere (TOA). A larger scatter is found for the comparison of transmissivity than for that of insolation. Month to month comparison of insolation reveals a weak seasonal trend in bias error with an amplitude of about 3 W/sq m. As for the insolation data from the GEWEX/SRB, larger bias errors of 5-10 W/sq m are evident with stronger seasonal trends and almost identical RMSEs.

Methods for estimating tributary streamflow in the Chattahoochee River basin between Buford Dam and Franklin, Georgia

USGS Publications Warehouse

Stamey, Timothy C.

1998-01-01

Simple and reliable methods for estimating hourly streamflow are needed for the calibration and verification of a Chattahoochee River basin model between Buford Dam and Franklin, Ga. The river basin model is being developed by Georgia Department of Natural Resources, Environmental Protection Division, as part of their Chattahoochee River Modeling Project. Concurrent streamflow data collected at 19 continuous-record, and 31 partial-record streamflow stations, were used in ordinary least-squares linear regression analyses to define estimating equations, and in verifying drainage-area prorations. The resulting regression or drainage-area ratio estimating equations were used to compute hourly streamflow at the partial-record stations. The coefficients of determination (r-squared values) for the regression estimating equations ranged from 0.90 to 0.99. Observed and estimated hourly and daily streamflow data were computed for May 1, 1995, through October 31, 1995. Comparisons of observed and estimated daily streamflow data for 12 continuous-record tributary stations, that had available streamflow data for all or part of the period from May 1, 1995, to October 31, 1995, indicate that the mean error of estimate for the daily streamflow was about 25 percent.

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

NASA Technical Reports Server (NTRS)

Tsaoussi, Lucia S.; Koblinsky, Chester J.

1994-01-01

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Iterative random vs. Kennard-Stone sampling for IR spectrum-based classification task using PLS2-DA

NASA Astrophysics Data System (ADS)

Lee, Loong Chuen; Liong, Choong-Yeun; Jemain, Abdul Aziz

2018-04-01

External testing (ET) is preferred over auto-prediction (AP) or k-fold-cross-validation in estimating more realistic predictive ability of a statistical model. With IR spectra, Kennard-stone (KS) sampling algorithm is often used to split the data into training and test sets, i.e. respectively for model construction and for model testing. On the other hand, iterative random sampling (IRS) has not been the favored choice though it is theoretically more likely to produce reliable estimation. The aim of this preliminary work is to compare performances of KS and IRS in sampling a representative training set from an attenuated total reflectance - Fourier transform infrared spectral dataset (of four varieties of blue gel pen inks) for PLS2-DA modeling. The `best' performance achievable from the dataset is estimated with AP on the full dataset (APF, error). Both IRS (n = 200) and KS were used to split the dataset in the ratio of 7:3. The classic decision rule (i.e. maximum value-based) is employed for new sample prediction via partial least squares - discriminant analysis (PLS2-DA). Error rate of each model was estimated repeatedly via: (a) AP on full data (APF, error); (b) AP on training set (APS, error); and (c) ET on the respective test set (ETS, error). A good PLS2-DA model is expected to produce APS, error and EVS, error that is similar to the APF, error. Bearing that in mind, the similarities between (a) APS, error vs. APF, error; (b) ETS, error vs. APF, error and; (c) APS, error vs. ETS, error were evaluated using correlation tests (i.e. Pearson and Spearman's rank test), using series of PLS2-DA models computed from KS-set and IRS-set, respectively. Overall, models constructed from IRS-set exhibits more similarities between the internal and external error rates than the respective KS-set, i.e. less risk of overfitting. In conclusion, IRS is more reliable than KS in sampling representative training set.

Feasibility of Coherent and Incoherent Backscatter Experiments from the AMPS Laboratory. Technical Section

NASA Technical Reports Server (NTRS)

Mozer, F. S.

1976-01-01

A computer program simulated the spectrum which resulted when a radar signal was transmitted into the ionosphere for a finite time and received for an equal finite interval. The spectrum derived from this signal is statistical in nature because the signal is scattered from the ionosphere, which is statistical in nature. Many estimates of any property of the ionosphere can be made. Their average value will approach the average property of the ionosphere which is being measured. Due to the statistical nature of the spectrum itself, the estimators will vary about this average. The square root of the variance about this average is called the standard deviation, an estimate of the error which exists in any particular radar measurement. In order to determine the feasibility of the space shuttle radar, the magnitude of these errors for measurements of physical interest must be understood.

Peak-flow characteristics of Wyoming streams

USGS Publications Warehouse

Miller, Kirk A.

2003-01-01

Peak-flow characteristics for unregulated streams in Wyoming are described in this report. Frequency relations for annual peak flows through water year 2000 at 364 streamflow-gaging stations in and near Wyoming were evaluated and revised or updated as needed. Analyses of historical floods, temporal trends, and generalized skew were included in the evaluation. Physical and climatic basin characteristics were determined for each gaging station using a geographic information system. Gaging stations with similar peak-flow and basin characteristics were grouped into six hydrologic regions. Regional statistical relations between peak-flow and basin characteristics were explored using multiple-regression techniques. Generalized least squares regression equations for estimating magnitudes of annual peak flows with selected recurrence intervals from 1.5 to 500 years were developed for each region. Average standard errors of estimate range from 34 to 131 percent. Average standard errors of prediction range from 35 to 135 percent. Several statistics for evaluating and comparing the errors in these estimates are described. Limitations of the equations are described. Methods for applying the regional equations for various circumstances are listed and examples are given.

Response Surface Analysis of Experiments with Random Blocks

DTIC Science & Technology

1988-09-01

partitioned into a lack of fit sum of squares, SSLOF, and a pure error sum of squares, SSPE . The latter is obtained by pooling the pure error sums of squares...from the blocks. Tests concerning the polynomial effects can then proceed using SSPE as the error term in the denominators of the F test statistics. 3.2...the center point in each of the three blocks is equal to SSPE = 2.0127 with 5 degrees of freedom. Hence, the lack of fit sum of squares is SSLoF

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

Estimating monthly temperature using point based interpolation techniques

NASA Astrophysics Data System (ADS)

Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi

2013-04-01

This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.

Pilot-based parametric channel estimation algorithm for DCO-OFDM-based visual light communications

NASA Astrophysics Data System (ADS)

Qian, Xuewen; Deng, Honggui; He, Hailang

2017-10-01

Due to wide modulation bandwidth in optical communication, multipath channels may be non-sparse and deteriorate communication performance heavily. Traditional compressive sensing-based channel estimation algorithm cannot be employed in this kind of situation. In this paper, we propose a practical parametric channel estimation algorithm for orthogonal frequency division multiplexing (OFDM)-based visual light communication (VLC) systems based on modified zero correlation code (ZCC) pair that has the impulse-like correlation property. Simulation results show that the proposed algorithm achieves better performances than existing least squares (LS)-based algorithm in both bit error ratio (BER) and frequency response estimation.

Buying a Better Air Force

DTIC Science & Technology

2006-03-01

identify if an explanatory variable may have been omitted due to model misspecification ( Ramsey , 1979). The RESET test resulted in failure to...Prob > F 0.0094 This model was also regressed using Huber-White estimators. Again, the Ramsey RESET test was done to ensure relevant...Aircraft. Annapolis, MD: Naval Institute Press, 2004. Ramsey , J. B. “ Tests for Specification Errors in Classical Least-Squares Regression Analysis

A Hedonic Approach to Estimating Software Cost Using Ordinary Least Squares Regression and Nominal Attribute Variables

DTIC Science & Technology

2006-03-01

included zero, there is insufficient evidence to indicate that the error mean is 35 not zero. The Breusch - Pagan test was used to test the constant...Multicollinearity .............................................................................. 33 Testing OLS Assumptions...programming styles used by developers (Stamelos and others, 2003:733). Kemerer tested to see how models utilizing SLOC as an independent variable

The relationship between purely stochastic sampling error and the number of technical replicates used to estimate concentration at an extreme dilution

USDA-ARS?s Scientific Manuscript database

For any analytical system the population mean (mu) number of entities (e.g., cells or molecules) per tested volume, surface area, or mass also defines the population standard deviation (sigma = square root of mu ). For a preponderance of analytical methods, sigma is very small relative to mu due to...

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

Parameter identification of JONSWAP spectrum acquired by airborne LIDAR

NASA Astrophysics Data System (ADS)

Yu, Yang; Pei, Hailong; Xu, Chengzhong

2017-12-01

In this study, we developed the first linear Joint North Sea Wave Project (JONSWAP) spectrum (JS), which involves a transformation from the JS solution to the natural logarithmic scale. This transformation is convenient for defining the least squares function in terms of the scale and shape parameters. We identified these two wind-dependent parameters to better understand the wind effect on surface waves. Due to its efficiency and high-resolution, we employed the airborne Light Detection and Ranging (LIDAR) system for our measurements. Due to the lack of actual data, we simulated ocean waves in the MATLAB environment, which can be easily translated into industrial programming language. We utilized the Longuet-Higgin (LH) random-phase method to generate the time series of wave records and used the fast Fourier transform (FFT) technique to compute the power spectra density. After validating these procedures, we identified the JS parameters by minimizing the mean-square error of the target spectrum to that of the estimated spectrum obtained by FFT. We determined that the estimation error is relative to the amount of available wave record data. Finally, we found the inverse computation of wind factors (wind speed and wind fetch length) to be robust and sufficiently precise for wave forecasting.

Error properties of Argos satellite telemetry locations using least squares and Kalman filtering.

PubMed

Boyd, Janice D; Brightsmith, Donald J

2013-01-01

Study of animal movements is key for understanding their ecology and facilitating their conservation. The Argos satellite system is a valuable tool for tracking species which move long distances, inhabit remote areas, and are otherwise difficult to track with traditional VHF telemetry and are not suitable for GPS systems. Previous research has raised doubts about the magnitude of position errors quoted by the satellite service provider CLS. In addition, no peer-reviewed publications have evaluated the usefulness of the CLS supplied error ellipses nor the accuracy of the new Kalman filtering (KF) processing method. Using transmitters hung from towers and trees in southeastern Peru, we show the Argos error ellipses generally contain <25% of the true locations and therefore do not adequately describe the true location errors. We also find that KF processing does not significantly increase location accuracy. The errors for both LS and KF processing methods were found to be lognormally distributed, which has important repercussions for error calculation, statistical analysis, and data interpretation. In brief, "good" positions (location codes 3, 2, 1, A) are accurate to about 2 km, while 0 and B locations are accurate to about 5-10 km. However, due to the lognormal distribution of the errors, larger outliers are to be expected in all location codes and need to be accounted for in the user's data processing. We evaluate five different empirical error estimates and find that 68% lognormal error ellipses provided the most useful error estimates. Longitude errors are larger than latitude errors by a factor of 2 to 3, supporting the use of elliptical error ellipses. Numerous studies over the past 15 years have also found fault with the CLS-claimed error estimates yet CLS has failed to correct their misleading information. We hope this will be reversed in the near future.

Accurate motion parameter estimation for colonoscopy tracking using a regression method

NASA Astrophysics Data System (ADS)

Liu, Jianfei; Subramanian, Kalpathi R.; Yoo, Terry S.

2010-03-01

Co-located optical and virtual colonoscopy images have the potential to provide important clinical information during routine colonoscopy procedures. In our earlier work, we presented an optical flow based algorithm to compute egomotion from live colonoscopy video, permitting navigation and visualization of the corresponding patient anatomy. In the original algorithm, motion parameters were estimated using the traditional Least Sum of squares(LS) procedure which can be unstable in the context of optical flow vectors with large errors. In the improved algorithm, we use the Least Median of Squares (LMS) method, a robust regression method for motion parameter estimation. Using the LMS method, we iteratively analyze and converge toward the main distribution of the flow vectors, while disregarding outliers. We show through three experiments the improvement in tracking results obtained using the LMS method, in comparison to the LS estimator. The first experiment demonstrates better spatial accuracy in positioning the virtual camera in the sigmoid colon. The second and third experiments demonstrate the robustness of this estimator, resulting in longer tracked sequences: from 300 to 1310 in the ascending colon, and 410 to 1316 in the transverse colon.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T2 mapping.

PubMed

Lankford, Christopher L; Does, Mark D

2018-02-01

Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T 2 mapping is explored. An analytical expression for the mean-squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision of T⁁2 for a variety of multi-echo T 2 mapping protocols. Constraining θ improved T⁁2 precision when the θ-map signal-to-noise ratio was greater than approximately one-half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean-squared error of T⁁2, for bias in θ⁁≲6%. The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T 2 mapping provided specific cases, depending on θ⁁ accuracy and precision, in which θ⁁ measurement and constraint would be beneficial to T⁁2 variance or mean-squared error. Magn Reson Med 79:673-682, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Mutual information estimation for irregularly sampled time series

NASA Astrophysics Data System (ADS)

Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.

2012-04-01

For the automated, objective and joint analysis of time series, similarity measures are crucial. Used in the analysis of climate records, they allow for a complimentary, unbiased view onto sparse datasets. The irregular sampling of many of these time series, however, makes it necessary to either perform signal reconstruction (e.g. interpolation) or to develop and use adapted measures. Standard linear interpolation comes with an inevitable loss of information and bias effects. We have recently developed a Gaussian kernel-based correlation algorithm with which the interpolation error can be substantially lowered, but this would not work should the functional relationship in a bivariate setting be non-linear. We therefore propose an algorithm to estimate lagged auto and cross mutual information from irregularly sampled time series. We have extended the standard and adaptive binning histogram estimators and use Gaussian distributed weights in the estimation of the (joint) probabilities. To test our method we have simulated linear and nonlinear auto-regressive processes with Gamma-distributed inter-sampling intervals. We have then performed a sensitivity analysis for the estimation of actual coupling length, the lag of coupling and the decorrelation time in the synthetic time series and contrast our results to the performance of a signal reconstruction scheme. Finally we applied our estimator to speleothem records. We compare the estimated memory (or decorrelation time) to that from a least-squares estimator based on fitting an auto-regressive process of order 1. The calculated (cross) mutual information results are compared for the different estimators (standard or adaptive binning) and contrasted with results from signal reconstruction. We find that the kernel-based estimator has a significantly lower root mean square error and less systematic sampling bias than the interpolation-based method. It is possible that these encouraging results could be further improved by using non-histogram mutual information estimators, like k-Nearest Neighbor or Kernel-Density estimators, but for short (<1000 points) and irregularly sampled datasets the proposed algorithm is already a great improvement.

A comparison of energy expenditure estimation of several physical activity monitors.

PubMed

Dannecker, Kathryn L; Sazonova, Nadezhda A; Melanson, Edward L; Sazonov, Edward S; Browning, Raymond C

2013-11-01

Accurately and precisely estimating free-living energy expenditure (EE) is important for monitoring energy balance and quantifying physical activity. Recently, single and multisensor devices have been developed that can classify physical activities, potentially resulting in improved estimates of EE. This study aimed to determine the validity of EE estimation of a footwear-based physical activity monitor and to compare this validity against a variety of research and consumer physical activity monitors. Nineteen healthy young adults (10 men, 9 women) completed a 4-h stay in a room calorimeter. Participants wore a footwear-based physical activity monitor as well as Actical, ActiGraph, IDEEA, DirectLife, and Fitbit devices. Each individual performed a series of postures/activities. We developed models to estimate EE from the footwear-based device, and we used the manufacturer's software to estimate EE for all other devices. Estimated EE using the shoe-based device was not significantly different than measured EE (mean ± SE; 476 ± 20 vs 478 ± 18 kcal, respectively) and had a root-mean-square error of 29.6 kcal (6.2%). The IDEEA and the DirectLlife estimates of EE were not significantly different than the measured EE, but the ActiGraph and the Fitbit devices significantly underestimated EE. Root-mean-square errors were 93.5 (19%), 62.1 kcal (14%), 88.2 kcal (18%), 136.6 kcal (27%), 130.1 kcal (26%), and 143.2 kcal (28%) for Actical, DirectLife, IDEEA, ActiGraph, and Fitbit, respectively. The shoe-based physical activity monitor provides a valid estimate of EE, whereas the other physical activity monitors tested have a wide range of validity when estimating EE. Our results also demonstrate that estimating EE based on classification of physical activities can be more accurate and precise than estimating EE based on total physical activity.

Maximum likelihood estimation in calibrating a stereo camera setup.

PubMed

Muijtjens, A M; Roos, J M; Arts, T; Hasman, A

1999-02-01

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x-ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.

Estimation of Magnitude and Frequency of Floods for Streams on the Island of Oahu, Hawaii

USGS Publications Warehouse

Wong, Michael F.

1994-01-01

This report describes techniques for estimating the magnitude and frequency of floods for the island of Oahu. The log-Pearson Type III distribution and methodology recommended by the Interagency Committee on Water Data was used to determine the magnitude and frequency of floods at 79 gaging stations that had 11 to 72 years of record. Multiple regression analysis was used to construct regression equations to transfer the magnitude and frequency information from gaged sites to ungaged sites. Oahu was divided into three hydrologic regions to define relations between peak discharge and drainage-basin and climatic characteristics. Regression equations are provided to estimate the 2-, 5-, 10-, 25-, 50-, and 100-year peak discharges at ungaged sites. Significant basin and climatic characteristics included in the regression equations are drainage area, median annual rainfall, and the 2-year, 24-hour rainfall intensity. Drainage areas for sites used in this study ranged from 0.03 to 45.7 square miles. Standard error of prediction for the regression equations ranged from 34 to 62 percent. Peak-discharge data collected through water year 1988, geographic information system (GIS) technology, and generalized least-squares regression were used in the analyses. The use of GIS seems to be a more flexible and consistent means of defining and calculating basin and climatic characteristics than using manual methods. Standard errors of estimate for the regression equations in this report are an average of 8 percent less than those published in previous studies.

Space-Time Data Fusion

NASA Technical Reports Server (NTRS)

Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel

2011-01-01

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Inertial sensor-based smoother for gait analysis.

PubMed

Suh, Young Soo

2014-12-17

An off-line smoother algorithm is proposed to estimate foot motion using an inertial sensor unit (three-axis gyroscopes and accelerometers) attached to a shoe. The smoother gives more accurate foot motion estimation than filter-based algorithms by using all of the sensor data instead of using the current sensor data. The algorithm consists of two parts. In the first part, a Kalman filter is used to obtain initial foot motion estimation. In the second part, the error in the initial estimation is compensated using a smoother, where the problem is formulated in the quadratic optimization problem. An efficient solution of the quadratic optimization problem is given using the sparse structure. Through experiments, it is shown that the proposed algorithm can estimate foot motion more accurately than a filter-based algorithm with reasonable computation time. In particular, there is significant improvement in the foot motion estimation when the foot is moving off the floor: the z-axis position error squared sum (total time: 3.47 s) when the foot is in the air is 0.0807 m2 (Kalman filter) and 0.0020 m2 (the proposed smoother).

A New Quaternion-Based Kalman Filter for Real-Time Attitude Estimation Using the Two-Step Geometrically-Intuitive Correction Algorithm.

PubMed

Feng, Kaiqiang; Li, Jie; Zhang, Xiaoming; Shen, Chong; Bi, Yu; Zheng, Tao; Liu, Jun

2017-09-19

In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.

A New Quaternion-Based Kalman Filter for Real-Time Attitude Estimation Using the Two-Step Geometrically-Intuitive Correction Algorithm

PubMed Central

Feng, Kaiqiang; Li, Jie; Zhang, Xiaoming; Shen, Chong; Bi, Yu; Zheng, Tao; Liu, Jun

2017-01-01

In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions. PMID:28925979

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis

PubMed Central

van de Schoot, Rens; Hox, Joop

2014-01-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions. PMID:29795827

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction. M.S. Thesis

NASA Technical Reports Server (NTRS)

Davis, John H.

1993-01-01

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Development of an errorable car-following driver model

NASA Astrophysics Data System (ADS)

Yang, H.-H.; Peng, H.

2010-06-01

An errorable car-following driver model is presented in this paper. An errorable driver model is one that emulates human driver's functions and can generate both nominal (error-free), as well as devious (with error) behaviours. This model was developed for evaluation and design of active safety systems. The car-following data used for developing and validating the model were obtained from a large-scale naturalistic driving database. The stochastic car-following behaviour was first analysed and modelled as a random process. Three error-inducing behaviours were then introduced. First, human perceptual limitation was studied and implemented. Distraction due to non-driving tasks was then identified based on the statistical analysis of the driving data. Finally, time delay of human drivers was estimated through a recursive least-square identification process. By including these three error-inducing behaviours, rear-end collisions with the lead vehicle could occur. The simulated crash rate was found to be similar but somewhat higher than that reported in traffic statistics.

Estimation of correlation functions by stochastic approximation.

NASA Technical Reports Server (NTRS)

Habibi, A.; Wintz, P. A.

1972-01-01

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Optimal Estimation of Clock Values and Trends from Finite Data

NASA Technical Reports Server (NTRS)

Greenhall, Charles

2005-01-01

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

European option pricing under the Student's t noise with jumps

NASA Astrophysics Data System (ADS)

Wang, Xiao-Tian; Li, Zhe; Zhuang, Le

2017-03-01

In this paper we present a new approach to price European options under the Student's t noise with jumps. Through the conditional delta hedging strategy and the minimal mean-square-error hedging, a closed-form solution of the European option value is obtained under the incomplete information case. In particular, we propose a Value-at-Risk-type procedure to estimate the volatility parameter σ such that the pricing error is in accord with the risk preferences of investors. In addition, the numerical results of us show that options are not priced in some cases in an incomplete information market.

Using ridge regression in systematic pointing error corrections

NASA Technical Reports Server (NTRS)

Guiar, C. N.

1988-01-01

A pointing error model is used in the antenna calibration process. Data from spacecraft or radio star observations are used to determine the parameters in the model. However, the regression variables are not truly independent, displaying a condition known as multicollinearity. Ridge regression, a biased estimation technique, is used to combat the multicollinearity problem. Two data sets pertaining to Voyager 1 spacecraft tracking (days 105 and 106 of 1987) were analyzed using both linear least squares and ridge regression methods. The advantages and limitations of employing the technique are presented. The problem is not yet fully resolved.

Cascade control of superheated steam temperature with neuro-PID controller.

PubMed

Zhang, Jianhua; Zhang, Fenfang; Ren, Mifeng; Hou, Guolian; Fang, Fang

2012-11-01

In this paper, an improved cascade control methodology for superheated processes is developed, in which the primary PID controller is implemented by neural networks trained by minimizing error entropy criterion. The entropy of the tracking error can be estimated recursively by utilizing receding horizon window technique. The measurable disturbances in superheated processes are input to the neuro-PID controller besides the sequences of tracking error in outer loop control system, hence, feedback control is combined with feedforward control in the proposed neuro-PID controller. The convergent condition of the neural networks is analyzed. The implementation procedures of the proposed cascade control approach are summarized. Compared with the neuro-PID controller using minimizing squared error criterion, the proposed neuro-PID controller using minimizing error entropy criterion may decrease fluctuations of the superheated steam temperature. A simulation example shows the advantages of the proposed method. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Estimating Dense Cardiac 3D Motion Using Sparse 2D Tagged MRI Cross-sections*

PubMed Central

Ardekani, Siamak; Gunter, Geoffrey; Jain, Saurabh; Weiss, Robert G.; Miller, Michael I.; Younes, Laurent

2015-01-01

In this work, we describe a new method, an extension of the Large Deformation Diffeomorphic Metric Mapping to estimate three-dimensional deformation of tagged Magnetic Resonance Imaging Data. Our approach relies on performing non-rigid registration of tag planes that were constructed from set of initial reference short axis tag grids to a set of deformed tag curves. We validated our algorithm using in-vivo tagged images of normal mice. The mapping allows us to compute root mean square distance error between simulated tag curves in a set of long axis image planes and the acquired tag curves in the same plane. Average RMS error was 0.31±0.36(SD) mm, which is approximately 2.5 voxels, indicating good matching accuracy. PMID:25571140

Linearised and non-linearised isotherm models optimization analysis by error functions and statistical means

PubMed Central

2014-01-01

In adsorption study, to describe sorption process and evaluation of best-fitting isotherm model is a key analysis to investigate the theoretical hypothesis. Hence, numerous statistically analysis have been extensively used to estimate validity of the experimental equilibrium adsorption values with the predicted equilibrium values. Several statistical error analysis were carried out. In the present study, the following statistical analysis were carried out to evaluate the adsorption isotherm model fitness, like the Pearson correlation, the coefficient of determination and the Chi-square test, have been used. The ANOVA test was carried out for evaluating significance of various error functions and also coefficient of dispersion were evaluated for linearised and non-linearised models. The adsorption of phenol onto natural soil (Local name Kalathur soil) was carried out, in batch mode at 30 ± 20 C. For estimating the isotherm parameters, to get a holistic view of the analysis the models were compared between linear and non-linear isotherm models. The result reveled that, among above mentioned error functions and statistical functions were designed to determine the best fitting isotherm. PMID:25018878

A negentropy minimization approach to adaptive equalization for digital communication systems.

PubMed

Choi, Sooyong; Lee, Te-Won

2004-07-01

In this paper, we introduce and investigate a new adaptive equalization method based on minimizing approximate negentropy of the estimation error for a finite-length equalizer. We consider an approximate negentropy using nonpolynomial expansions of the estimation error as a new performance criterion to improve performance of a linear equalizer based on minimizing minimum mean squared error (MMSE). Negentropy includes higher order statistical information and its minimization provides improved converge, performance and accuracy compared to traditional methods such as MMSE in terms of bit error rate (BER). The proposed negentropy minimization (NEGMIN) equalizer has two kinds of solutions, the MMSE solution and the other one, depending on the ratio of the normalization parameters. The NEGMIN equalizer has best BER performance when the ratio of the normalization parameters is properly adjusted to maximize the output power(variance) of the NEGMIN equalizer. Simulation experiments show that BER performance of the NEGMIN equalizer with the other solution than the MMSE one has similar characteristics to the adaptive minimum bit error rate (AMBER) equalizer. The main advantage of the proposed equalizer is that it needs significantly fewer training symbols than the AMBER equalizer. Furthermore, the proposed equalizer is more robust to nonlinear distortions than the MMSE equalizer.

Regularized estimation of Euler pole parameters

NASA Astrophysics Data System (ADS)

Aktuğ, Bahadir; Yildirim, Ömer

2013-07-01

Euler vectors provide a unified framework to quantify the relative or absolute motions of tectonic plates through various geodetic and geophysical observations. With the advent of space geodesy, Euler parameters of several relatively small plates have been determined through the velocities derived from the space geodesy observations. However, the available data are usually insufficient in number and quality to estimate both the Euler vector components and the Euler pole parameters reliably. Since Euler vectors are defined globally in an Earth-centered Cartesian frame, estimation with the limited geographic coverage of the local/regional geodetic networks usually results in highly correlated vector components. In the case of estimating the Euler pole parameters directly, the situation is even worse, and the position of the Euler pole is nearly collinear with the magnitude of the rotation rate. In this study, a new method, which consists of an analytical derivation of the covariance matrix of the Euler vector in an ideal network configuration, is introduced and a regularized estimation method specifically tailored for estimating the Euler vector is presented. The results show that the proposed method outperforms the least squares estimation in terms of the mean squared error.

On-Board Event-Based State Estimation for Trajectory Approaching and Tracking of a Vehicle

PubMed Central

Martínez-Rey, Miguel; Espinosa, Felipe; Gardel, Alfredo; Santos, Carlos

2015-01-01

For the problem of pose estimation of an autonomous vehicle using networked external sensors, the processing capacity and battery consumption of these sensors, as well as the communication channel load should be optimized. Here, we report an event-based state estimator (EBSE) consisting of an unscented Kalman filter that uses a triggering mechanism based on the estimation error covariance matrix to request measurements from the external sensors. This EBSE generates the events of the estimator module on-board the vehicle and, thus, allows the sensors to remain in stand-by mode until an event is generated. The proposed algorithm requests a measurement every time the estimation distance root mean squared error (DRMS) value, obtained from the estimator's covariance matrix, exceeds a threshold value. This triggering threshold can be adapted to the vehicle's working conditions rendering the estimator even more efficient. An example of the use of the proposed EBSE is given, where the autonomous vehicle must approach and follow a reference trajectory. By making the threshold a function of the distance to the reference location, the estimator can halve the use of the sensors with a negligible deterioration in the performance of the approaching maneuver. PMID:26102489

Adaptive Error Estimation in Linearized Ocean General Circulation Models

NASA Technical Reports Server (NTRS)

Chechelnitsky, Michael Y.

1999-01-01

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

An Inequality Constrained Least-Squares Approach as an Alternative Estimation Procedure for Atmospheric Parameters from VLBI Observations

NASA Astrophysics Data System (ADS)

Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel

2016-12-01

On its way through the atmosphere, radio signals are delayed and affected by bending and attenuation effects relative to a theoretical path in vacuum. In particular, the neutral part of the atmosphere contributes considerably to the error budget of space-geodetic observations. At the same time, space-geodetic techniques become more and more important in the understanding of the Earth's atmosphere, because atmospheric parameters can be linked to the water vapor content in the atmosphere. The tropospheric delay is usually taken into account by applying an adequate model for the hydrostatic component and by additionally estimating zenith wet delays for the highly variable wet component. Sometimes, the Ordinary Least Squares (OLS) approach leads to negative estimates, which would be equivalent to negative water vapor in the atmosphere and does, of course, not reflect meteorological and physical conditions in a plausible way. To cope with this phenomenon, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization and use inequality constraints to force the tropospheric parameters to be non-negative allowing for a more realistic tropospheric parameter estimation in a meteorological sense. Because deficiencies in the a priori hydrostatic modeling are almost fully compensated by the tropospheric estimates, the ICLS approach urgently requires suitable a priori hydrostatic delays. In this paper, we briefly describe the ICLS method and validate its impact with regard to station positions.

Methods for estimating selected low-flow frequency statistics for unregulated streams in Kentucky

USGS Publications Warehouse

Martin, Gary R.; Arihood, Leslie D.

2010-01-01

This report provides estimates of, and presents methods for estimating, selected low-flow frequency statistics for unregulated streams in Kentucky including the 30-day mean low flows for recurrence intervals of 2 and 5 years (30Q2 and 30Q5) and the 7-day mean low flows for recurrence intervals of 5, 10, and 20 years (7Q2, 7Q10, and 7Q20). Estimates of these statistics are provided for 121 U.S. Geological Survey streamflow-gaging stations with data through the 2006 climate year, which is the 12-month period ending March 31 of each year. Data were screened to identify the periods of homogeneous, unregulated flows for use in the analyses. Logistic-regression equations are presented for estimating the annual probability of the selected low-flow frequency statistics being equal to zero. Weighted-least-squares regression equations were developed for estimating the magnitude of the nonzero 30Q2, 30Q5, 7Q2, 7Q10, and 7Q20 low flows. Three low-flow regions were defined for estimating the 7-day low-flow frequency statistics. The explicit explanatory variables in the regression equations include total drainage area and the mapped streamflow-variability index measured from a revised statewide coverage of this characteristic. The percentage of the station low-flow statistics correctly classified as zero or nonzero by use of the logistic-regression equations ranged from 87.5 to 93.8 percent. The average standard errors of prediction of the weighted-least-squares regression equations ranged from 108 to 226 percent. The 30Q2 regression equations have the smallest standard errors of prediction, and the 7Q20 regression equations have the largest standard errors of prediction. The regression equations are applicable only to stream sites with low flows unaffected by regulation from reservoirs and local diversions of flow and to drainage basins in specified ranges of basin characteristics. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features.

Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

PubMed

Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

2016-03-01

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, Leslie D.; Glatfelter, Dale R.

1991-01-01

Equations for estimating the 7-day, 2-year and 7oday, 10-year low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low-flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow-duration ratio, which is the 20-percent flow duration divided by the 90-percent flow duration. Flow-duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from the plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow-duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low-flow characteristics at 82 gaging stations where flow-duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-year and 7-day, 10-year low flows are 19 and 28 percent. When flow-duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46 and 61 percent. However, when stations having drainage areas of less than 10 square miles are excluded from the test, the standard errors decrease to 38 and 49 percent. Standard errors increase when stations with small basins are included, probably because some of the flow-duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow-duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and central physiographic zones of the State. Low-flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low-flow characteristic can be adjusted. The method is most accurate for sites having drainage areas ranging from 10 to 1,000 square miles and for predictions of 7-day, 10-year low flows ranging from 0.5 to 340 cubic feet per second.

Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise

NASA Technical Reports Server (NTRS)

Sedlak, J.; Hashmall, J.

1997-01-01

Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

On the equivalence of generalized least-squares approaches to the evaluation of measurement comparisons

NASA Astrophysics Data System (ADS)

Koo, A.; Clare, J. F.

2012-06-01

Analysis of CIPM international comparisons is increasingly being carried out using a model-based approach that leads naturally to a generalized least-squares (GLS) solution. While this method offers the advantages of being easier to audit and having general applicability to any form of comparison protocol, there is a lack of consensus over aspects of its implementation. Two significant results are presented that show the equivalence of three differing approaches discussed by or applied in comparisons run by Consultative Committees of the CIPM. Both results depend on a mathematical condition equivalent to the requirement that any two artefacts in the comparison are linked through a sequence of measurements of overlapping pairs of artefacts. The first result is that a GLS estimator excluding all sources of error common to all measurements of a participant is equal to the GLS estimator incorporating all sources of error, including those associated with any bias in the standards or procedures of the measuring laboratory. The second result identifies the component of uncertainty in the estimate of bias that arises from possible systematic effects in the participants' measurement standards and procedures. The expression so obtained is a generalization of an expression previously published for a one-artefact comparison with no inter-participant correlations, to one for a comparison comprising any number of repeat measurements of multiple artefacts and allowing for inter-laboratory correlations.

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

The Effectiveness of Using Limited Gauge Measurements for Bias Adjustment of Satellite-Based Precipitation Estimation over Saudi Arabia

NASA Astrophysics Data System (ADS)

Alharbi, Raied; Hsu, Kuolin; Sorooshian, Soroosh; Braithwaite, Dan

2018-01-01

Precipitation is a key input variable for hydrological and climate studies. Rain gauges are capable of providing reliable precipitation measurements at point scale. However, the uncertainty of rain measurements increases when the rain gauge network is sparse. Satellite -based precipitation estimations appear to be an alternative source of precipitation measurements, but they are influenced by systematic bias. In this study, a method for removing the bias from the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Cloud Classification System (PERSIANN-CCS) over a region where the rain gauge is sparse is investigated. The method consists of monthly empirical quantile mapping, climate classification, and inverse-weighted distance method. Daily PERSIANN-CCS is selected to test the capability of the method for removing the bias over Saudi Arabia during the period of 2010 to 2016. The first six years (2010 - 2015) are calibrated years and 2016 is used for validation. The results show that the yearly correlation coefficient was enhanced by 12%, the yearly mean bias was reduced by 93% during validated year. Root mean square error was reduced by 73% during validated year. The correlation coefficient, the mean bias, and the root mean square error show that the proposed method removes the bias on PERSIANN-CCS effectively that the method can be applied to other regions where the rain gauge network is sparse.

Estimating patient-specific soft-tissue properties in a TKA knee.

PubMed

Ewing, Joseph A; Kaufman, Michelle K; Hutter, Erin E; Granger, Jeffrey F; Beal, Matthew D; Piazza, Stephen J; Siston, Robert A

2016-03-01

Surgical technique is one factor that has been identified as critical to success of total knee arthroplasty. Researchers have shown that computer simulations can aid in determining how decisions in the operating room generally affect post-operative outcomes. However, to use simulations to make clinically relevant predictions about knee forces and motions for a specific total knee patient, patient-specific models are needed. This study introduces a methodology for estimating knee soft-tissue properties of an individual total knee patient. A custom surgical navigation system and stability device were used to measure the force-displacement relationship of the knee. Soft-tissue properties were estimated using a parameter optimization that matched simulated tibiofemoral kinematics with experimental tibiofemoral kinematics. Simulations using optimized ligament properties had an average root mean square error of 3.5° across all tests while simulations using generic ligament properties taken from literature had an average root mean square error of 8.4°. Specimens showed large variability among ligament properties regardless of similarities in prosthetic component alignment and measured knee laxity. These results demonstrate the importance of soft-tissue properties in determining knee stability, and suggest that to make clinically relevant predictions of post-operative knee motions and forces using computer simulations, patient-specific soft-tissue properties are needed. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

NASA Astrophysics Data System (ADS)

Becker, Roland; Vexler, Boris

2005-06-01

We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.

Diagnosing and dealing with multicollinearity.

PubMed

Schroeder, M A

1990-04-01

The purpose of this article was to increase nurse researchers' awareness of the effects of collinear data in developing theoretical models for nursing practice. Collinear data distort the true value of the estimates generated from ordinary least-squares analysis. Theoretical models developed to provide the underpinnings of nursing practice need not be abandoned, however, because they fail to produce consistent estimates over repeated applications. It is also important to realize that multicollinearity is a data problem, not a problem associated with misspecification of a theorectical model. An investigator must first be aware of the problem, and then it is possible to develop an educated solution based on the degree of multicollinearity, theoretical considerations, and sources of error associated with alternative, biased, least-square regression techniques. Decisions based on theoretical and statistical considerations will further the development of theory-based nursing practice.

Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daly, Don S.; Anderson, Kevin K.; White, Amanda M.

Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensitymore » that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting, and reliably estimates believable prediction errors. For the 50% of the real data sets fit well by both methods, spline and logistic predictions are practically indistinguishable, varying in accuracy by less than 15%. The spline method may be useful when automated prediction across simultaneous assays of numerous proteins must be applied routinely with minimal user intervention.« less

Power of tests for comparing trend curves with application to national immunization survey (NIS).

PubMed

Zhao, Zhen

2011-02-28

To develop statistical tests for comparing trend curves of study outcomes between two socio-demographic strata across consecutive time points, and compare statistical power of the proposed tests under different trend curves data, three statistical tests were proposed. For large sample size with independent normal assumption among strata and across consecutive time points, the Z and Chi-square test statistics were developed, which are functions of outcome estimates and the standard errors at each of the study time points for the two strata. For small sample size with independent normal assumption, the F-test statistic was generated, which is a function of sample size of the two strata and estimated parameters across study period. If two trend curves are approximately parallel, the power of Z-test is consistently higher than that of both Chi-square and F-test. If two trend curves cross at low interaction, the power of Z-test is higher than or equal to the power of both Chi-square and F-test; however, at high interaction, the powers of Chi-square and F-test are higher than that of Z-test. The measurement of interaction of two trend curves was defined. These tests were applied to the comparison of trend curves of vaccination coverage estimates of standard vaccine series with National Immunization Survey (NIS) 2000-2007 data. Copyright © 2011 John Wiley & Sons, Ltd.

Error propagation of partial least squares for parameters optimization in NIR modeling.

PubMed

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-05

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models. Copyright © 2017. Published by Elsevier B.V.

Error propagation of partial least squares for parameters optimization in NIR modeling

NASA Astrophysics Data System (ADS)

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-01

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models.

Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters.

PubMed

Chung, SungWon; Lu, Ying; Henry, Roland G

2006-11-01

Bootstrap is an empirical non-parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor MRI (DTI) parameters, useful in tractography and in assessing DTI methods. The current bootstrap method (repetition bootstrap) used for DTI analysis performs resampling within the data sharing common diffusion gradients, requiring multiple acquisitions for each diffusion gradient. Recently, wild bootstrap was proposed that can be applied without multiple acquisitions. In this paper, two new approaches are introduced called residual bootstrap and repetition bootknife. We show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and, therefore, better estimates the standard errors. Like wild bootstrap, residual bootstrap is applicable to single acquisition scheme, and both are based on regression residuals (called model-based resampling). Residual bootstrap is based on the assumption that non-constant variance of measured diffusion-attenuated signals can be modeled, which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor. The performances of these bootstrap approaches were compared in terms of bias, variance, and overall error of bootstrap-estimated standard error by Monte Carlo simulation. We demonstrate that residual bootstrap has smaller biases and overall errors, which enables estimation of uncertainties with higher accuracy. Understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on DTI parameters, probabilistic fiber tracking, and optimizing DTI methods.

Parameter estimation for terrain modeling from gradient data. [navigation system for Martian rover

NASA Technical Reports Server (NTRS)

Dangelo, K. R.

1974-01-01

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

The Influence of Observation Errors on Analysis Error and Forecast Skill Investigated with an Observing System Simulation Experiment

NASA Technical Reports Server (NTRS)

Prive, N. C.; Errico, R. M.; Tai, K.-S.

2013-01-01

The Global Modeling and Assimilation Office (GMAO) observing system simulation experiment (OSSE) framework is used to explore the response of analysis error and forecast skill to observation quality. In an OSSE, synthetic observations may be created that have much smaller error than real observations, and precisely quantified error may be applied to these synthetic observations. Three experiments are performed in which synthetic observations with magnitudes of applied observation error that vary from zero to twice the estimated realistic error are ingested into the Goddard Earth Observing System Model (GEOS-5) with Gridpoint Statistical Interpolation (GSI) data assimilation for a one-month period representing July. The analysis increment and observation innovation are strongly impacted by observation error, with much larger variances for increased observation error. The analysis quality is degraded by increased observation error, but the change in root-mean-square error of the analysis state is small relative to the total analysis error. Surprisingly, in the 120 hour forecast increased observation error only yields a slight decline in forecast skill in the extratropics, and no discernable degradation of forecast skill in the tropics.

Estimation of Foot Plantar Center of Pressure Trajectories with Low-Cost Instrumented Insoles Using an Individual-Specific Nonlinear Model.

PubMed

Hu, Xinyao; Zhao, Jun; Peng, Dongsheng; Sun, Zhenglong; Qu, Xingda

2018-02-01

Postural control is a complex skill based on the interaction of dynamic sensorimotor processes, and can be challenging for people with deficits in sensory functions. The foot plantar center of pressure (COP) has often been used for quantitative assessment of postural control. Previously, the foot plantar COP was mainly measured by force plates or complicated and expensive insole-based measurement systems. Although some low-cost instrumented insoles have been developed, their ability to accurately estimate the foot plantar COP trajectory was not robust. In this study, a novel individual-specific nonlinear model was proposed to estimate the foot plantar COP trajectories with an instrumented insole based on low-cost force sensitive resistors (FSRs). The model coefficients were determined by a least square error approximation algorithm. Model validation was carried out by comparing the estimated COP data with the reference data in a variety of postural control assessment tasks. We also compared our data with the COP trajectories estimated by the previously well accepted weighted mean approach. Comparing with the reference measurements, the average root mean square errors of the COP trajectories of both feet were 2.23 mm (±0.64) (left foot) and 2.72 mm (±0.83) (right foot) along the medial-lateral direction, and 9.17 mm (±1.98) (left foot) and 11.19 mm (±2.98) (right foot) along the anterior-posterior direction. The results are superior to those reported in previous relevant studies, and demonstrate that our proposed approach can be used for accurate foot plantar COP trajectory estimation. This study could provide an inexpensive solution to fall risk assessment in home settings or community healthcare center for the elderly. It has the potential to help prevent future falls in the elderly.

Estimation of Foot Plantar Center of Pressure Trajectories with Low-Cost Instrumented Insoles Using an Individual-Specific Nonlinear Model

PubMed Central

Hu, Xinyao; Zhao, Jun; Peng, Dongsheng

2018-01-01

Postural control is a complex skill based on the interaction of dynamic sensorimotor processes, and can be challenging for people with deficits in sensory functions. The foot plantar center of pressure (COP) has often been used for quantitative assessment of postural control. Previously, the foot plantar COP was mainly measured by force plates or complicated and expensive insole-based measurement systems. Although some low-cost instrumented insoles have been developed, their ability to accurately estimate the foot plantar COP trajectory was not robust. In this study, a novel individual-specific nonlinear model was proposed to estimate the foot plantar COP trajectories with an instrumented insole based on low-cost force sensitive resistors (FSRs). The model coefficients were determined by a least square error approximation algorithm. Model validation was carried out by comparing the estimated COP data with the reference data in a variety of postural control assessment tasks. We also compared our data with the COP trajectories estimated by the previously well accepted weighted mean approach. Comparing with the reference measurements, the average root mean square errors of the COP trajectories of both feet were 2.23 mm (±0.64) (left foot) and 2.72 mm (±0.83) (right foot) along the medial–lateral direction, and 9.17 mm (±1.98) (left foot) and 11.19 mm (±2.98) (right foot) along the anterior–posterior direction. The results are superior to those reported in previous relevant studies, and demonstrate that our proposed approach can be used for accurate foot plantar COP trajectory estimation. This study could provide an inexpensive solution to fall risk assessment in home settings or community healthcare center for the elderly. It has the potential to help prevent future falls in the elderly. PMID:29389857

Stochastic growth logistic model with aftereffect for batch fermentation process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Quantitative coronary angiography using image recovery techniques for background estimation in unsubtracted images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Jerry T.; Kamyar, Farzad; Molloi, Sabee

2007-10-15

Densitometry measurements have been performed previously using subtracted images. However, digital subtraction angiography (DSA) in coronary angiography is highly susceptible to misregistration artifacts due to the temporal separation of background and target images. Misregistration artifacts due to respiration and patient motion occur frequently, and organ motion is unavoidable. Quantitative densitometric techniques would be more clinically feasible if they could be implemented using unsubtracted images. The goal of this study is to evaluate image recovery techniques for densitometry measurements using unsubtracted images. A humanoid phantom and eight swine (25-35 kg) were used to evaluate the accuracy and precision of the followingmore » image recovery techniques: Local averaging (LA), morphological filtering (MF), linear interpolation (LI), and curvature-driven diffusion image inpainting (CDD). Images of iodinated vessel phantoms placed over the heart of the humanoid phantom or swine were acquired. In addition, coronary angiograms were obtained after power injections of a nonionic iodinated contrast solution in an in vivo swine study. Background signals were estimated and removed with LA, MF, LI, and CDD. Iodine masses in the vessel phantoms were quantified and compared to known amounts. Moreover, the total iodine in left anterior descending arteries was measured and compared with DSA measurements. In the humanoid phantom study, the average root mean square errors associated with quantifying iodine mass using LA and MF were approximately 6% and 9%, respectively. The corresponding average root mean square errors associated with quantifying iodine mass using LI and CDD were both approximately 3%. In the in vivo swine study, the root mean square errors associated with quantifying iodine in the vessel phantoms with LA and MF were approximately 5% and 12%, respectively. The corresponding average root mean square errors using LI and CDD were both 3%. The standard deviations in the differences between measured iodine mass in left anterior descending arteries using DSA and LA, MF, LI, or CDD were calculated. The standard deviations in the DSA-LA and DSA-MF differences (both {approx}21 mg) were approximately a factor of 3 greater than that of the DSA-LI and DSA-CDD differences (both {approx}7 mg). Local averaging and morphological filtering were considered inadequate for use in quantitative densitometry. Linear interpolation and curvature-driven diffusion image inpainting were found to be effective techniques for use with densitometry in quantifying iodine mass in vitro and in vivo. They can be used with unsubtracted images to estimate background anatomical signals and obtain accurate densitometry results. The high level of accuracy and precision in quantification associated with using LI and CDD suggests the potential of these techniques in applications where background mask images are difficult to obtain, such as lumen volume and blood flow quantification using coronary arteriography.« less

Continuous correction of differential path length factor in near-infrared spectroscopy

PubMed Central

Moore, Jason H.; Diamond, Solomon G.

2013-01-01

Abstract. In continuous-wave near-infrared spectroscopy (CW-NIRS), changes in the concentration of oxyhemoglobin and deoxyhemoglobin can be calculated by solving a set of linear equations from the modified Beer-Lambert Law. Cross-talk error in the calculated hemodynamics can arise from inaccurate knowledge of the wavelength-dependent differential path length factor (DPF). We apply the extended Kalman filter (EKF) with a dynamical systems model to calculate relative concentration changes in oxy- and deoxyhemoglobin while simultaneously estimating relative changes in DPF. Results from simulated and experimental CW-NIRS data are compared with results from a weighted least squares (WLSQ) method. The EKF method was found to effectively correct for artificially introduced errors in DPF and to reduce the cross-talk error in simulation. With experimental CW-NIRS data, the hemodynamic estimates from EKF differ significantly from the WLSQ (p<0.001). The cross-correlations among residuals at different wavelengths were found to be significantly reduced by the EKF method compared to WLSQ in three physiologically relevant spectral bands 0.04 to 0.15 Hz, 0.15 to 0.4 Hz and 0.4 to 2.0 Hz (p<0.001). This observed reduction in residual cross-correlation is consistent with reduced cross-talk error in the hemodynamic estimates from the proposed EKF method. PMID:23640027

Continuous correction of differential path length factor in near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Talukdar, Tanveer; Moore, Jason H.; Diamond, Solomon G.

2013-05-01

In continuous-wave near-infrared spectroscopy (CW-NIRS), changes in the concentration of oxyhemoglobin and deoxyhemoglobin can be calculated by solving a set of linear equations from the modified Beer-Lambert Law. Cross-talk error in the calculated hemodynamics can arise from inaccurate knowledge of the wavelength-dependent differential path length factor (DPF). We apply the extended Kalman filter (EKF) with a dynamical systems model to calculate relative concentration changes in oxy- and deoxyhemoglobin while simultaneously estimating relative changes in DPF. Results from simulated and experimental CW-NIRS data are compared with results from a weighted least squares (WLSQ) method. The EKF method was found to effectively correct for artificially introduced errors in DPF and to reduce the cross-talk error in simulation. With experimental CW-NIRS data, the hemodynamic estimates from EKF differ significantly from the WLSQ (p<0.001). The cross-correlations among residuals at different wavelengths were found to be significantly reduced by the EKF method compared to WLSQ in three physiologically relevant spectral bands 0.04 to 0.15 Hz, 0.15 to 0.4 Hz and 0.4 to 2.0 Hz (p<0.001). This observed reduction in residual cross-correlation is consistent with reduced cross-talk error in the hemodynamic estimates from the proposed EKF method.

Optimal dental age estimation practice in United Arab Emirates' children.

PubMed

Altalie, Salem; Thevissen, Patrick; Fieuws, Steffen; Willems, Guy

2014-03-01

The aim of the study was to detect whether the Willems model, developed on a Belgian reference sample, can be used for age estimations in United Arab Emirates (UAE) children. Furthermore, it was verified that if added third molars development information in children provided more accurate age predictions. On 1900 panoramic radiographs, the development of left mandibular permanent teeth (PT) and third molars (TM) was registered according the Demirjian and the Kohler technique, respectively. The PT data were used to verify the Willems model and to develop a UAE model and to verify it. Multiple regression models with PT, TM, and PT + TM scores as independent and age as dependent factor were developed. Comparing the verified Willems- and the UAE model revealed differences in mean error of -0.01 year, mean absolute error of 0.01 year and root mean squared error of 0.90 year. Neglectable overall decrease in RMSE was detected combining PM and TM developmental information. © 2013 American Academy of Forensic Sciences.