Computational requirements for a discrete Kalman filter.
NASA Technical Reports Server (NTRS)
Mendel, J. M.
1971-01-01
Computational requirements - i.e., computing time per cycle (iteration) and required storage - which determine minimum sampling rates and computer memory size, were obtained as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then use sequential processing than to process them together via simultaneous processing.
NASA Astrophysics Data System (ADS)
Stubberud, Allen R.
2017-01-01
When considering problems of linear sequential estimation, two versions of the Kalman filter, the continuous-time version and the discrete-time version, are often used. (A hybrid filter also exists.) In many applications in which the Kalman filter is used, the system to which the filter is applied is a linear continuous-time system, but the Kalman filter is implemented on a digital computer, a discrete-time device. The two general approaches for developing a discrete-time filter for implementation on a digital computer are: (1) approximate the continuous-time system by a discrete-time system (called discretization of the continuous-time system) and develop a filter for the discrete-time approximation; and (2) develop a continuous-time filter for the system and then discretize the continuous-time filter. Generally, the two discrete-time filters will be different, that is, it can be said that discretization and filter generation are not, in general, commutative operations. As a result, any relationship between the discrete-time and continuous-time versions of the filter for the same continuous-time system is often obfuscated. This is particularly true when an attempt is made to generate the continuous-time version of the Kalman filter through a simple limiting process (the sample period going to zero) applied to the discrete-time version. The correct result is, generally, not obtained. In a 1961 research report, Kalman showed that the continuous-time Kalman filter can be obtained from the discrete-time Kalman filter by taking limits as the sample period goes to zero if the white noise process for the continuous-time version is appropriately defined. Using this basic concept, a discrete-time Kalman filter can be developed for a continuous-time system as follows: (1) discretize the continuous-time system using Kalman's technique; and (2) develop a discrete-time Kalman filter for that discrete-time system. Kalman's results show that the discrete-time filter generated in
NASA Technical Reports Server (NTRS)
Skliar, M.; Ramirez, W. F.
1997-01-01
For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.
Requirements for Kalman filtering on the GE-701 whole word computer
NASA Technical Reports Server (NTRS)
Pines, S.; Schmidt, S. F.
1978-01-01
The results of a study to determine scaling, storage, and word length requirements for programming the Kalman filter on the GE-701 Whole Word Computer are reported. Simulation tests are presented which indicate that the Kalman filter, using a square root formulation with process noise added, utilizing MLS, radar altimeters, and airspeed as navigation aids, may be programmed for the GE-701 computer to successfully navigate and control the Boeing B737-100 during landing approach, landing rollout, and turnoff. The report contains flow charts, equations, computer storage, scaling, and word length recommendations for the Kalman filter on the GE-701 Whole Word computer.
Systolic VLSI for Kalman filters
NASA Technical Reports Server (NTRS)
Yeh, H.-G.; Chang, J. J.
1986-01-01
A novel two-dimensional parallel computing method for real-time Kalman filtering is presented. The mathematical formulation of a Kalman filter algorithm is rearranged to be the type of Faddeev algorithm for generalizing signal processing. The data flow mapping from the Faddeev algorithm to a two-dimensional concurrent computing structure is developed. The architecture of the resulting processor cells is regular, simple, expandable, and therefore naturally suitable for VLSI chip implementation. The computing methodology and the two-dimensional systolic arrays are useful for Kalman filter applications as well as other matrix/vector based algebraic computations.
Generic Kalman Filter Software
NASA Technical Reports Server (NTRS)
Lisano, Michael E., II; Crues, Edwin Z.
2005-01-01
The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on
Multilevel ensemble Kalman filtering
Hoel, Hakon; Law, Kody J. H.; Tempone, Raul
2016-06-14
This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
Multilevel ensemble Kalman filtering
Hoel, Hakon; Law, Kody J. H.; Tempone, Raul
2016-06-14
This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
A cognition-based method to ease the computational load for an extended Kalman filter.
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-12-03
The extended Kalman filter (EKF) is the nonlinear model of a Kalman filter (KF). It is a useful parameter estimation method when the observation model and/or the state transition model is not a linear function. However, the computational requirements in EKF are a difficulty for the system. With the help of cognition-based designation and the Taylor expansion method, a novel algorithm is proposed to ease the computational load for EKF in azimuth predicting and localizing under a nonlinear observation model. When there are nonlinear functions and inverse calculations for matrices, this method makes use of the major components (according to current performance and the performance requirements) in the Taylor expansion. As a result, the computational load is greatly lowered and the performance is ensured. Simulation results show that the proposed measure will deliver filtering output with a similar precision compared to the regular EKF. At the same time, the computational load is substantially lowered.
NASA Technical Reports Server (NTRS)
Brown, R. G.
1984-01-01
The formulation of appropriate state-space models for Kalman filtering applications is studied. The so-called model is completely specified by four matrix parameters and the initial conditions of the recursive equations. Once these are determined, the die is cast, and the way in which the measurements are weighted is determined foreverafter. Thus, finding a model that fits the physical situation at hand is all important. Also, it is often the most difficult aspect of designing a Kalman filter. Formulation of discrete state models from the spectral density and ARMA random process descriptions is discussed. Finally, it is pointed out that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.
Rucci, Michael; Hardie, Russell C; Barnard, Kenneth J
2014-05-01
In this paper, we present a computationally efficient video restoration algorithm to address both blur and noise for a Nyquist sampled imaging system. The proposed method utilizes a temporal Kalman filter followed by a correlation-model based spatial adaptive Wiener filter (AWF). The Kalman filter employs an affine background motion model and novel process-noise variance estimate. We also propose and demonstrate a new multidelay temporal Kalman filter designed to more robustly treat local motion. The AWF is a spatial operation that performs deconvolution and adapts to the spatially varying residual noise left in the Kalman filter stage. In image areas where the temporal Kalman filter is able to provide significant noise reduction, the AWF can be aggressive in its deconvolution. In other areas, where less noise reduction is achieved with the Kalman filter, the AWF balances the deconvolution with spatial noise reduction. In this way, the Kalman filter and AWF work together effectively, but without the computational burden of full joint spatiotemporal processing. We also propose a novel hybrid system that combines a temporal Kalman filter and BM3D processing. To illustrate the efficacy of the proposed methods, we test the algorithms on both simulated imagery and video collected with a visible camera.
Adaptable Iterative and Recursive Kalman Filter Schemes
NASA Technical Reports Server (NTRS)
Zanetti, Renato
2014-01-01
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
Robust Kriged Kalman Filtering
Baingana, Brian; Dall'Anese, Emiliano; Mateos, Gonzalo; Giannakis, Georgios B.
2015-11-11
Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.
Reduced-order Kalman filtering with incomplete observability
NASA Technical Reports Server (NTRS)
Yonezawa, K.
1980-01-01
Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.
Extended Kalman filtering of point process observation.
Salimpour, Yousef; Soltanian-Zadeh, Hamid; Abolhassani, Mohammad D
2010-01-01
A temporal point process is a stochastic time series of binary events that occurs in continuous time. In computational neuroscience, the point process is used to model neuronal spiking activity; however, estimating the model parameters from spike train is a challenging problem. The state space point process filtering theory is a new technique for the estimation of the states and parameters. In order to use the stochastic filtering theory for the states of neuronal system with the Gaussian assumption, we apply the extended Kalman filter. In this regard, the extended Kalman filtering equations are derived for the point process observation. We illustrate the new filtering algorithm by estimating the effect of visual stimulus on the spiking activity of object selective neurons from the inferior temporal cortex of macaque monkey. Based on the goodness-offit assessment, the extended Kalman filter provides more accurate state estimate than the conventional methods.
NASA Technical Reports Server (NTRS)
Thompson, E. H.; Farrell, J. L.
1976-01-01
Monte Carlo simulation of autonomous orbit determination has validated the use of an 18-bit NASA Standard Spacecraft Computer (NSSC) for the extended Kalman filter. Dimensionally consistent scales are chosen for all variables in the algorithm, such that nearly all of the onboard computation can be performed in single precision without matrix square root formulations. Allowable simplifications in algorithm implementation and practical means of ensuring convergence are verified for accuracies of a few km provided by star/vertical observations
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L. C.
1984-01-01
AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.
Zhang, Yin; Chase, Steve M
2013-01-01
Neural prosthetics are a promising technology for alleviating paralysis by actuating devices directly from the intention to move. Typical implementations of these devices require a calibration session to define decoding parameters that map recorded neural activity into movement of the device. However, a major factor limiting the clinical deployment of this technology is stability: with fixed decoding parameters, control of the prosthetic device has been shown to degrade over time. Here we apply a dual estimation procedure to adaptively capture changes in decoding parameters. In simulation, we find that our stabilized dual Kalman filter can run autonomously for hundreds of thousands of trials with little change in performance. Further, when we apply our algorithm off-line to estimate arm trajectories from neural data recorded over five consecutive days, we find that it outperforms a static Kalman filter, even when it is re-calibrated at the beginning of each day.
The Kalman Filter and High Performance Computing at NASA's Data Assimilation Office (DAO)
NASA Technical Reports Server (NTRS)
Lyster, Peter M.
1999-01-01
Atmospheric data assimilation is a method of combining actual observations with model simulations to produce a more accurate description of the earth system than the observations alone provide. The output of data assimilation, sometimes called "the analysis", are accurate regular, gridded datasets of observed and unobserved variables. This is used not only for weather forecasting but is becoming increasingly important for climate research. For example, these datasets may be used to assess retrospectively energy budgets or the effects of trace gases such as ozone. This allows researchers to understand processes driving weather and climate, which have important scientific and policy implications. The primary goal of the NASA's Data Assimilation Office (DAO) is to provide datasets for climate research and to support NASA satellite and aircraft missions. This presentation will: (1) describe ongoing work on the advanced Kalman/Lagrangian filter parallel algorithm for the assimilation of trace gases in the stratosphere; and (2) discuss the Kalman filter in relation to other presentations from the DAO on Four Dimensional Data Assimilation at this meeting. Although the designation "Kalman filter" is often used to describe the overarching work, the series of talks will show that the scientific software and the kind of parallelization techniques that are being developed at the DAO are very different depending on the type of problem being considered, the extent to which the problem is mission critical, and the degree of Software Engineering that has to be applied.
A class of quaternion Kalman filters.
Jahanchahi, Cyrus; Mandic, Danilo P
2014-03-01
The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters.
Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Attitude Representations for Kalman Filtering
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Bauer, Frank H. (Technical Monitor)
2001-01-01
The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.
MR fingerprinting reconstruction with Kalman filter.
Zhang, Xiaodi; Zhou, Zechen; Chen, Shiyang; Chen, Shuo; Li, Rui; Hu, Xiaoping
2017-09-01
Magnetic resonance fingerprinting (MR fingerprinting or MRF) is a newly introduced quantitative magnetic resonance imaging technique, which enables simultaneous multi-parameter mapping in a single acquisition with improved time efficiency. The current MRF reconstruction method is based on dictionary matching, which may be limited by the discrete and finite nature of the dictionary and the computational cost associated with dictionary construction, storage and matching. In this paper, we describe a reconstruction method based on Kalman filter for MRF, which avoids the use of dictionary to obtain continuous MR parameter measurements. With this Kalman filter framework, the Bloch equation of inversion-recovery balanced steady state free-precession (IR-bSSFP) MRF sequence was derived to predict signal evolution, and acquired signal was entered to update the prediction. The algorithm can gradually estimate the accurate MR parameters during the recursive calculation. Single pixel and numeric brain phantom simulation were implemented with Kalman filter and the results were compared with those from dictionary matching reconstruction algorithm to demonstrate the feasibility and assess the performance of Kalman filter algorithm. The results demonstrated that Kalman filter algorithm is applicable for MRF reconstruction, eliminating the need for a pre-define dictionary and obtaining continuous MR parameter in contrast to the dictionary matching algorithm. Copyright © 2017 Elsevier Inc. All rights reserved.
Practical Aspects of Kalman Filtering Implementation
1976-03-01
compjensation is the specific- foroe vector umeid by the navigation equations. The compu~ted platform rate required to keep the platformn level io...ranges computed from the WSMR cine theodelite tracking data) along with the computed range-rate histories are shown in Figure 12. There is an obvious...estimate computed from the cine theodolite data and three Kalman-filter estimates computed by the onboard softwvare using the software -cor rected PRS data
Optical Kalman filtering for missile guidance
NASA Technical Reports Server (NTRS)
Casasent, D.; Neuman, C. P.; Lycas, J.
1984-01-01
Optical systolic array processors constitute a powerful and general-purpose set of optical architectures with high computational rates. In this paper, Kalman filtering, a novel application for these architectures, is investigated. All required operations are detailed; their realization by optical and special-purpose analog electronics are specified; and the processing time of the system is quantified. The specific Kalman filter application chosen is for an air-to-air missile guidance controller. The architecture realized in this paper meets the design goal of a fully adaptive Kalman filter which processes a measurement every 1 msec. The vital issue of flow and pipelining of data and operations in a systolic array processor is addressed. The approach is sufficiently general and can be realized on an optical or digital systolic array processor.
NASA Astrophysics Data System (ADS)
Xiao, Guorui; Mayer, Michael; Heck, Bernhard; Sui, Lifen; Cong, Mingri
2017-04-01
Integer ambiguity resolution (AR) can significantly shorten the convergence time and improve the accuracy of Precise Point Positioning (PPP). Phase fractional cycle biases (FCB) originating from satellites destroy the integer nature of carrier phase ambiguities. To isolate the satellite FCB, observations from a global reference network are required. Firstly, float ambiguities containing FCBs are obtained by PPP processing. Secondly, the least squares method (LSM) is adopted to recover FCBs from all the float ambiguities. Finally, the estimated FCB products can be applied by the user to achieve PPP-AR. During the estimation of FCB, the LSM step can be very time-consuming, considering the large number of observations from hundreds of stations and thousands of epochs. In addition, iterations are required to deal with the one-cycle inconsistency among observations. Since the integer ambiguities are derived by directly rounding float ambiguities, the one-cycle inconsistency arises whenever the fractional parts of float ambiguities exceed the rounding boundary (e.g., 0.5 and -0.5). The iterations of LSM and the large number of observations require a long time to finish the estimation. Consequently, only a sparse global network containing a limited number of stations was processed in former research. In this paper, we propose to isolate the FCB based on a Kalman filter. The large number of observations is handled epoch-by-epoch, which significantly reduces the dimension of the involved matrix and accelerates the computation. In addition, it is also suitable for real-time applications. As for the one-cycle inconsistency, a pre-elimination method is developed to avoid the iteration of the whole process. According to the analysis of the derived satellite FCB products, we find that both wide-lane (WL) and narrow-lane (NL) FCB are very stable over time (e.g., WL FCB over several days rsp. NL FCB over tens of minutes). The stability implies that the satellite FCB can be removed
The discrete-time compensated Kalman filter
NASA Technical Reports Server (NTRS)
Lee, W. H.; Athans, M.
1978-01-01
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
Multirate and event-driven Kalman filters for helicopter flight
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Smith, Phillip; Suorsa, Raymond E.; Hussien, Bassam
1993-01-01
A vision-based obstacle detection system that provides information about objects as a function of azimuth and elevation is discussed. The range map is computed using a sequence of images from a passive sensor, and an extended Kalman filter is used to estimate range to obstacles. The magnitude of the optical flow that provides measurements for each Kalman filter varies significantly over the image depending on the helicopter motion and object location. In a standard Kalman filter, the measurement update takes place at fixed intervals. It may be necessary to use a different measurement update rate in different parts of the image in order to maintain the same signal to noise ratio in the optical flow calculations. A range estimation scheme that accepts the measurement only under certain conditions is presented. The estimation results from the standard Kalman filter are compared with results from a multirate Kalman filter and an event-driven Kalman filter for a sequence of helicopter flight images.
Kalman filter based control for Adaptive Optics
NASA Astrophysics Data System (ADS)
Petit, Cyril; Quiros-Pacheco, Fernando; Conan, Jean-Marc; Kulcsár, Caroline; Raynaud, Henri-François; Fusco, Thierry
2004-12-01
Classical Adaptive Optics suffer from a limitation of the corrected Field Of View. This drawback has lead to the development of MultiConjugated Adaptive Optics. While the first MCAO experimental set-ups are presently under construction, little attention has been paid to the control loop. This is however a key element in the optimization process especially for MCAO systems. Different approaches have been proposed in recent articles for astronomical applications : simple integrator, Optimized Modal Gain Integrator and Kalman filtering. We study here Kalman filtering which seems a very promising solution. Following the work of Brice Leroux, we focus on a frequential characterization of kalman filters, computing a transfer matrix. The result brings much information about their behaviour and allows comparisons with classical controllers. It also appears that straightforward improvements of the system models can lead to static aberrations and vibrations filtering. Simulation results are proposed and analysed thanks to our frequential characterization. Related problems such as model errors, aliasing effect reduction or experimental implementation and testing of Kalman filter control loop on a simplified MCAO experimental set-up could be then discussed.
NASA Astrophysics Data System (ADS)
Bürger, Gerd; Cane, Mark A.
1994-04-01
Data assimilation via the extended Kaiman filter can become problematic when the assimilating model is strongly nonlinear, primarily in connection with sharp, "switchlike" changes between different regimes of the system. The filter seems too inert to follow those switches quickly enough, a fact that can lead to a complete failure when the switches occur often enough. In this paper we replace the key feature of the filter, the use of local linearity for the error model update, with a principle that uses a more global approach through the utilization of a set of preselected regimes. The method uses all regime error models simultaneously. Being mutually incompatible, a compromise between the different error models is found through the use of a weighting function that reflects the `closeness' of the error model to the correct model. To test the interactive Kaiman filter a series of numerical experiments is performed using the double-well system and the well-known Lorenz system, and the results are compared to the extended Kaiman filter. It turns out that, depending on the set of preselected regimes, the performance is worse than, comparable to, or better than that of the extended Kaiman filter.
Beretta, Elisa; De Momi, Elena; Camomilla, Valentina; Cereatti, Andrea; Cappozzo, Aurelio; Ferrigno, Giancarlo
2014-09-01
In computer-assisted knee surgery, the accuracy of the localization of the femur centre of rotation relative to the hip-bone (hip joint centre) is affected by the unavoidable and untracked pelvic movements because only the femoral pose is acquired during passive pivoting manoeuvres. We present a dual unscented Kalman filter algorithm that allows the estimation of the hip joint centre also using as input the position of a pelvic reference point that can be acquired with a skin marker placed on the hip, without increasing the invasiveness of the surgical procedure. A comparative assessment of the algorithm was carried out using data provided by in vitro experiments mimicking in vivo surgical conditions. Soft tissue artefacts were simulated and superimposed onto the position of a pelvic landmark. Femoral pivoting made of a sequence of star-like quasi-planar movements followed by a circumduction was performed. The dual unscented Kalman filter method proved to be less sensitive to pelvic displacements, which were shown to be larger during the manoeuvres in which the femur was more adducted. Comparable accuracy between all the analysed methods resulted for hip joint centre displacements smaller than 1 mm (error: 2.2 ± [0.2; 0.3] mm, median ± [inter-quartile range 25%; inter-quartile range 75%]) and between 1 and 6 mm (error: 4.8 ± [0.5; 0.8] mm) during planar movements. When the hip joint centre displacement exceeded 6 mm, the dual unscented Kalman filter proved to be more accurate than the other methods by 30% during multi-planar movements (error: 5.2 ± [1.2; 1] mm). © IMechE 2014.
A quantum extended Kalman filter
NASA Astrophysics Data System (ADS)
Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.
2017-06-01
In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.
Fast Kalman filtering on quasilinear dendritic trees.
Paninski, Liam
2010-04-01
Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem-the vector of voltages at every compartment-is very high-dimensional: realistic multicompartmental models often have on the order of N = 10(4) compartments. Standard implementations of the Kalman filter require O(N (3)) time and O(N (2)) space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in O(N) time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in O(N) time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require O(N) time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations.
A comprehensive comparison of sigma-point Kalman filters applied on a complex maneuvering road
NASA Astrophysics Data System (ADS)
Al Shabi, Mohammad; Hatamleh, Khaled; Al Shaer, Samer; Salameh, Iyad; Gadsden, S. Andrew
2016-05-01
In this paper, a comprehensive comparison is made of the following sigma-point Kalman filters: unscented Kalman filter (UKF), cubature Kalman filter (CKF), and the central difference Kalman filter (CDKF). A simulation based on a complex maneuvering road (an s-path) is used as a benchmark problem. This paper studies the response, stability, robustness, convergence, and computational complexity of the filters. Future work will look at implementing the methods on a robot built for experimentation.
Speed adaptation as Kalman filtering.
Barraza, Jose F; Grzywacz, Norberto M
2008-10-01
If the purpose of adaptation is to fit sensory systems to different environments, it may implement an optimization of the system. What the optimum is depends on the statistics of these environments. Therefore, the system should update its parameters as the environment changes. A Kalman-filtering strategy performs such an update optimally by combining current estimations of the environment with those from the past. We investigate whether the visual system uses such a strategy for speed adaptation. We performed a matching-speed experiment to evaluate the time course of adaptation to an abrupt velocity change. Experimental results are in agreement with Kalman-modeling predictions for speed adaptation. When subjects adapt to a low speed and it suddenly increases, the time course of adaptation presents two phases, namely, a rapid decrease of perceived speed followed by a slower phase. In contrast, when speed changes from fast to slow, adaptation presents a single phase. In the Kalman-model simulations, this asymmetry is due to the prevalence of low speeds in natural images. However, this asymmetry disappears both experimentally and in simulations when the adapting stimulus is noisy. In both transitions, adaptation now occurs in a single phase. Finally, the model also predicts the change in sensitivity to speed discrimination produced by the adaptation.
Kalman Filtering Approach to Blind Equalization
1993-12-01
Update weighing probabilities (3.11) vi. Compute one step predictions p(j..Nb I X’) S(tlp (D,.,,,IX,) B. ADMISSIBILITY OF THE BLIND EQUALIZATION BY...NAVAL POSTGRADUATE SCHOOL Monterey, California •GR AD13 DTIC 94-07381 AR 0C199 THESIS S 0 LECTE4u KALMAN FILTERING APPROACH TO BLIND EQUALIZATION by...FILTERING APPROACH 5. FUNDING NUMBERS TO BLIND EQUALIZATION S. AUTHOR(S) Mehmet Kutlu 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) S
Mandel, Jan; Beezley, Jonathan D.; Cobb, Loren; Krishnamurthy, Ashok
2010-01-01
The FFT EnKF data assimilation method is proposed and applied to a stochastic cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF combines spatial statistics and ensemble filtering methodologies into a localized and computationally inexpensive version of EnKF with a very small ensemble, and it is further combined with the morphing EnKF to assimilate changes in the position of the epidemic. PMID:21031155
Application of Kalman filters to robot calibration
NASA Technical Reports Server (NTRS)
Whitney, D. E.; Junkel, E. F.
1983-01-01
This report explores new uses of Kalman filter theory in manufacturing systems (robots in particular). The Kalman filter allows the robot to read its sensors plus external sensors and learn from its experience. In effect, the robot is given primitive intelligence. The study, which is applicable to any type of powered kinematic linkage, focuses on the calibration of a manipulator.
A Kalman Filtering Perspective for Multiatlas Segmentation.
Gao, Yi; Zhu, Liangjia; Cates, Joshua; MacLeod, Rob S; Bouix, Sylvain; Tannenbaum, Allen
In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.
Objects tracking with adaptive correlation filters and Kalman filtering
NASA Astrophysics Data System (ADS)
Ontiveros-Gallardo, Sergio E.; Kober, Vitaly
2015-09-01
Object tracking is commonly used for applications such as video surveillance, motion based recognition, and vehicle navigation. In this work, a tracking system using adaptive correlation filters and robust Kalman prediction of target locations is proposed. Tracking is performed by means of multiple object detections in reduced frame areas. A bank of filters is designed from multiple views of a target using synthetic discriminant functions. An adaptive approach is used to improve discrimination capability of the synthesized filters adapting them to multiple types of backgrounds. With the help of computer simulation, the performance of the proposed algorithm is evaluated in terms of detection efficiency and accuracy of object tracking.
Phase and amplitude imaging from noisy images by Kalman filtering.
Waller, Laura; Tsang, Mankei; Ponda, Sameera; Yang, Se Young; Barbastathis, George
2011-01-31
We propose and demonstrate a computational method for complex-field imaging from many noisy intensity images with varying defocus, using an extended complex Kalman filter. The technique offers dynamic smoothing of noisy measurements and is recursive rather than iterative, so is suitable for adaptive measurements. The Kalman filter provides near-optimal results in very low-light situations and may be adapted to propagation through turbulent, scattering, or nonlinear media.
NASA Astrophysics Data System (ADS)
Bhattacharya, Kolahal; Banerjee, Sudeshna; Mondal, Naba K.
2016-07-01
In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work complements the form of the process noise matrix obtained by Mankel [1].
Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Kalman filter to update forest cover estimates
Raymond L. Czaplewski
1990-01-01
The Kalman filter is a statistical estimator that combines a time-series of independent estimates, using a prediction model that describes expected changes in the state of a system over time. An expensive inventory can be updated using model predictions that are adjusted with more recent, but less expensive and precise, monitoring data. The concepts of the Kalman...
UDU/T/ covariance factorization for Kalman filtering
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1980-01-01
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Theory and application of Kalman filtering
NASA Technical Reports Server (NTRS)
Teng, L.
1970-01-01
As a unified extension of a group of related mathematical procedures, Kalman filtering is of assistance in the design of aircraft- and ground-based guidance and navigation data reduction and display systems.
Reduced-Order Kalman Filtering for Processing Relative Measurements
NASA Technical Reports Server (NTRS)
Bayard, David S.
2008-01-01
A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented
Attitude Error Representations for Kalman Filtering
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Bauer, Frank H. (Technical Monitor)
2002-01-01
The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.
Numerical comparison of Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1977-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Numerical comparison of Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1977-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Kalman Filter Tracking on Parallel Architectures
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Lantz, Steven; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-12-01
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors, but the future will be even more exciting. In order to stay within the power density limits but still obtain Moore's Law performance/price gains, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Example technologies today include Intel's Xeon Phi and GPGPUs. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High Luminosity LHC, for example, this will be by far the dominant problem. The need for greater parallelism has driven investigations of very different track finding techniques including Cellular Automata or returning to Hough Transform. The most common track finding techniques in use today are however those based on the Kalman Filter [2]. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. They are known to provide high physics performance, are robust and are exactly those being used today for the design of the tracking system for HL-LHC. Our previous investigations showed that, using optimized data structures, track fitting with Kalman Filter can achieve large speedup both with Intel Xeon and Xeon Phi. We report here our further progress towards an end-to-end track reconstruction algorithm fully exploiting vectorization and parallelization techniques in a realistic simulation setup.
Kalman Filter Tracking on Parallel Architectures
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Krutelyov, Slava; Lantz, Steven; Lefebvre, Matthieu; McDermott, Kevin; Riley, Daniel; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2016-11-01
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors such as GPGPU, ARM and Intel MIC. In order to achieve the theoretical performance gains of these processors, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High-Luminosity Large Hadron Collider (HL-LHC), for example, this will be by far the dominant problem. The need for greater parallelism has driven investigations of very different track finding techniques such as Cellular Automata or Hough Transforms. The most common track finding techniques in use today, however, are those based on a Kalman filter approach. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. They are known to provide high physics performance, are robust, and are in use today at the LHC. Given the utility of the Kalman filter in track finding, we have begun to port these algorithms to parallel architectures, namely Intel Xeon and Xeon Phi. We report here on our progress towards an end-to-end track reconstruction algorithm fully exploiting vectorization and parallelization techniques in a simplified experimental environment.
Detection of atomic clock frequency jumps with the Kalman filter.
Galleani, Lorenzo; Tavella, Patrizia
2012-03-01
Frequency jumps are common anomalies in atomic clocks aboard navigation system satellites. These anomalous behaviors must be detected quickly and accurately to minimize the impact on user positioning. We develop a detector for frequency jumps based on the Kalman filter. Numerical simulations show that the detector is fast, with high probability of detection and low probability of false alarms. It also has a low computational cost because it takes advantage of the recursive nature of the Kalman filter. Therefore, it can be used in applications in which little computational power is available, such as aboard navigation system satellites.
Oceanographic applications of the Kalman filter
NASA Technical Reports Server (NTRS)
Barbieri, R. W.; Schopf, P. S.
1982-01-01
The Kalman filter is a data-processing algorithm with a distinguished history in systems theory. Its application to oceanographic problems is in the embryo stage. The behavior of the filter is demonstrated in the context of an internal equatorial Rossby wave propagation problem.
Reduced Kalman Filters for Clock Ensembles
NASA Technical Reports Server (NTRS)
Greenhall, Charles A.
2011-01-01
This paper summarizes the author's work ontimescales based on Kalman filters that act upon the clock comparisons. The natural Kalman timescale algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each post-measurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability.
Reduced Kalman Filters for Clock Ensembles
NASA Technical Reports Server (NTRS)
Greenhall, Charles A.
2011-01-01
This paper summarizes the author's work ontimescales based on Kalman filters that act upon the clock comparisons. The natural Kalman timescale algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each post-measurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability.
Kalman Filter for Spinning Spacecraft Attitude Estimation
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Sedlak, Joseph E.
2008-01-01
This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.
Recursive three-dimensional model reconstruction based on Kalman filtering.
Yu, Ying Kin; Wong, Kin Hong; Chang, Michael Ming Yuen
2005-06-01
A recursive two-step method to recover structure and motion from image sequences based on Kalman filtering is described in this paper. The algorithm consists of two major steps. The first step is an extended Kalman filter (EKF) for the estimation of the object's pose. The second step is a set of EKFs, one for each model point, for the refinement of the positions of the model features in the three-dimensional (3-D) space. These two steps alternate from frame to frame. The initial model converges to the final structure as the image sequence is scanned sequentially. The performance of the algorithm is demonstrated with both synthetic data and real-world objects. Analytical and empirical comparisons are made among our approach, the interleaved bundle adjustment method, and the Kalman filtering-based recursive algorithm by Azarbayejani and Pentland. Our approach outperformed the other two algorithms in terms of computation speed without loss in the quality of model reconstruction.
An improved conscan algorithm based on a Kalman filter
NASA Technical Reports Server (NTRS)
Eldred, D. B.
1994-01-01
Conscan is commonly used by DSN antennas to allow adaptive tracking of a target whose position is not precisely known. This article describes an algorithm that is based on a Kalman filter and is proposed to replace the existing fast Fourier transform based (FFT-based) algorithm for conscan. Advantages of this algorithm include better pointing accuracy, continuous update information, and accommodation of missing data. Additionally, a strategy for adaptive selection of the conscan radius is proposed. The performance of the algorithm is illustrated through computer simulations and compared to the FFT algorithm. The results show that the Kalman filter algorithm is consistently superior.
Unscented Kalman filters for polarization state tracking and phase noise mitigation.
Jignesh, Jokhakar; Corcoran, Bill; Zhu, Chen; Lowery, Arthur
2016-09-19
Simultaneous polarization and phase noise tracking and compensation is proposed based on an unscented Kalman filter (UKF). We experimentally demonstrate the tracking under noise-loading and after 800-km single-mode fiber transmission with 20-Gbaud QPSK and 16-QAM signals. These experiments show that the proposed UKF outperforms both conventional blind tracing algorithms and a previously proposed extended Kalman filter, at the cost of higher complexity. Additionally, we propose and test modified Kalman filter algorithms to reduce computational complexity.
Compressed state Kalman filter for large systems
NASA Astrophysics Data System (ADS)
Kitanidis, Peter K.
2015-02-01
The Kalman filter (KF) is a recursive filter that allows the assimilation of data in real time and has found numerous applications. In earth sciences, the method is applied to systems with very large state vectors obtained from the discretization of functions such as pressure, velocity, solute concentration, and voltage. With state dimension running in the millions, the implementation of the standard or textbook version of KF is very expensive and low-rank approximations have been devised such as EnKF and SEEK. Although widely applied, the error behavior of these methods is not adequately understood. This article focuses on very large linear systems and presents a complete computational method that scales roughly linearly with the dimension of the state vector. The method is suited for problems for which the effective rank of the state covariance matrix is much smaller than its dimension. This method is closest to SEEK but uses a fixed basis that should be selected in accordance with the characteristics of the problem, mainly the transition matrix and the system noise covariance. The method is matrix free, i.e., does not require computation of Jacobian matrices and uses the forward model as a black box. Computational results demonstrate the ability of the method to solve very large, say 106 , state vectors.
Kalman filter estimation model in flood forecasting
NASA Astrophysics Data System (ADS)
Husain, Tahir
Elementary precipitation and runoff estimation problems associated with hydrologic data collection networks are formulated in conjunction with the Kalman Filter Estimation Model. Examples involve the estimation of runoff using data from a single precipitation station and also from a number of precipitation stations. The formulations demonstrate the role of state-space, measurement, and estimation equations of the Kalman Filter Model in flood forecasting. To facilitate the formulation, the unit hydrograph concept and antecedent precipitation index is adopted in the estimation model. The methodology is then applied to estimate various flood events in the Carnation Creek of British Columbia.
Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.
Kelly, David; Majda, Andrew J; Tong, Xin T
2015-08-25
The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.
Concrete ensemble Kalman filters with rigorous catastrophic filter divergence
Kelly, David; Majda, Andrew J.; Tong, Xin T.
2015-01-01
The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature. PMID:26261335
Discovery of the Kalman filter as a practical tool for aerospace and industry
NASA Technical Reports Server (NTRS)
Mcgee, L. A.; Schmidt, S. F.
1985-01-01
The sequence of events which led the researchers at Ames Research Center to the early discovery of the Kalman filter shortly after its introduction into the literature is recounted. The scientific breakthroughs and reformulations that were necessary to transform Kalman's work into a useful tool for a specific aerospace application are described. The resulting extended Kalman filter, as it is now known, is often still referred to simply as the Kalman filter. As the filter's use gained in popularity in the scientific community, the problems of implementation on small spaceborne and airborne computers led to a square-root formulation of the filter to overcome numerical difficulties associated with computer word length. The work that led to this new formulation is also discussed, including the first airborne computer implementation and flight test. Since then the applications of the extended and square-root formulations of the Kalman filter have grown rapidly throughout the aerospace industry.
Q-Method Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Zanetti, Renato; Ainscough, Thomas; Christian, John; Spanos, Pol D.
2012-01-01
A new algorithm is proposed that smoothly integrates non-linear estimation of the attitude quaternion using Davenport s q-method and estimation of non-attitude states through an extended Kalman filter. The new method is compared to a similar existing algorithm showing its similarities and differences. The validity of the proposed approach is confirmed through numerical simulations.
Real-time shipboard orbit determination using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Brammer, R. F.
1974-01-01
The real-time tracking and orbit determination program used on board the NASA tracking ship, the USNS Vanguard, is described in this paper. The computer program uses a variety of filtering algorithms, including an extended Kalman filter, to derive real-time orbit determinations (position-velocity state vectors) from shipboard tracking and navigation data. Results from Apollo missions are given to show that orbital parameters can be estimated quickly and accurately using these methods.
NASA Technical Reports Server (NTRS)
1979-01-01
The computer program DEKFIS (discrete extended Kalman filter/smoother), formulated for aircraft and helicopter state estimation and data consistency, is described. DEKFIS is set up to pre-process raw test data by removing biases, correcting scale factor errors and providing consistency with the aircraft inertial kinematic equations. The program implements an extended Kalman filter/smoother using the Friedland-Duffy formulation.
Simplification of the Kalman filter for meteorological data assimilation
NASA Technical Reports Server (NTRS)
Dee, Dick P.
1991-01-01
The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.
Simplification of the Kalman filter for meteorological data assimilation
NASA Technical Reports Server (NTRS)
Dee, Dick P.
1991-01-01
The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.
NASA Astrophysics Data System (ADS)
Hut, Rolf; Amisigo, Barnabas A.; Steele-Dunne, Susan; van de Giesen, Nick
2015-12-01
Reduction of Used Memory Ensemble Kalman Filtering (RumEnKF) is introduced as a variant on the Ensemble Kalman Filter (EnKF). RumEnKF differs from EnKF in that it does not store the entire ensemble, but rather only saves the first two moments of the ensemble distribution. In this way, the number of ensemble members that can be calculated is less dependent on available memory, and mainly on available computing power (CPU). RumEnKF is developed to make optimal use of current generation super computer architecture, where the number of available floating point operations (flops) increases more rapidly than the available memory and where inter-node communication can quickly become a bottleneck. RumEnKF reduces the used memory compared to the EnKF when the number of ensemble members is greater than half the number of state variables. In this paper, three simple models are used (auto-regressive, low dimensional Lorenz and high dimensional Lorenz) to show that RumEnKF performs similarly to the EnKF. Furthermore, it is also shown that increasing the ensemble size has a similar impact on the estimation error from the three algorithms.
Kalman Filter Residual Expert System.
1987-12-01
Matching). 5. SITAN (Sandia Inertial Terrain Aided Navigation). 6. JTIDS Datalink (Joint Tactical Information Distribution System). The ATN uses a Basic...INS, GPS3 S3 INS, SITAN S4 INS, Doppler, SAR/LANTIRN S5 IIS3 Doppler, IBaro S6 GPS3, Baro 0S7 INS, Doppler S8 INS, SAR/LANTIRN S9 INS S11 Doppler...decrease while those of filters A and B increase. Sin , the target has stopped accelerating, the best filter to select would be filter A. ltow- ever, the
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.
Kalman filtering for spacecraft attitude estimation
NASA Technical Reports Server (NTRS)
Lefferts, E. J.; Markley, F. L.; Shuster, M. D.
1982-01-01
Several schemes in current use for sequential estimation of spacecraft attitude using Kalman filters are examined. These differ according to their treatment of the attitude error, namely: using the complete four-component quaternion; using a truncated quaternion in which one of the components has been eliminated; or using a quaternion referred to approximate body-fixed axes. These schemes are examined for the case of a spacecraft carrying line-of-sight attitude sensors and three-axis gyros whose measurements are corrupted by noise on both the drift rate and the drift-rate ramp. The analysis of the covariance is carried out in detail. The historical development of Kalman filtering of attitude is reviewed.
Kalman filtering for spacecraft attitude estimation
NASA Technical Reports Server (NTRS)
Lefferts, E. J.; Markley, F. L.; Shuster, M. D.
1982-01-01
Several schemes in current use for sequential estimation of spacecraft attitude using Kalman filters are examined. These differ according to their treatment of the attitude error, namely: using the complete four-component quaternion; using a truncated quaternion in which one of the components has been eliminated; or using a quaternion referred to approximate body-fixed axes. These schemes are examined for the case of a spacecraft carrying line-of-sight attitude sensors and three-axis gyros whose measurements are corrupted by noise on both the drift rate and the drift-rate ramp. The analysis of the covariance is carried out in detail. The historical development of Kalman filtering of attitude is reviewed.
NASA Astrophysics Data System (ADS)
Ahrens, H.; Argin, F.; Klinkenbusch, L.
2013-07-01
The non-invasive and radiation-free imaging of the electrical activity of the heart with Electrocardiography (ECG) or Magnetocardiography (MCG) can be helpful for physicians for instance in the localization of the origin of cardiac arrhythmia. In this paper we compare two Kalman Filter algorithms for the solution of a nonlinear state-space model and for the subsequent imaging of the activation/depolarization times of the heart muscle: the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The algorithms are compared for simulations of a (6×6) magnetometer array, a torso model with piecewise homogeneous conductivities, 946 current dipoles located in a small part of the heart (apex), and several noise levels. It is found that for all tested noise levels the convergence of the activation times is faster for the UKF.
Unscented Kalman Filter for Brain-Machine Interfaces
Li, Zheng; O'Doherty, Joseph E.; Hanson, Timothy L.; Lebedev, Mikhail A.; Henriquez, Craig S.; Nicolelis, Miguel A. L.
2009-01-01
Brain machine interfaces (BMIs) are devices that convert neural signals into commands to directly control artificial actuators, such as limb prostheses. Previous real-time methods applied to decoding behavioral commands from the activity of populations of neurons have generally relied upon linear models of neural tuning and were limited in the way they used the abundant statistical information contained in the movement profiles of motor tasks. Here, we propose an n-th order unscented Kalman filter which implements two key features: (1) use of a non-linear (quadratic) model of neural tuning which describes neural activity significantly better than commonly-used linear tuning models, and (2) augmentation of the movement state variables with a history of n-1 recent states, which improves prediction of the desired command even before incorporating neural activity information and allows the tuning model to capture relationships between neural activity and movement at multiple time offsets simultaneously. This new filter was tested in BMI experiments in which rhesus monkeys used their cortical activity, recorded through chronically implanted multielectrode arrays, to directly control computer cursors. The 10th order unscented Kalman filter outperformed the standard Kalman filter and the Wiener filter in both off-line reconstruction of movement trajectories and real-time, closed-loop BMI operation. PMID:19603074
Application of Kalman filtering to spacecraft range residual prediction
NASA Technical Reports Server (NTRS)
Madrid, G. A.; Bierman, G. J.
1977-01-01
One function of the Deep Space Network is validation of the range data that they receive. In this paper we present an automated online sequential range predictor which shows promise of significantly reducing computational and manpower expenditures. The proposed algorithm, a U-D covariance factored Kalman filter, is demonstrated by processing a four-month record of Viking spacecraft data taken enroute to Mars.
Application of Kalman Filter on Multisensor Fusion Tracking
1992-12-01
AD-A257 335 NAVAL POSTGRADUATE SCHOOL Monterey, California DTIC ELCT THESIS APPLICATION OF KALMAN FILTER ON MULTISENSOR FUSION TRACKING by Brian...WORK UNIT ELEMENT NO NO NO ACCESSION NO 11 TITLE (Include Security Classification) PPLICATION OF KALMAN FILTER ON MULTISENSOR FUSION TRACKING 12...FIELD GROUP SUB-GROUP fusion, Kalman Filter Multisensor Fusion Tracking 19 ABSTRACT (Continue on reverse if necessary and identify by block number)he
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2006-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).
Spacecraft Dynamics Should be Considered in Kalman Filter Attitude Estimation
NASA Technical Reports Server (NTRS)
Yang, Yaguang; Zhou, Zhiqiang
2016-01-01
Kalman filter based spacecraft attitude estimation has been used in some high-profile missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no comparison on which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This treatment is more elegant in mathematics and easier in computation. We use some simulation example to verify our claims.
Kalman filter estimation of human pilot-model parameters
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Roland, V. R.
1975-01-01
The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters.
Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem
NASA Astrophysics Data System (ADS)
Man, J.; Li, W.; Zeng, L.; Wu, L.
2015-12-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the Polynomial Chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so called "cure of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF is even more computationally expensive than EnKF. Motivated by recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problem. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to alleviate the inconsistency between model parameters and states. The performance of RAPCKF is tested by unsaturated flow numerical cases. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.
Flexible Generation of Kalman Filter Code
NASA Technical Reports Server (NTRS)
Richardson, Julian; Wilson, Edward
2006-01-01
Domain-specific program synthesis can automatically generate high quality code in complex domains from succinct specifications, but the range of programs which can be generated by a given synthesis system is typically narrow. Obtaining code which falls outside this narrow scope necessitates either 1) extension of the code generator, which is usually very expensive, or 2) manual modification of the generated code, which is often difficult and which must be redone whenever changes are made to the program specification. In this paper, we describe adaptations and extensions of the AUTOFILTER Kalman filter synthesis system which greatly extend the range of programs which can be generated. Users augment the input specification with a specification of code fragments and how those fragments should interleave with or replace parts of the synthesized filter. This allows users to generate a much wider range of programs without their needing to modify the synthesis system or edit generated code. We demonstrate the usefulness of the approach by applying it to the synthesis of a complex state estimator which combines code from several Kalman filters with user-specified code. The work described in this paper allows the complex design decisions necessary for real-world applications to be reflected in the synthesized code. When executed on simulated input data, the generated state estimator was found to produce comparable estimates to those produced by a handcoded estimator
Lagrangian data assimilation and hybrid particle - ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Apte, Amit; Slivinski, Laura; Spiller, Elaine; Jones, Chris
2017-04-01
Lagrangian data assimilation (LaDA) refers to the use of observations provided by (pseudo-)Lagrangian instruments such as drifters, floats, and gliders, which are important sources of surface and subsurface data for the oceans. After giving a brief introduction to augmented state approach to LaDA, I will discuss issues specific to this problem, in particular, due to the highly nonlinear Lagrangian dynamics leading to non-Gaussian probability distributions. (doi:10.5194/npg-20-329-2013) I will then describe a recent proposal for a hybrid particle-Kalman filter method for LaDA. The main motivation for the hybrid filter is as follows: particle filters work well for nonlinear systems but the computational effort required grows exponentially with dimensions of the system, whereas ensemble Kalman filters are successful in dealing with large dimensional problems which are close to being linear and Gaussian. Thus neither of them work well for high dimensional, highly nonlinear systems. On the other hand, in LaDA, the dynamics of the Lagrangian drifters is typically low dimensional but highly nonlinear, whereas the flow in which they move is high dimensional but less nonlinear. The hybrid filter attempts to combine the strengths of both these filters and the specific structure of the Lagrangian dynamics, by using an ensemble Kalman filter for the velocity flow while at the same time using a particle filter for the Lagrangian drifters. I present promising results about the efficacy of this proposed method for low and high dimensional problems and discuss its shortcomings. (doi:10.1175/MWR-D-14-00051.1, doi:10.1007/978-3-319-25138-7_24)
Multiscale Systems, Kalman Filters, and Riccati Equations
2006-01-01
Rauch -Tung-Striebel algorithm- consisting of a fine-to-coarse Kalman-filter-like sweep followed by a coarse-to-fine smoothing step- was developed. In...MODELS 5 wv(t) = w(t) - E[w(t)lx(t)] (2.9) E[w(t)ifT(t)] = I- B T(t)P -l(t)B(t) - (t) (2.10) In [1] we derive a generalization of the Rauch -Tung...particular, this framework leads to an extremely efficient and highly parallelizable scale-recursive optimal estimation algorithm generalizing the Rauch
Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters
NASA Astrophysics Data System (ADS)
Sun, Tao; Xin, Ming
2017-05-01
Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.
Global systems for mobile position tracking using Kalman and Lainiotis filters.
Assimakis, Nicholas; Adam, Maria
2014-01-01
We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement in x-axis and y-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.
Training neural networks using sequential extended Kalman filtering
Plumer, E.S.
1995-03-01
Recent work has demonstrated the use of the extended Kalman filter (EKF) as an alternative to gradient-descent backpropagation when training multi-layer perceptrons. The EKF approach significantly improves convergence properties but at the cost of greater storage and computational complexity. Feldkamp et al. have described a decoupled version of the EKF which preserves the training advantages of the general EKF but which reduces the storage and computational requirements. This paper reviews the general and decoupled EKF approaches and presents sequentialized versions which provide further computational savings over the batch forms. The usefulness of the sequentialized EKF algorithms is demonstrated on a pattern classification problem.
VLBI TRF determination via Kalman filtering
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Karbon, Maria; Nilsson, Tobias; Glaser, Susanne; Balidakis, Kyriakos; Heinkelmann, Robert; Schuh, Harald
2015-04-01
The determination of station positions is one of the primary tasks for space geodetic techniques. Station coordinate offsets are usually determined with respect to a linear coordinate model after removing elastic displacements caused by mass redistributions within the Earth's system. In operational VLBI analysis, the coordinate offsets are estimated in a least-squares adjustment as a constant over the duration of a 24-hour VLBI experiment. Terrestrial reference frames (TRF) are usually derived by adjusting the normal equations that contain the 24-hour constant offsets in order to estimate a linear model, possibly including breaks, for the station positions. We have created a VLBI TRF solution without the assumption of negligible subdaily motion and of linear behavior on longer time scales by applying a Kalman filter. As a preparation for the upcoming VLBI Global Observing System (VGOS), which aims for continuous observations that are available in real-time, a Kalman filter has been implemented into the VLBI software VieVS@GFZ. In addition to the real-time capability, the filter offers the possibility of stochastically modeling the parameters of interest. For station coordinates, changes in a subdaily time frame occur, for instance, from un- or mismodeled geophysical effects. The models for tidal and non-tidal ocean, atmosphere, and hydrology loading are known to have deficiencies and inconsistencies which propagate into the estimated station coordinates. The stochastic model of the Kalman filter can be adapted to take these subdaily effects into account. Comparing the resulting station coordinate time series with daily values from a least squares fit, we have investigated to what extent and in which regions the loading models currently have deficiencies. Due to the high correlation between station height and tropospheric delays, it is possible that errors in one group of parameters are partly absorbed by the other group. To detect problems with correlations and to
Software Would Largely Automate Design of Kalman Filter
NASA Technical Reports Server (NTRS)
Chuang, Jason C. H.; Negast, William J.
2005-01-01
Embedded Navigation Filter Automatic Designer (ENFAD) is a computer program being developed to automate the most difficult tasks in designing embedded software to implement a Kalman filter in a navigation system. The most difficult tasks are selection of error states of the filter and tuning of filter parameters, which are timeconsuming trial-and-error tasks that require expertise and rarely yield optimum results. An optimum selection of error states and filter parameters depends on navigation-sensor and vehicle characteristics, and on filter processing time. ENFAD would include a simulation module that would incorporate all possible error states with respect to a given set of vehicle and sensor characteristics. The first of two iterative optimization loops would vary the selection of error states until the best filter performance was achieved in Monte Carlo simulations. For a fixed selection of error states, the second loop would vary the filter parameter values until an optimal performance value was obtained. Design constraints would be satisfied in the optimization loops. Users would supply vehicle and sensor test data that would be used to refine digital models in ENFAD. Filter processing time and filter accuracy would be computed by ENFAD.
Telescope Multi-Field Wavefront Control with a Kalman Filter
NASA Technical Reports Server (NTRS)
Lou, John Z.; Redding, David; Sigrist, Norbert; Basinger, Scott
2008-01-01
An effective multi-field wavefront control (WFC) approach is demonstrated for an actuated, segmented space telescope using wavefront measurements at the exit pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the wavefront control process to further improve the robustness of the optical alignment of the telescope will also be discussed. Through a comparison of WFC performances between on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based computer simulation results will be presented and discussed.
Restoration of color images by multichannel Kalman filtering
NASA Technical Reports Server (NTRS)
Galatsanos, Nikolas P.; Chin, Roland T.
1991-01-01
A Kalman filter for optimal restoration of multichannel images is presented. This filter is derived using a multichannel semicausal image model that includes between-channel degradation. Both stationary and nonstationary image models are developed. This filter is implemented in the Fourier domain and computation is reduced from O(Lambda3N3M4) to O(Lambda3N3M2) for an M x M N-channel image with degradation length Lambda. Color (red, green, and blue (RGB)) images are used as examples of multichannel images, and restoration in the RGB and YIQ domains is investigated. Simulations are presented in which the effectiveness of this filter is tested for different types of degradation and different image model estimates.
A recursive solution for a fading memory filter derived from Kalman filter theory
NASA Technical Reports Server (NTRS)
Statman, J. I.
1986-01-01
A simple recursive solution for a class of fading memory tracking filters is presented. A fading memory filter provides estimates of filter states based on past measurements, similar to a traditional Kalman filter. Unlike a Kalman filter, an exponentially decaying weight is applied to older measurements, discounting their effect on present state estimates. It is shown that Kalman filters and fading memory filters are closely related solutions to a general least squares estimator problem. Closed form filter transfer functions are derived for a time invariant, steady state, fading memory filter. These can be applied in loop filter implementation of the Deep Space Network (DSN) Advanced Receiver carrier phase locked loop (PLL).
Statistical process control of a Kalman filter model.
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A
2014-09-26
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations.
Statistical Process Control of a Kalman Filter Model
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A.
2014-01-01
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations. PMID:25264959
Human movement tracking based on Kalman filter
NASA Astrophysics Data System (ADS)
Zhang, Yi; Luo, Yuan
2006-11-01
During the rehabilitation process of the post-stroke patients is conducted, their movements need to be localized and learned so that incorrect movement can be instantly modified or tuned. Therefore, tracking these movement becomes vital and necessary for the rehabilitative course. In the technologies of human movement tracking, the position prediction of human movement is very important. In this paper, we first analyze the configuration of the human movement system and choice of sensors. Then, The Kalman filter algorithm and its modified algorithm are proposed and to be used to predict the position of human movement. In the end, on the basis of analyzing the performance of the method, it is clear that the method described can be used to the system of human movement tracking.
Kalman filtering approach to blind equalization
NASA Astrophysics Data System (ADS)
Kutlu, Mehmet
1993-12-01
Digital communication systems suffer from the channel distortion problem which introduces errors due to intersymbol interference. The solution to this problem is provided by equalizers which use a training sequence to adapt to the channel. However in many cases in which a training sequence is unfeasible, the channel must be adapted blindly. Most of the blind equalization algorithms known so far have problems of convergence to local minima. Our intention is to offer an alternative approach by using extended Kalman filtering and hidden Markov models. They seem to yield more efficient algorithms which take the statistics of the transmitted sequence into consideration. The theoretical development of these new algorithms is discussed in this thesis. Also these algorithms have been simulated under different conditions. The results of simulations and comparisons with existing systems are provided. The models for simulations are presented as MATLAB codes.
ON THE CONVERGENCE OF THE ENSEMBLE KALMAN FILTER
Mandel, Jan; Cobb, Loren; Beezley, Jonathan D.
2013-01-01
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and Lp bounds on the ensemble then give Lp convergence. PMID:24843228
Study on GPS attitude determination system aided INS using adaptive Kalman filter
NASA Astrophysics Data System (ADS)
Bian, Hongwei; Jin, Zhihua; Tian, Weifeng
2005-10-01
A marine INS/GPS (inertial navigation system/global positioning system) adaptive navigation system is presented in this paper. The GPS with two antennae providing vessel attitude is selected as the auxiliary system to fuse with INS. The Kalman filter is the most frequently used algorithm in the integrated navigation system, which is capable of estimating INS errors online based on the measured errors between INS and GPS. The conventional Kalman filter (CKF) assumes that the statistics of the noise of each sensor are given. As long as the noise distributions do not change, the Kalman filter will give the optimal estimation. However, the GPS receiver will be disturbed easily and thus temporally changing measurement noise will join into the outputs of GPS, which will lead to performance degradation of the Kalman filter. Many researchers introduce a fuzzy logic control method into innovation-based adaptive estimation Kalman filtering (IAE-AKF) algorithm, and accordingly propose various adaptive Kalman filters. However, how to design the fuzzy logic controller is a very complicated problem, which is still without a convincing solution. A novel IAE-AKF is proposed herein, which is based on the maximum likelihood criterion for the proper computation of the filter innovation covariance and hence of the filter gain. The approach is direct and simple without having to establish fuzzy inference rules. After having deduced the proposed IAE-AKF algorithm theoretically in detail, the approach is tested in the developed INS/GPS integrated marine navigation system. Real field test results show that the adaptive Kalman filter outperforms the CKF with higher accuracy and robustness. It is demonstrated that this proposed approach is a valid solution for the unknown changing measurement noise existing in the Kalman filter.
A Stabilized Sparse-Matrix U-D Square-Root Implementation of a Large-State Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Boggs, D.; Ghil, M.; Keppenne, C.
1995-01-01
The full nonlinear Kalman filter sequential algorithm is, in theory, well-suited to the four-dimensional data assimilation problem in large-scale atmospheric and oceanic problems. However, it was later discovered that this algorithm can be very sensitive to computer roundoff, and that results may cease to be meaningful as time advances. Implementations of a modified Kalman filter are given.
The discrete Kalman filtering approach for seismic signals deconvolution
Kurniadi, Rizal; Nurhandoko, Bagus Endar B.
2012-06-20
Seismic signals are a convolution of reflectivity and seismic wavelet. One of the most important stages in seismic data processing is deconvolution process; the process of deconvolution is inverse filters based on Wiener filter theory. This theory is limited by certain modelling assumptions, which may not always valid. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The main advantage of Kalman filtering is capability of technique to handling continually time varying models and has high resolution capabilities. In this work, we use discrete Kalman filter that it was combined with primitive deconvolution. Filtering process works on reflectivity function, hence the work flow of filtering is started with primitive deconvolution using inverse of wavelet. The seismic signals then are obtained by convoluting of filtered reflectivity function with energy waveform which is referred to as the seismic wavelet. The higher frequency of wavelet gives smaller wave length, the graphs of these results are presented.
Longitudinal Factor Score Estimation Using the Kalman Filter.
ERIC Educational Resources Information Center
Oud, Johan H.; And Others
1990-01-01
How longitudinal factor score estimation--the estimation of the evolution of factor scores for individual examinees over time--can profit from the Kalman filter technique is described. The Kalman estimates change more cautiously over time, have lower estimation error variances, and reproduce the LISREL program latent state correlations more…
Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2005-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.
Stable Kalman filters for processing clock measurement data
NASA Technical Reports Server (NTRS)
Clements, P. A.; Gibbs, B. P.; Vandergraft, J. S.
1989-01-01
Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.
Kalman filtering for real-time navigator processing.
Spincemaille, Pascal; Nguyen, Thanh D; Prince, Martin R; Wang, Yi
2008-07-01
Navigator echoes are used in high-resolution cardiac MRI for tracking physiological motion to suppress motion artifacts. Alternatives to the conventional diaphragm navigator such as the cardiac fat navigator and the k-space center signal (self-navigator) were developed to monitor heart motion directly. These navigator data can be noisy or may contain undesirable frequency components. Real-time filtering of navigator data without delay, as opposed to the previously used retrospective frequency band filtering, is required for effective prospective navigator gating. One of the commonly used real-time filtering techniques is the Kalman filter, which adaptively estimates motion and suppresses measurement noise by using Bayesian statistics and a motion model. The Kalman filter is investigated in this work to filter noise and distinguish cardiac and respiratory components in navigator data. Preliminary imaging data demonstrate the feasibility of real-time Kalman filtering for prospective respiratory self-gating in CINE cardiac MRI.
Stochastic stability of the derivative unscented Kalman filter
NASA Astrophysics Data System (ADS)
Hu, Gao-Ge; Gao, She-Sheng; Zhong, Yong-Min; Gao, Bing-Bing
2015-07-01
This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discrete-time system with linear system state equation. The first paper established a derivative unscented Kalman filter (DUKF) to eliminate the redundant computational load of the unscented Kalman filter (UKF) due to the use of unscented transformation (UT) in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique. Project supported by the National Natural Science Foundation of China (Grant No. 61174193) and the Doctorate Foundation of Northwestern Polytechnical University, China (Grant No. CX201409).
NASA Technical Reports Server (NTRS)
Schmidt, S. F.; Flanagan, P. F.; Sorenson, J. A.
1978-01-01
A Kalman filter for aircraft terminal area and landing navigation was implemented and flight tested in the NASA Ames STOLAND avionics computer onboard a Twin Otter aircraft. This system combines navaid measurements from TACAN, MODILS, air data, radar altimeter sensors along with measurements from strap-down accelerometer and attitude angle sensors. The flight test results demonstrate that the Kalman filter provides improved estimates of the aircraft position and velocity as compared with estimates from the more standard complementary filter. The onboard computer implementation requirements to achieve this improved performance are discussed.
Initial Flight Results of the TRMM Kalman Filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Morgenstern, Wendy M.
1998-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls attitude based on the Earth Sensor Assembly (ESA) output. After a potential single point failure in the ESA was identified, the contingency attitude determination method chosen to backup the ESA-based system was a sixth-order extended Kalman filter that uses magnetometer and digital sun sensor measurements. A brief description of the TRMM Kalman filter will be given, including some implementation issues and algorithm heritage. Operational aspects of the Kalman filter and some failure detection and correction will be described. The Kalman filter was tested in a sun pointing attitude and in a nadir pointing attitude during the in-orbit checkout period, and results from those tests will be presented. This paper will describe some lessons learned from the experience of the TRMM team.
Kalman filter data assimilation: Targeting observations and parameter estimation
Bellsky, Thomas Kostelich, Eric J.; Mahalov, Alex
2014-06-15
This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.
Kalman filter data assimilation: targeting observations and parameter estimation.
Bellsky, Thomas; Kostelich, Eric J; Mahalov, Alex
2014-06-01
This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.
Initial flight results of the TRMM Kalman filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Morgenstern, Wendy M.
1998-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls attitude based on the Earth Sensor Assembly (ESA) output. After a potential single point failure in the ESA was identified, the contingency attitude determination method chosen to backup the ESA-based system was a sixth-order extended Kalman filter that uses magnetometer and digital sun sensor measurements. A brief description of the TRMM Kalman filter will be given, including some implementation issues and algorithm heritage. Operational aspects of the Kalman filter and some failure detection and correction will be described. The Kalman filter was tested in a sun pointing attitude and in a nadir pointing attitude during the in-orbit checkout period, and results from those tests will be presented. This paper will describe some lessons learned from the experience of the TRMM team.
Nonlinear Kalman filters for atmospheric chemistry models
NASA Astrophysics Data System (ADS)
Segers, Arjo; Heemink, Arnold; Verlaan, Martin; van Loon, Maarten
Four non linear Kaiman filter implementations are applied to an atmospheric chemistry model. The type of non linear dynamics present in such a model complicates an accurate forecast of the state of the system. Therefore, different non linear forecast methods are applied as part of the Reduced Rank Square Root formulation of the Kaiman filter, either based on ensemble statistics or on linearizations. A filter based on minimal exact sampling proves to produce an accurate forecast of state and covariance, using only a few model evaluations. Ensemble statistics are able to produce even more accurate results, but with the cost of at least a double amount of computation time.
Multiharmonic tracking using sigma-point Kalman filter.
Kim, Sunghan; Paul, Anindya S; Wan, Eric A; McNames, James
2008-01-01
Several groups have proposed the state-space approach to track time-varying frequencies ofmulti-harmonic quasi-periodic signals contaminated with white Gaussian noise. We compared the extended Kalman filter (EKF) and sigma-point Kalman filter (SPKF) algorithms on this problem. On average, the SPKF outperformed the EKF and more accurately tracked the instantaneous frequency over a wide range of signal-to-noise (SNR) ratios.
3D hand tracking using Kalman filter in depth space
NASA Astrophysics Data System (ADS)
Park, Sangheon; Yu, Sunjin; Kim, Joongrock; Kim, Sungjin; Lee, Sangyoun
2012-12-01
Hand gestures are an important type of natural language used in many research areas such as human-computer interaction and computer vision. Hand gestures recognition requires the prior determination of the hand position through detection and tracking. One of the most efficient strategies for hand tracking is to use 2D visual information such as color and shape. However, visual-sensor-based hand tracking methods are very sensitive when tracking is performed under variable light conditions. Also, as hand movements are made in 3D space, the recognition performance of hand gestures using 2D information is inherently limited. In this article, we propose a novel real-time 3D hand tracking method in depth space using a 3D depth sensor and employing Kalman filter. We detect hand candidates using motion clusters and predefined wave motion, and track hand locations using Kalman filter. To verify the effectiveness of the proposed method, we compare the performance of the proposed method with the visual-based method. Experimental results show that the performance of the proposed method out performs visual-based method.
Multivariate localization methods for ensemble Kalman filtering
NASA Astrophysics Data System (ADS)
Roh, S.; Jun, M.; Szunyogh, I.; Genton, M. G.
2015-05-01
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (entry-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
Multivariate localization methods for ensemble Kalman filtering
NASA Astrophysics Data System (ADS)
Roh, S.; Jun, M.; Szunyogh, I.; Genton, M. G.
2015-12-01
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1976-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1976-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Motion estimation using point cluster method and Kalman filter.
Senesh, M; Wolf, A
2009-05-01
The most frequently used method in a three dimensional human gait analysis involves placing markers on the skin of the analyzed segment. This introduces a significant artifact, which strongly influences the bone position and orientation and joint kinematic estimates. In this study, we tested and evaluated the effect of adding a Kalman filter procedure to the previously reported point cluster technique (PCT) in the estimation of a rigid body motion. We demonstrated the procedures by motion analysis of a compound planar pendulum from indirect opto-electronic measurements of markers attached to an elastic appendage that is restrained to slide along the rigid body long axis. The elastic frequency is close to the pendulum frequency, as in the biomechanical problem, where the soft tissue frequency content is similar to the actual movement of the bones. Comparison of the real pendulum angle to that obtained by several estimation procedures--PCT, Kalman filter followed by PCT, and low pass filter followed by PCT--enables evaluation of the accuracy of the procedures. When comparing the maximal amplitude, no effect was noted by adding the Kalman filter; however, a closer look at the signal revealed that the estimated angle based only on the PCT method was very noisy with fluctuation, while the estimated angle based on the Kalman filter followed by the PCT was a smooth signal. It was also noted that the instantaneous frequencies obtained from the estimated angle based on the PCT method is more dispersed than those obtained from the estimated angle based on Kalman filter followed by the PCT method. Addition of a Kalman filter to the PCT method in the estimation procedure of rigid body motion results in a smoother signal that better represents the real motion, with less signal distortion than when using a digital low pass filter. Furthermore, it can be concluded that adding a Kalman filter to the PCT procedure substantially reduces the dispersion of the maximal and minimal
NASA Astrophysics Data System (ADS)
Tao, Dongwang; Li, Hui; Ma, Qiang
2016-04-01
Complete structure identification of complicate nonlinear system using extend Kalman filter (EKF) or unscented Kalman filter (UKF) may have the problems of divergence, huge computation and low estimation precision due to the large dimension of the extended state space for the system. In this article, a decentralized identification method of hysteretic system based on the joint EKF and UKF is proposed. The complete structure is divided into linear substructures and nonlinear substructures. The substructures are identified from the top to the bottom. For the linear substructure, EKF is used to identify the extended space including the displacements, velocities, stiffness and damping coefficients of the substructures, using the limited absolute accelerations and the identified interface force above the substructure. Similarly, for the nonlinear substructure, UKF is used to identify the extended space including the displacements, velocities, stiffness, damping coefficients and control parameters for the hysteretic Bouc-Wen model and the force at the interface of substructures. Finally a 10-story shear-type structure with multiple inter-story hysteresis is used for numerical simulation and is identified using the decentralized approach, and the identified results are compared with those using only EKF or UKF for the complete structure identification. The results show that the decentralized approach has the advantage of more stability, relative less computation and higher estimation precision.
Recursive least squares estimation and Kalman filtering by systolic arrays
NASA Technical Reports Server (NTRS)
Chen, M. J.; Yao, K.
1988-01-01
One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).
Recursive least squares estimation and Kalman filtering by systolic arrays
NASA Technical Reports Server (NTRS)
Chen, M. J.; Yao, K.
1988-01-01
One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).
Efficient Decoding With Steady-State Kalman Filter in Neural Interface Systems
Malik, Wasim Q.; Truccolo, Wilson; Brown, Emery N.; Hochberg, Leigh R.
2011-01-01
The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5 ± 0.5 s (mean ± s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25 ± 3 single units by a factor of 7.0 ± 0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems. PMID:21078582
Efficient decoding with steady-state Kalman filter in neural interface systems.
Malik, Wasim Q; Truccolo, Wilson; Brown, Emery N; Hochberg, Leigh R
2011-02-01
The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5±0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.
Estimation of Permeability Field via Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Jafarpour, B.; McLaughlin, D. B.
2005-12-01
History matching, as commonly referred to in petroleum industry, is an inverse parameter estimation problem which uses sparse observations of the states of the reservoir/aquifer (e.g. pressure) to tune spatially distributed parameters such as permeability and porosity. Even though significant progress is made in improving history matching algorithms, current history matching techniques are not suitable for real-time updating of the reservoir models using the frequent observations obtained form smart/intelligent fields and time-lapsed seismic. Recursive data assimilation algorithms, such as those based on the Kalman filter, can update the reservoir model (by tuning unknown parameters) without including previously used data, thereby saving computational cost. They are very convenient to apply with reservoir simulators, do not require adjoint models, and can easily incorporate 4D seismic attributes as areal measurements. Further, these algorithms readily provide an estimate of the uncertainty of the updated parameters and the states as a byproduct of the estimation process. This fits very well into the uncertainty and risk analysis aspects of the reservoir management. Our research focuses on the application of Ensemble Kalman Filter (EnKF) technique in updating reservoir models by integrating static/dynamic point and areal measurements such as frequent production and 4D seismic data. We present our preliminary results from the application of the EnKF in updating reservoir models with and without tuning heterogeneous permeability fields. A discussion of the issues and challenges encountered in our preliminary work will be provided.
Tractography from HARDI using an intrinsic unscented Kalman filter.
Cheng, Guang; Salehian, Hesamoddin; Forder, John R; Vemuri, Baba C
2015-01-01
A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multitensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multitensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords.
NASA Astrophysics Data System (ADS)
Silbert, Mark; Mazzuchi, Thomas; Sarkani, Shahram
2011-09-01
Providing accurate state estimates of a maneuvering target is an important problem. This problem occurs when tracking maneuvering boats or even people wandering around. In our earlier paper, a specialized grid-based filter (GBF) was introduced as an effective method to produce accurate state estimates of a target moving in two dimensions, while requiring only a two-dimensional grid. The paper showed that this GBF produces accurate state estimates because the filter can capture the kinematic constraints of the target directly, and thus account for them in the estimation process. In this paper, the relative performance of a GBF to a Kalman filter is investigated. The state estimates (position and velocity) from a GBF are compared to those from a Kalman filter, against a maneuvering target. This study will employ the comparison paradigm presented by Kirubarajan and Bar-Shalom. The paradigm incrementally increases the maneuverability of a target to determine how the two different track filters compare as the target becomes more maneuverable. The intent of this study is to determine how maneuverable the target must be to gain the benefit from a GBF over a Kalman filter. The paper will discuss the target motion model, the GBF implementation, and the Kalman filter used for the study. Our results show that the GBF outperforms a Kalman filter, especially as the target becomes more maneuverable. A disadvantage of the GBF is that it is more computational than a Kalman filter. The paper will discuss the grid and sample sizing needed to obtain quality estimates from a GBF. It will be shown that the sizes are much smaller than what may be expected and is quite stable over a large range of sizes. Furthermore, this GBF can exploit parallelization of the computations, making the processing time significantly less.
Realizations and performances of least-squares estimation and Kalman filtering by systolic arrays
Chen, M.J.
1987-01-01
Fast least-squares (LS) estimation and Kalman-filtering algorithms utilizing systolic-array implementation are studied. Based on a generalized systolic QR algorithm, a modified LS method is proposed and shown to have superior computational and inter-cell connection complexities, and is more practical for systolic-array implementation. After whitening processing, the Kalman filter can be formulated as a SRIF data-processing problem followed by a simple LS operation. This approach simplifies the computational structure, and is more reliable when the system has singular or near singular coefficient matrix. To improve the throughput rate of the systolic Kalman filter, a topology for stripe QR processing is also proposed. By skewing the order of input matrices, a fully pipelined systolic Kalman-filtering operation can be achieved. With the number of processing units of the O(n/sup 2/), the system throughput rate becomes of the O(n). The numerical properties of the systolic LS estimation and the Kalman filtering algorithms under finite word-length effect are studied via analysis and computer simulations, and are compared with that of conventional approaches. Fault tolerance of the LS estimation algorithm is also discussed. It is shown that by using a simple bypass register, reasonable estimation performance is still possible for a transient defective processing unit.
Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters
NASA Astrophysics Data System (ADS)
Branicki, M.; Gershgorin, B.; Majda, A. J.
2012-02-01
The filtering skill for turbulent signals from nature is often limited by errors due to utilizing an imperfect forecast model. In particular, real-time filtering and prediction when very limited or no a posteriori analysis is possible (e.g. spread of pollutants, storm surges, tsunami detection, etc.) introduces a number of additional challenges to the problem. Here, a suite of filters implementing stochastic parameter estimation for mitigating model error through additive and multiplicative bias correction is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities associated with positive finite-time Lyapunov exponents to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF), used as a benchmark here, involves exact formulas for propagating the mean and covariance of the augmented forecast model including the unresolved parameters. The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various moment closure errors which are enhanced by additional model errors due to incorrect parameters inducing additive and multiplicative stochastic biases. The estimation skill of the unresolved stochastic parameters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many turbulent regimes for both parameter estimation and filtering; moreover, regimes of filter divergence for the linear tangent filter are identified. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with more general model errors, as well as
Application of Consider Covariance to the Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Lundberg, John B.
1996-01-01
The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.
Switching Kalman filter for failure prognostic
NASA Astrophysics Data System (ADS)
Lim, Chi Keong Reuben; Mba, David
2015-02-01
The use of condition monitoring (CM) data to predict remaining useful life have been growing with increasing use of health and usage monitoring systems on aircraft. There are many data-driven methodologies available for the prediction and popular ones include artificial intelligence and statistical based approach. The drawback of such approaches is that they require a lot of failure data for training which can be scarce in practice. In lieu of this, methods using state-space and regression-based models that extract information from the data history itself have been explored. However, such methods have their own limitations as they utilize a single time-invariant model which does not represent changing degradation path well. This causes most degradation modeling studies to focus only on segments of their CM data that behaves close to the assumed model. In this paper, a state-space based method; the Switching Kalman Filter (SKF), is adopted for model estimation and life prediction. The SKF approach however, uses multiple models from which the most probable model is inferred from the CM data using Bayesian estimation before it is applied for prediction. At the same time, the inference of the degradation model itself can provide maintainers with more information for their planning. This SKF approach is demonstrated with a case study on gearbox bearings that were found defective from the Republic of Singapore Air Force AH64D helicopter. The use of in-service CM data allows the approach to be applied in a practical scenario and results showed that the developed SKF approach is a promising tool to support maintenance decision-making.
A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.
Mobile indoor localization using Kalman filter and trilateration technique
NASA Astrophysics Data System (ADS)
Wahid, Abdul; Kim, Su Mi; Choi, Jaeho
2015-12-01
In this paper, an indoor localization method based on Kalman filtered RSSI is presented. The indoor communications environment however is rather harsh to the mobiles since there is a substantial number of objects distorting the RSSI signals; fading and interference are main sources of the distortion. In this paper, a Kalman filter is adopted to filter the RSSI signals and the trilateration method is applied to obtain the robust and accurate coordinates of the mobile station. From the indoor experiments using the WiFi stations, we have found that the proposed algorithm can provide a higher accuracy with relatively lower power consumption in comparison to a conventional method.
An optimal modification of a Kalman filter for time scales
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
2003-01-01
The Kalman filter in question, which was implemented in the time scale algorithm TA(NIST), produces time scales with poor short-term stability. A simple modification of the error covariance matrix allows the filter to produce time scales with good stability at all averaging times, as verified by simulations of clock ensembles.
An optimal modification of a Kalman filter for time scales
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
2003-01-01
The Kalman filter in question, which was implemented in the time scale algorithm TA(NIST), produces time scales with poor short-term stability. A simple modification of the error covariance matrix allows the filter to produce time scales with good stability at all averaging times, as verified by simulations of clock ensembles.
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-05-09
The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.
A modified iterative ensemble Kalman filter data assimilation method
NASA Astrophysics Data System (ADS)
Xu, Baoxiong; Bai, Yulong; Wang, Yizhao; Li, Zhe; Ma, Boyang
2017-08-01
High nonlinearity is a typical characteristic associated with data assimilation systems. Additionally, iterative ensemble based methods have attracted a large amount of research attention, which has been focused on dealing with nonlinearity problems. To solve the local convergence problem of the iterative ensemble Kalman filter, a modified iterative ensemble Kalman filter algorithm was put forward, which was based on a global convergence strategy from the perspective of a Gauss-Newton iteration. Through self-adaption, the step factor was adjusted to enable every iteration to approach expected values during the process of the data assimilation. A sensitivity experiment was carried out in a low dimensional Lorenz-63 chaotic system, as well as a Lorenz-96 model. The new method was tested via ensemble size, observation variance, and inflation factor changes, along with other aspects. Meanwhile, comparative research was conducted with both a traditional ensemble Kalman filter and an iterative ensemble Kalman filter. The results showed that the modified iterative ensemble Kalman filter algorithm was a data assimilation method that was able to effectively estimate a strongly nonlinear system state.
Investigation of Adaptive Robust Kalman Filtering Algorithms for GPS/DR Navigation System Filters
NASA Astrophysics Data System (ADS)
Elzoghby, MOSTAFA; Arif, USMAN; Li, FU; Zhi Yu, XI
2017-03-01
The conventional Kalman filter (KF) algorithm is suitable if the characteristic noise covariance for states as well as measurements is readily known but in most cases these are unknown. Similarly robustness is required instead of smoothing if states are changing abruptly. Such an adaptive as well as robust Kalman filter is vital for many real time applications, like target tracking and navigating aerial vehicles. A number of adaptive as well as robust Kalman filtering methods are available in the literature. In order to investigate the performance of some of these methods, we have selected three different Kalman filters, namely Sage Husa KF, Modified Adaptive Robust KF and Adaptively Robust KF, which are easily simulate able as well as implementable for real time applications. These methods are simulated for land based vehicle and the results are compared with conventional Kalman filter. Results show that the Modified Adaptive Robust KF is best amongst the selected methods and can be used for Navigation applications.
AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS
NASA Technical Reports Server (NTRS)
Lehtinen, B.
1994-01-01
AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user
Kalman Filter for Calibrating a Telescope Focal Plane
NASA Technical Reports Server (NTRS)
Kang, Bryan; Bayard, David
2006-01-01
The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.
An extended Kalman filter based automatic frequency control loop
NASA Technical Reports Server (NTRS)
Hinedi, S.
1988-01-01
An Automatic Frequency Control (AFC) loop based on an Extended Kalman Filter (EKF) is introduced and analyzed in detail. The scheme involves an EKF which operates on a modified set of data in order to track the frequency of the incoming signal. The algorithm can also be viewed as a modification to the well known cross-product AFC loop. A low carrier-to-noise ratio (CNR), high-dynamic environment is used to test the algorithm and the probability of loss-of-lock is assessed via computer simulations. The scheme is best suited for scenarios in which the frequency error variance can be compromised to achieve a very low operating CNR threshold. This technique can easily be incorporated in the Advanced Receiver (ARX), requiring minimum software modifications.
Tracking whole hand kinematics using extended Kalman filter.
Fu, Qiushi; Santello, Marco
2010-01-01
This paper describes the general procedure, model construction, and experimental results of tracking whole hand kinematics using extended Kalman filter (EKF) based on data recorded from active surface markers. We used a hand model with 29 degrees of freedom that consists of hand global posture, wrist, and digits. The marker protocol had 4 markers on the distal forearm and 20 markers on the dorsal surface of the joints of the digits. To reduce computational load, we divided the state space into four sub-spaces, each of which were estimated with an EKF in a specific order. We tested our framework and found reasonably accurate results (2-4 mm tip position error) when sampling tip to tip pinch at 120 Hz.
Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Zhou, Weidong; Hou, Jiaxin; Liu, Lu; Sun, Tian; Liu, Jing
2017-04-01
The integrated navigation system is used to estimate the position, velocity, and attitude of a vehicle with the output of inertial sensors. This paper concentrates on the problem of the INS/GPS integrated navigation system design and simulation. The structure of the INS/GPS integrated navigation system is made up of four parts: 1) GPS receiver, 2) Inertial Navigation System, 3) Extended Kalman filter, and 4) Integrated navigation scheme. Afterwards, we illustrate how to simulate the integrated navigation system with the extended Kalman filter by measuring position, velocity and attitude. Particularly, the extended Kalman filter can estimate states of the nonlinear system in the noisy environment. In extended Kalman filter, the estimation of the state vector and the error covariance matrix are computed by steps: 1) time update and 2) measurement update. Finally, the simulation process is implemented by Matlab, and simulation results prove that the error rate of statement measuring is lower when applying the extended Kalman filter in the INS/GPS integrated navigation system.
Systolic VLSI array for implementing the Kalman filter algorithm
NASA Technical Reports Server (NTRS)
Chang, Jaw J. (Inventor); Yeh, Hen-Geul (Inventor)
1989-01-01
A method and apparatus for processing signals representative of a complex matrix/vector equation is disclosed and claimed. More particularly, signals representing an orderly sequence of the combined matrix and vector equation, known as a Kalman filter algorithm, is processed in real-time in accordance with the principles of this invention. The Kalman filter algorithm is converted into a Faddeev algorithm, which is a matrix-only algorithm. The Faddeev algorithm is modified to represent both the matrix and vector portions of the Kalman filter algorithm. The modified Faddeev algorithm is embodied into electrical signals which are applied as inputs to a systolic array processor, which performs triangulation and nullification on the input signals, and delivers an output signal to a real-time utilization circuit.
Nonlinear dynamical system identification using unscented Kalman filter
NASA Astrophysics Data System (ADS)
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Tropospheric delay determination by Kalman filtering VLBI data
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Zus, Florian; Dick, Galina; Deng, Zhiguo; Wickert, Jens; Heinkelmann, Robert; Schuh, Harald
2015-09-01
The troposphere is one of the most important error sources for space geodetic techniques relying on radio signals. Since it is not possible to model the wet part of the tropospheric delay with sufficient accuracy, it needs to be estimated from the observational data. In the analysis of very long baseline interferometry (VLBI) data, the parameter estimation is routinely performed using a least squares adjustment. In this paper, we investigate the application of a Kalman filter for parameter estimation, specifically focusing on the tropospheric delays. The main advantages of a Kalman filter are its real-time capability and stochastic approach. We focused on the latter and derived stochastic models for VLBI zenith wet delays, taking into account temporal and location-based differences. Compared to a static noise model, the quality of station coordinates, also estimated in the Kalman filter, increased as a result. In terms of baseline length and station coordinate repeatabilities, this improvement amounted to 2.3 %. Additionally, we compared the Kalman filter and least squares results for VLBI with zenith wet delays derived from GPS (Global Positioning System), water vapor radiometers, and ray tracing in numerical weather models. The agreement of the Kalman filter VLBI solution with respect to water vapor radiometer data was larger than that of the least squares solution by 6-15 %. Our investigations are based on selected VLBI data (CONT campaigns) that are closest to how future VLBI infrastructure is designed to operate. With the aim for continuous and near real-time parameter estimation and the promising results which we have achieved in this study, we expect Kalman filtering to grow in importance in VLBI analysis.
Adaptive robust Kalman filtering for precise point positioning
NASA Astrophysics Data System (ADS)
Guo, Fei; Zhang, Xiaohong
2014-10-01
The optimality of precise point postioning (PPP) solution using a Kalman filter is closely connected to the quality of the a priori information about the process noise and the updated mesurement noise, which are sometimes difficult to obtain. Also, the estimation enviroment in the case of dynamic or kinematic applications is not always fixed but is subject to change. To overcome these problems, an adaptive robust Kalman filtering algorithm, the main feature of which introduces an equivalent covariance matrix to resist the unexpected outliers and an adaptive factor to balance the contribution of observational information and predicted information from the system dynamic model, is applied for PPP processing. The basic models of PPP including the observation model, dynamic model and stochastic model are provided first. Then an adaptive robust Kalmam filter is developed for PPP. Compared with the conventional robust estimator, only the observation with largest standardized residual will be operated by the IGG III function in each iteration to avoid reducing the contribution of the normal observations or even filter divergence. Finally, tests carried out in both static and kinematic modes have confirmed that the adaptive robust Kalman filter outperforms the classic Kalman filter by turning either the equivalent variance matrix or the adaptive factor or both of them. This becomes evident when analyzing the positioning errors in flight tests at the turns due to the target maneuvering and unknown process/measurement noises.
Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.
Xie, Xianming
2016-08-22
A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.
Cuff-less blood pressure measurement using pulse arrival time and a Kalman filter
NASA Astrophysics Data System (ADS)
Zhang, Qiang; Chen, Xianxiang; Fang, Zhen; Xue, Yongjiao; Zhan, Qingyuan; Yang, Ting; Xia, Shanhong
2017-02-01
The present study designs an algorithm to increase the accuracy of continuous blood pressure (BP) estimation. Pulse arrival time (PAT) has been widely used for continuous BP estimation. However, because of motion artifact and physiological activities, PAT-based methods are often troubled with low BP estimation accuracy. This paper used a signal quality modified Kalman filter to track blood pressure changes. A Kalman filter guarantees that BP estimation value is optimal in the sense of minimizing the mean square error. We propose a joint signal quality indice to adjust the measurement noise covariance, pushing the Kalman filter to weigh more heavily on measurements from cleaner data. Twenty 2 h physiological data segments selected from the MIMIC II database were used to evaluate the performance. Compared with straightforward use of the PAT-based linear regression model, the proposed model achieved higher measurement accuracy. Due to low computation complexity, the proposed algorithm can be easily transplanted into wearable sensor devices.
Osborn, Graham Wordsworth
2010-12-01
Several regions of the brain which represent kinematic quantities are grouped under a single state-estimator framework. A theoretic effort is made to predict the activity of each cell population as a function of time using a simple state estimator (the Kalman filter). Three brain regions are considered in detail: the parietal cortex (reaching cells), the hippocampus (place cells and head-direction cells), and the entorhinal cortex (grid cells). For the reaching cell and place cell examples, we compute the perceived probability distributions of objects in the environment as a function of the observations. For the grid cell example, we show that the elastic behavior of the grids observed in experiments arises naturally from the Kalman filter. To our knowledge, the application of a tensor Kalman filter to grid cells is completely novel.
On the equivalence of Kalman filtering and least-squares estimation
NASA Astrophysics Data System (ADS)
Mysen, E.
2017-01-01
The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
NASA Astrophysics Data System (ADS)
Souza, André L. G.; Ishihara, João Y.; Ferreira, Henrique C.; Borges, Renato A.; Borges, Geovany A.
2016-12-01
The present work proposes a new approach for an antenna pointing system for satellite tracking. Such a system uses the received signal to estimate the beam pointing deviation and then adjusts the antenna pointing. The present work has two contributions. First, the estimation is performed by a Kalman filter based conical scan technique. This technique uses the Kalman filter avoiding the batch estimator and applies a mathematical manipulation avoiding the linearization approximations. Secondly, a control technique based on the model predictive control together with an explicit state feedback solution are obtained in order to reduce the computational burden. Numerical examples illustrate the results.
2014-01-01
total computational time needed for the Kalman filters is under 25% of the total signal length rendering it possible to perform the filtering in real-time. Conclusions It is possible to measure in real-time heart and breathing rates using an adaptive Kalman filter approach. Adapting the Kalman filter matrices improves the estimation results and makes the filter universally deployable when measuring cardiorespiratory signals. PMID:24886253
Foussier, Jerome; Teichmann, Daniel; Jia, Jing; Misgeld, Berno; Leonhardt, Steffen
2014-05-09
Extracting cardiorespiratory signals from non-invasive and non-contacting sensor arrangements, i.e. magnetic induction sensors, is a challenging task. The respiratory and cardiac signals are mixed on top of a large and time-varying offset and are likely to be disturbed by measurement noise. Basic filtering techniques fail to extract relevant information for monitoring purposes. We present a real-time filtering system based on an adaptive Kalman filter approach that separates signal offsets, respiratory and heart signals from three different sensor channels. It continuously estimates respiration and heart rates, which are fed back into the system model to enhance performance. Sensor and system noise covariance matrices are automatically adapted to the aimed application, thus improving the signal separation capabilities. We apply the filtering to two different subjects with different heart rates and sensor properties and compare the results to the non-adaptive version of the same Kalman filter. Also, the performance, depending on the initialization of the filters, is analyzed using three different configurations ranging from best to worst case. Extracted data are compared with reference heart rates derived from a standard pulse-photoplethysmographic sensor and respiration rates from a flowmeter. In the worst case for one of the subjects the adaptive filter obtains mean errors (standard deviations) of -0.2 min(-1) (0.3 min(-1)) and -0.7 bpm (1.7 bpm) (compared to -0.2 min(-1) (0.4 min(-1)) and 42.0 bpm (6.1 bpm) for the non-adaptive filter) for respiration and heart rate, respectively. In bad conditions the heart rate is only correctly measurable when the Kalman matrices are adapted to the target sensor signals. Also, the reduced mean error between the extracted offset and the raw sensor signal shows that adapting the Kalman filter continuously improves the ability to separate the desired signals from the raw sensor data. The average total computational time needed
Filtering Meteoroid Flights Using Multiple Unscented Kalman Filters
NASA Astrophysics Data System (ADS)
Sansom, E. K.; Bland, P. A.; Rutten, M. G.; Paxman, J.; Towner, M. C.
2016-11-01
Estimator algorithms are immensely versatile and powerful tools that can be applied to any problem where a dynamic system can be modeled by a set of equations and where observations are available. A well designed estimator enables system states to be optimally predicted and errors to be rigorously quantified. Unscented Kalman filters (UKFs) and interactive multiple models can be found in methods from satellite tracking to self-driving cars. The luminous trajectory of the Bunburra Rockhole fireball was observed by the Desert Fireball Network in mid-2007. The recorded data set is used in this paper to examine the application of these two techniques as a viable approach to characterizing fireball dynamics. The nonlinear, single-body system of equations, used to model meteoroid entry through the atmosphere, is challenged by gross fragmentation events that may occur. The incorporation of the UKF within an interactive multiple model smoother provides a likely solution for when fragmentation events may occur as well as providing a statistical analysis of the state uncertainties. In addition to these benefits, another advantage of this approach is its automatability for use within an image processing pipeline to facilitate large fireball data analyses and meteorite recoveries.
Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems.
Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing
2016-07-26
This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches.
Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems
Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing
2016-01-01
This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches. PMID:27472336
Lall, Pradeep; Wei, Junchao; Davis, J Lynn
2014-06-24
Abstract— Solid-state lighting (SSL) luminaires containing light emitting diodes (LEDs) have the potential of seeing excessive temperatures when being transported across country or being stored in non-climate controlled warehouses. They are also being used in outdoor applications in desert environments that see little or no humidity but will experience extremely high temperatures during the day. This makes it important to increase our understanding of what effects high temperature exposure for a prolonged period of time will have on the usability and survivability of these devices. Traditional light sources “burn out” at end-of-life. For an incandescent bulb, the lamp life is defined by B50 life. However, the LEDs have no filament to “burn”. The LEDs continually degrade and the light output decreases eventually below useful levels causing failure. Presently, the TM-21 test standard is used to predict the L70 life of LEDs from LM-80 test data. Several failure mechanisms may be active in a LED at a single time causing lumen depreciation. The underlying TM-21 Model may not capture the failure physics in presence of multiple failure mechanisms. Correlation of lumen maintenance with underlying physics of degradation at system-level is needed. In this paper, Kalman Filter (KF) and Extended Kalman Filters (EKF) have been used to develop a 70-percent Lumen Maintenance Life Prediction Model for LEDs used in SSL luminaires. Ten-thousand hour LM-80 test data for various LEDs have been used for model development. System state at each future time has been computed based on the state space at preceding time step, system dynamics matrix, control vector, control matrix, measurement matrix, measured vector, process noise and measurement noise. The future state of the lumen depreciation has been estimated based on a second order Kalman Filter model and a Bayesian Framework. Life prediction of L70 life for the LEDs used in SSL luminaires from KF and EKF based models have
State estimation Kalman filter using optical processings Noise statistics known
NASA Technical Reports Server (NTRS)
Jackson, J.; Casasent, D.
1984-01-01
Reference is made to a study by Casasent et al. (1983), which gave a description of a frequency-multiplexed acoustooptic processor and showed how it was capable of performing all the individual operations required in Kalman filtering. The data flow and organization of all required operations however, were not detailed in that study. Consideration is given here to a simpler Kalman filter state estimation problem. Equally spaced time-sampled intervals (k times T sub s, with k the iterative time index) are assumed. It is further assumed that the system noise vector w and the measurement noise vector v are uncorrelated and Gaussian distributed and that the noise statistics (Q and R) and the system model (Phi, Gamma, H) are known. The error covariance matrix P and the extrapolated error covariance matrix M can thus be precomputed and the Kalman gain matrix K sub k can be precomputed and stored for each input time sample.
Parallelized unscented Kalman filters for carrier recovery in coherent optical communication.
Jignesh, Jokhakar; Corcoran, Bill; Lowery, Arthur
2016-07-15
We show that unscented Kalman filters can be used to mitigate local oscillator phase noise and to compensate carrier frequency offset in coherent single-carrier optical communication systems. A parallel processing architecture implementing the unscented Kalman filter is proposed, improving upon a previous parallelized linear Kalman filter (LKF) implementation.
Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters
2010-01-01
Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters WILLIAM F. CAMPBELL, CRAIG H. BISHOP, AND DANIEL HODYSS Naval...being used in the operational data assimila- tion system at Environment Canada for their ensemble Corresponding author address: Dr. William F...here. Acknowledgments. The authors thank Jeff Whitaker, Peter Houtekamer, Herschel Mitchell, and our anony- mous reviewer for their valuable comments. We
Nonlinear Kalman filtering in the presence of additive noise
NASA Astrophysics Data System (ADS)
Kraszewski, Tomasz; Czopik, Grzegorz
2017-04-01
Each modern navigation or localization system designed for ground, water or air objects should provide information on the estimated parameters continuously and as accurately as possible. The implementation of such a process requires the application to operate on non-linear transformations. The defined expectations necessitate the use of nonlinear filtering elements with particular emphasis on the extended Kalman filter. The article presents the simulation research elements of this filter type in the aspect of the possibility of its practical implementation. In the initial phase of the study the conclusion was based on nonlinear one-dimensional model. The possibility of improving the precision of the output through the use of unscented Kalman filters was also analyzed.
Ensemble Kalman filtering in presence of inequality constraints
NASA Astrophysics Data System (ADS)
van Leeuwen, P. J.
2009-04-01
Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.
Identification of observer/Kalman filter Markov parameters: Theory and experiments
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh; Horta, Lucas G.; Longman, Richard W.
1991-01-01
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.
Identification of observer/Kalman filter Markov parameters - Theory and experiments
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh; Horta, Lucas G.; Longman, Richard W.
1991-01-01
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on a ten-bay truss structure.
Adaptive distributed Kalman filtering with wind estimation for astronomical adaptive optics.
Massioni, Paolo; Gilles, Luc; Ellerbroek, Brent
2015-12-01
In the framework of adaptive optics (AO) for astronomy, it is a common assumption to consider the atmospheric turbulent layers as "frozen flows" sliding according to the wind velocity profile. For this reason, having knowledge of such a velocity profile is beneficial in terms of AO control system performance. In this paper we show that it is possible to exploit the phase estimate from a Kalman filter running on an AO system in order to estimate wind velocity. This allows the update of the Kalman filter itself with such knowledge, making it adaptive. We have implemented such an adaptive controller based on the distributed version of the Kalman filter, for a realistic simulation of a multi-conjugate AO system with laser guide stars on a 30 m telescope. Simulation results show that this approach is effective and promising and the additional computational cost with respect to the distributed filter is negligible. Comparisons with a previously published slope detection and ranging wind profiler are made and the impact of turbulence profile quantization is assessed. One of the main findings of the paper is that all flavors of the adaptive distributed Kalman filter are impacted more significantly by turbulence profile quantization than the static minimum mean square estimator which does not incorporate wind profile information.
Adaptive error covariances estimation methods for ensemble Kalman filters
Zhen, Yicun; Harlim, John
2015-08-01
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for using information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.
Development of Real-Time Error Ellipses as an Indicator of Kalman Filter Performance.
1984-03-01
S q often than 3 to 5 seconds. However, before the HP-86 can e considered feasible for real-time Kalman filtr procssinz, more investigaz ion i: needi...Subtitle) S. TYPE OF REPORT & PERIOD COVERED Development of Real-Time Error Master’s Thesis; Ellipses as an Indicator of Kalman March 1984 Filter...SUPP.LEETARY NOTES 19. KEY WORDS (Cmntine on reveo ole, It ndeeaey md Identil by block number) Error Ellipsoids; Kalman Filter; Extended Kalman Filter
Star spot location estimation using Kalman filter for star tracker.
Liu, Hai-bo; Yang, Jian-kun; Wang, Jiong-qi; Tan, Ji-chun; Li, Xiu-jian
2011-04-20
Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient.
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation.
Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng
2016-09-20
A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
Estimating short-period dynamics using an extended Kalman filter
NASA Technical Reports Server (NTRS)
Bauer, Jeffrey E.; Andrisani, Dominick
1990-01-01
An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.
A Hierarchical Bayes Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Tsyrulnikov, Michael; Rakitko, Alexander
2017-01-01
A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filters.
Nonlinear Kalman Filtering for acoustic emission source localization in anisotropic panels.
Dehghan Niri, E; Farhidzadeh, A; Salamone, S
2014-02-01
Nonlinear Kalman Filtering is an established field in applied probability and control systems, which plays an important role in many practical applications from target tracking to weather and climate prediction. However, its application for acoustic emission (AE) source localization has been very limited. In this paper, two well-known nonlinear Kalman Filtering algorithms are presented to estimate the location of AE sources in anisotropic panels: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These algorithms are applied to two cases: velocity profile known (CASE I) and velocity profile unknown (CASE II). The algorithms are compared with a more traditional nonlinear least squares method. Experimental tests are carried out on a carbon-fiber reinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers to validate the proposed approaches. AE sources are simulated using an instrumented miniature impulse hammer. In order to evaluate the performance of the algorithms, two metrics are used: (1) accuracy of the AE source localization and (2) computational cost. Furthermore, it is shown that both EKF and UKF can provide a confidence interval of the estimated AE source location and can account for uncertainty in time of flight measurements.
Nonlinear control of valves in diesel engines using the derivative-free nonlinear Kalman Filter
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan
2014-10-01
The paper studies robust nonlinear control for gas exchange valves in diesel engines, with the use of the Derivative-free nonlinear Kalman Filter. Robust control of gas exchange valves is important for improving the efficiency in the operation of diesel engines. By applying differential flatness theory the initial nonlinear model of the system is transformed in the linear canonical (Brunovsky) form. For the latter model it is possible to design a state feedback controller that enables accurate tracking of the valve's reference set-points. To estimate the nonmeasurable state variables of the model and the unknown external disturbances the Derivative-free nonlinear Kalman Filter is used as a disturbance observer. The Derivative-free nonlinear Kalman Filter consists of the standard Kalman Filter recursion on the linearized equivalent model of the valve and of computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. Evaluation tests are performed for assessing the performance of the proposed control scheme.
Model-Based Engine Control Architecture with an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Csank, Jeffrey T.; Connolly, Joseph W.
2016-01-01
This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.
Model-Based Engine Control Architecture with an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Csank, Jeffrey T.; Connolly, Joseph W.
2016-01-01
This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.
Upper Atmosphere Research Satellite (UARS) onboard attitude determination using a Kalman filter
NASA Technical Reports Server (NTRS)
Garrick, Joseph
1993-01-01
The Upper Atmospheric Research Satellite (UARS) requires a highly accurate knowledge of its attitude to accomplish its mission. Propagation of the attitude state using gyro measurements is not sufficient to meet the accuracy requirements, and must be supplemented by a observer/compensation process to correct for dynamics and observation anomalies. The process of amending the attitude state utilizes a well known method, the discrete Kalman Filter. This study is a sensitivity analysis of the discrete Kalman Filter as implemented in the UARS Onboard Computer (OBC). The stability of the Kalman Filter used in the normal on-orbit control mode within the OBC, is investigated for the effects of corrupted observations and nonlinear errors. Also, a statistical analysis on the residuals of the Kalman Filter is performed. These analysis is based on simulations using the UARS Dynamics Simulator (UARSDSIM) and compared against attitude requirements as defined by General Electric (GE). An independent verification of expected accuracies is performed using the Attitude Determination Error Analysis System (ADEAS).
State estimation using parallel extended Kalman filters on nonlinear measurements
Sheives, T.C.
1980-01-01
The extended Kalman filter applied to state estimation using nonlinear measurements has demonstrated divergence in many applications involving large initial uncertainties because of invalid linearizations performed by the filter on the nonlinear measurement functions. No quantitative results can be found as to how invalid these linearizations must be before divergence occurs. An attempt is made to fill this void by deriving the extended Kalman filter as an approximate nonlinear least squares estimator, through the minimization of a measurement squared error function. The convergence of the extended Kalman filter is then determined by examining the squared error function and verifying the usefulness of this function through Monte Carlo simulation. The results of this analysis are then used to specify parameters for the Gaussian sum approximation. Simulation results for nonlinear measurements generated by harmonic and Gauss-Markov processes demonstrate that successful state estimation occurs using the Gaussian sum approximation, through proper parameter specification obtained by the convergence analysis. This technique is then applied to estimating the errors in an inertial navigation system through the use of nonlinear radar altimeter measurements and terrain elevation data. The results of applying this technique to terrain-aided navigation demonstrate that the Gaussian sum approximation provides good terrain-aided navigation performance for large initial uncertainties.
An Adaptive Kalman Filter Using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
An Adaptive Kalman Filter using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
An Adaptive Kalman Filter using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
An Adaptive Kalman Filter Using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
Spitzer Instrument Pointing Frame (IPF) Kalman Filter Algorithm
NASA Technical Reports Server (NTRS)
Bayard, David S.; Kang, Bryan H.
2004-01-01
This paper discusses the Spitzer Instrument Pointing Frame (IPF) Kalman Filter algorithm. The IPF Kalman filter is a high-order square-root iterated linearized Kalman filter, which is parametrized for calibrating the Spitzer Space Telescope focal plane and aligning the science instrument arrays with respect to the telescope boresight. The most stringent calibration requirement specifies knowledge of certain instrument pointing frames to an accuracy of 0.1 arcseconds, per-axis, 1-sigma relative to the Telescope Pointing Frame. In order to achieve this level of accuracy, the filter carries 37 states to estimate desired parameters while also correcting for expected systematic errors due to: (1) optical distortions, (2) scanning mirror scale-factor and misalignment, (3) frame alignment variations due to thermomechanical distortion, and (4) gyro bias and bias-drift in all axes. The resulting estimated pointing frames and calibration parameters are essential for supporting on-board precision pointing capability, in addition to end-to-end 'pixels on the sky' ground pointing reconstruction efforts.
Acoustic cardiac signals analysis: a Kalman filter-based approach.
Salleh, Sheik Hussain; Hussain, Hadrina Sheik; Swee, Tan Tian; Ting, Chee-Ming; Noor, Alias Mohd; Pipatsart, Surasak; Ali, Jalil; Yupapin, Preecha P
2012-01-01
Auscultation of the heart is accompanied by both electrical activity and sound. Heart auscultation provides clues to diagnose many cardiac abnormalities. Unfortunately, detection of relevant symptoms and diagnosis based on heart sound through a stethoscope is difficult. The reason GPs find this difficult is that the heart sounds are of short duration and separated from one another by less than 30 ms. In addition, the cost of false positives constitutes wasted time and emotional anxiety for both patient and GP. Many heart diseases cause changes in heart sound, waveform, and additional murmurs before other signs and symptoms appear. Heart-sound auscultation is the primary test conducted by GPs. These sounds are generated primarily by turbulent flow of blood in the heart. Analysis of heart sounds requires a quiet environment with minimum ambient noise. In order to address such issues, the technique of denoising and estimating the biomedical heart signal is proposed in this investigation. Normally, the performance of the filter naturally depends on prior information related to the statistical properties of the signal and the background noise. This paper proposes Kalman filtering for denoising statistical heart sound. The cycles of heart sounds are certain to follow first-order Gauss-Markov process. These cycles are observed with additional noise for the given measurement. The model is formulated into state-space form to enable use of a Kalman filter to estimate the clean cycles of heart sounds. The estimates obtained by Kalman filtering are optimal in mean squared sense.
Spitzer Instrument Pointing Frame (IPF) Kalman Filter Algorithm
NASA Technical Reports Server (NTRS)
Bayard, David S.; Kang, Bryan H.
2004-01-01
This paper discusses the Spitzer Instrument Pointing Frame (IPF) Kalman Filter algorithm. The IPF Kalman filter is a high-order square-root iterated linearized Kalman filter, which is parametrized for calibrating the Spitzer Space Telescope focal plane and aligning the science instrument arrays with respect to the telescope boresight. The most stringent calibration requirement specifies knowledge of certain instrument pointing frames to an accuracy of 0.1 arcseconds, per-axis, 1-sigma relative to the Telescope Pointing Frame. In order to achieve this level of accuracy, the filter carries 37 states to estimate desired parameters while also correcting for expected systematic errors due to: (1) optical distortions, (2) scanning mirror scale-factor and misalignment, (3) frame alignment variations due to thermomechanical distortion, and (4) gyro bias and bias-drift in all axes. The resulting estimated pointing frames and calibration parameters are essential for supporting on-board precision pointing capability, in addition to end-to-end 'pixels on the sky' ground pointing reconstruction efforts.
Parallelized Kalman-Filter-Based Reconstruction of Particle Tracks on Many-Core Processors and GPUs
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Krutelyov, Slava; Lantz, Steven; Lefebvre, Matthieu; Masciovecchio, Mario; McDermott, Kevin; Riley, Daniel; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2017-08-01
For over a decade now, physical and energy constraints have limited clock speed improvements in commodity microprocessors. Instead, chipmakers have been pushed into producing lower-power, multi-core processors such as Graphical Processing Units (GPU), ARM CPUs, and Intel MICs. Broad-based efforts from manufacturers and developers have been devoted to making these processors user-friendly enough to perform general computations. However, extracting performance from a larger number of cores, as well as specialized vector or SIMD units, requires special care in algorithm design and code optimization. One of the most computationally challenging problems in high-energy particle experiments is finding and fitting the charged-particle tracks during event reconstruction. This is expected to become by far the dominant problem at the High-Luminosity Large Hadron Collider (HL-LHC), for example. Today the most common track finding methods are those based on the Kalman filter. Experience with Kalman techniques on real tracking detector systems has shown that they are robust and provide high physics performance. This is why they are currently in use at the LHC, both in the trigger and offine. Previously we reported on the significant parallel speedups that resulted from our investigations to adapt Kalman filters to track fitting and track building on Intel Xeon and Xeon Phi. Here, we discuss our progresses toward the understanding of these processors and the new developments to port the Kalman filter to NVIDIA GPUs.
Estimating Power System Dynamic States Using Extended Kalman Filter
Huang, Zhenyu; Schneider, Kevin P.; Nieplocha, Jaroslaw; Zhou, Ning
2014-10-31
Abstract—The state estimation tools which are currently deployed in power system control rooms are based on a steady state assumption. As a result, the suite of operational tools that rely on state estimation results as inputs do not have dynamic information available and their accuracy is compromised. This paper investigates the application of Extended Kalman Filtering techniques for estimating dynamic states in the state estimation process. The new formulated “dynamic state estimation” includes true system dynamics reflected in differential equations, not like previously proposed “dynamic state estimation” which only considers the time-variant snapshots based on steady state modeling. This new dynamic state estimation using Extended Kalman Filter has been successfully tested on a multi-machine system. Sensitivity studies with respect to noise levels, sampling rates, model errors, and parameter errors are presented as well to illustrate the robust performance of the developed dynamic state estimation process.
Real time estimation of ship motions using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Triantafyllou, M. S.; Bodson, M.; Athans, M.
1983-01-01
The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering techniques, for application in VTOL aircraft landing. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.
Recent Flight Results of the TRMM Kalman Filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Bilanow, Stephen; Bauer, Frank (Technical Monitor)
2002-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls the roll and pitch attitude based on the Earth Sensor Assembly (ESA) output. TRMM's nominal orbit altitude was 350 km, until raised to 402 km to prolong mission life. During the boost, the ESA experienced a decreasing signal to noise ratio, until sun interference at 393 km altitude made the ESA data unreliable for attitude determination. At that point, the backup attitude determination algorithm, an extended Kalman filter, was enabled. After the boost finished, TRMM reacquired its nadir-pointing attitude, and continued its mission. This paper will briefly discuss the boost and the decision to turn on the backup attitude determination algorithm. A description of the extended Kalman filter algorithm will be given. In addition, flight results from analyzing attitude data and the results of software changes made onboard TRMM will be discussed. Some lessons learned are presented.
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Peterfreund, N.
1997-06-01
Using results from robust Kalman filtering, the author presents a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise.
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Peterfreund, N.
1998-12-31
Using results from robust Kalman filtering, we present a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise. 19 refs., 3 figs.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
A Kalman filter approach to adaptive estimation of multispectral signatures
NASA Technical Reports Server (NTRS)
Crane, R. B.
1973-01-01
The signatures of remote sensing data from agricultural crops exhibit significant non-stationarity, so that the performance of fixed parameter classifiers degenerates with time and distance from the initial training data. A class of adaptive decision-directed classifiers are being developed, based on Kalman filter theory. Limited results to date on two data sets indicate approximately a 25 to 40% reduction in rates of misclassification.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
Hip joint centre localisation with an unscented Kalman filter.
De Momi, Elena; Beretta, Elisa; Ferrigno, Giancarlo
2013-01-01
The accurate estimation of the hip joint centre (HJC) in gait analysis and in computer assisted orthopaedic procedures is a basic requirement. Functional methods, based on rigid body localisation, assessing the kinematics of the femur during circumduction movements (pivoting) have been used for estimating the HJC. Localising the femoral segment only, as it is usually done in total knee replacement procedure, can give rise to estimation errors, since the pelvis, during the passive pivoting manoeuvre, might undergo spatial displacements. This paper presents the design and test of an unscented Kalman filter that allows the estimation of the HJC by observing the pose of the femur and the 3D coordinates of a single marker attached to the pelvis. This new approach was validated using a hip joint mechanical simulator, mimicking both hard and soft tissues. The algorithm performances were compared with the literature standards and proved to have better performances in case of pelvis translation greater than 8 mm, thus satisfying the clinical requirements of the application.
Flood Nowcasting With Linear Catchment Models, Radar and Kalman Filters
NASA Astrophysics Data System (ADS)
Pegram, Geoff; Sinclair, Scott
A pilot study using real time rainfall data as input to a parsimonious linear distributed flood forecasting model is presented. The aim of the study is to deliver an operational system capable of producing flood forecasts, in real time, for the Mgeni and Mlazi catchments near the city of Durban in South Africa. The forecasts can be made at time steps which are of the order of a fraction of the catchment response time. To this end, the model is formulated in Finite Difference form in an equation similar to an Auto Regressive Moving Average (ARMA) model; it is this formulation which provides the required computational efficiency. The ARMA equation is a discretely coincident form of the State-Space equations that govern the response of an arrangement of linear reservoirs. This results in a functional relationship between the reservoir response con- stants and the ARMA coefficients, which guarantees stationarity of the ARMA model. Input to the model is a combined "Best Estimate" spatial rainfall field, derived from a combination of weather RADAR and Satellite rainfield estimates with point rain- fall given by a network of telemetering raingauges. Several strategies are employed to overcome the uncertainties associated with forecasting. Principle among these are the use of optimal (double Kalman) filtering techniques to update the model states and parameters in response to current streamflow observations and the application of short term forecasting techniques to provide future estimates of the rainfield as input to the model.
Multisource Image Kalman Filtering for Rapid Phenological Monitoring and Forecasting
NASA Astrophysics Data System (ADS)
Gray, J. M.; Friedl, M. A.; Singh, K. K.
2016-12-01
The availability of images from Earth observing satellites continues to grow as new sensors become operational, and existing archives are expanded and made more accessible. This wealth of data, along with computational advances that enable large archive processing, provides a valuable opportunity to investigate large-scale phenological dynamics and the climate drivers of phenological variability. Fusion methods capable of exploiting complementary aspects of spatial, temporal, and spectral resolutions from multiple sources are necessary to fully realize the potential of this asset. However, existing multisensor fusion approaches are designed for specific applications and/or sensor combinations, and most cannot incorporate knowledge of physical drivers of variability. Here, we explore the potential of the Kalman Filter to address these shortcomings, and demonstrate its applications to landscape-scale phenological monitoring. We demonstrate the fusion of Landsat, Sentinel, and MODIS data for the purposes of rapid phenological state estimation and forecasting, and extend the methodology to incorporate climate drivers of phenological variation. We conclude by discussing some outstanding challenges related to process and error model specification, along with potential solutions.
Three-dimensional motion tracking by Kalman filtering
NASA Astrophysics Data System (ADS)
Gao, Jean; Kosaka, Akio; Kak, Avinash C.
2000-10-01
In this paper, a 3D semantic object motion tracking method based on Kalman filtering is proposed. First, we use a specially designed Color Image Segmentation Editor (CISE) to devise shapes that more accurately describe the object to be tracked. CISE is an integration of edge and region detection, which is based on edge-linking, split-and-merge and the energy minimization for active contour detection. An ROI is further segmented into single motion blobs by considering the constancy of the motion parameters in each blob. Over short time intervals, each blob can be tracked separately and, over longer times, the blobs can be allowed to fragment and coalesce into new blobs as motion evolves. The tracking of each blob is based on a Kalman filter derived from linearization of a constraint equation satisfied by the pinhole model of a camera. The Kalman filter allows the tracker to project the uncertainties associated with a blob center (or with the coordinates of any other features) into the next frame. This projected uncertainty region can then be searched rot eh pixels belonging to the blob. Future work includes investigation of the effects of illumination changes and simultaneous tracking of multiple targets.
Kalman filter analysis of delayed neutron nondestructive assay measurements.
Aumeier, S. E.
1998-04-29
The ability to nondestructively determine the presence and quantity of fissile and fertile nuclei in various matrices is important in several nuclear applications including international and domestics safeguards, radioactive waste characterization and nuclear facility operations. Material irradiation followed by delayed neutron counting is a well known and useful nondestructive assay technique used to determine the fissile-effective content of assay samples. Previous studies have demonstrated the feasibility of using Kalman filters to unfold individual isotopic contributions to delayed neutron measurements resulting from the assay of mixes of uranium and plutonium isotopes. However, the studies in question used simulated measurement data and idealized parameters. We present the results of the Kalman filter analysis of several measurements of U/Pu mixes taken using Argonne National Laboratory's delayed neutron nondestructive assay device. The results demonstrate the use of Kalman filters as a signal processing tool to determine the fissile and fertile isotopic content of an assay sample from the aggregate delayed neutron response following neutron irradiation.
The Navstar GPS master control station's Kalman filter experience
NASA Technical Reports Server (NTRS)
Scardera, Michael P.
1990-01-01
The Navstar Global Positioning System (GPS) is a highly accurate space based navigation system providing all weather, 24 hour a day service to both military and civilian users. The system provides a Gaussian position solution with four satellites, each providing its ephemeris and clock offset with respect to GPS time. The GPS Master Clock Station (MCS) is charged with tracking each Navstar spacecraft and precisely defining the ephemeris and clock parameters for upload into the vehicle's navigation message. Briefly described here are the Navstar system and the Kalman filter estimation process used by MCS to determine, predict, and ensure quality control for each of the satellite's ephemeris and clock states. Routine performance is shown. Kalman filter reaction and response is discussed for anomalous clock behavior and trajectory perturbations. Particular attention is given to MCS efforts to improve orbital adjust modeling. The satellite out of service time due to orbital maneuvering has been reduced in the past year from four days to under twelve hours. The planning, reference trajectory model, and Kalman filter management improvements are explained.
Relationship between Allan variances and Kalman Filter parameters
NASA Technical Reports Server (NTRS)
Vandierendonck, A. J.; Mcgraw, J. B.; Brown, R. G.
1984-01-01
A relationship was constructed between the Allan variance parameters (H sub z, H sub 1, H sub 0, H sub -1 and H sub -2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source is reviewed. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.
Three-axis attitude determination via Kalman filtering of magnetometer data
NASA Technical Reports Server (NTRS)
Martel, Francois; Pal, Parimal K.; Psiaki, Mark L.
1988-01-01
A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system.
An adaptive Kalman filter for ECG signal enhancement.
Vullings, Rik; de Vries, Bert; Bergmans, Jan W M
2011-04-01
The ongoing trend of ECG monitoring techniques to become more ambulatory and less obtrusive generally comes at the expense of decreased signal quality. To enhance this quality, consecutive ECG complexes can be averaged triggered on the heartbeat, exploiting the quasi-periodicity of the ECG. However, this averaging constitutes a tradeoff between improvement of the SNR and loss of clinically relevant physiological signal dynamics. Using a bayesian framework, in this paper, a sequential averaging filter is developed that, in essence, adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal. The filter has the form of an adaptive Kalman filter. The adaptive estimation of the process and measurement noise covariances is performed by maximizing the bayesian evidence function of the sequential ECG estimation and by exploiting the spatial correlation between several simultaneously recorded ECG signals, respectively. The noise covariance estimates thus obtained render the filter capable of ascribing more weight to newly arriving data when these data contain morphological variability, and of reducing this weight in cases of no morphological variability. The filter is evaluated by applying it to a variety of ECG signals. To gauge the relevance of the adaptive noise-covariance estimation, the performance of the filter is compared to that of a Kalman filter with fixed, (a posteriori) optimized noise covariance. This comparison demonstrates that, without using a priori knowledge on signal characteristics, the filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance, favoring the adaptive filter in cases where no a priori information is available or where signal characteristics are expected to fluctuate.
Hybrid vs Adaptive Ensemble Kalman Filtering for Storm Surge Forecasting
NASA Astrophysics Data System (ADS)
Altaf, M. U.; Raboudi, N.; Gharamti, M. E.; Dawson, C.; McCabe, M. F.; Hoteit, I.
2014-12-01
Recent storm surge events due to Hurricanes in the Gulf of Mexico have motivated the efforts to accurately forecast water levels. Toward this goal, a parallel architecture has been implemented based on a high resolution storm surge model, ADCIRC. However the accuracy of the model notably depends on the quality and the recentness of the input data (mainly winds and bathymetry), model parameters (e.g. wind and bottom drag coefficients), and the resolution of the model grid. Given all these uncertainties in the system, the challenge is to build an efficient prediction system capable of providing accurate forecasts enough ahead of time for the authorities to evacuate the areas at risk. We have developed an ensemble-based data assimilation system to frequently assimilate available data into the ADCIRC model in order to improve the accuracy of the model. In this contribution we study and analyze the performances of different ensemble Kalman filter methodologies for efficient short-range storm surge forecasting, the aim being to produce the most accurate forecasts at the lowest possible computing time. Using Hurricane Ike meteorological data to force the ADCIRC model over a domain including the Gulf of Mexico coastline, we implement and compare the forecasts of the standard EnKF, the hybrid EnKF and an adaptive EnKF. The last two schemes have been introduced as efficient tools for enhancing the behavior of the EnKF when implemented with small ensembles by exploiting information from a static background covariance matrix. Covariance inflation and localization are implemented in all these filters. Our results suggest that both the hybrid and the adaptive approach provide significantly better forecasts than those resulting from the standard EnKF, even when implemented with much smaller ensembles.
Ensemble Kalman filtering with residual nudging: some recent progress
NASA Astrophysics Data System (ADS)
Luo, Xiaodong; Hoteit, Ibrahim
2014-05-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies (Luo and Hoteit, 2012, 2013b,a), the authors proposed an observation-space based strategy, called residual nudging, in order to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor, and if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In a more present study (Luo and Hoteit, 2014), residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that is able to achieve the objective of residual nudging in the presence of nonlinear observation operators, under suitable conditions. The 40 dimensional Lorenz 96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge in the presence of nonlinear observation operators, the proposed iterative filter performs very stably and leads to reasonable estimation accuracies under various experiment settings. REFERENCES Luo, X. and H. Hoteit, 2014: Ensemble kalman filtering with residual nudging: an extension to the state estimation problems with nonlinear observation operators. Submitted. Luo, X. and I. Hoteit, 2012: Ensemble Kalman filtering with residual nudging. Tellus A, 64, 17130, open access, doi:10.3402/tellusa.v64i0.17130. Luo, X. and I. Hoteit, 2013a: Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications. Mon. Wea. Rev., 141, 3360-3368, doi:10.1175/MWR-D-13-00067.1. Luo, X. and I. Hoteit, 2013b: Efficient particle filtering through residual nudging. Quart. J. Roy. Meteor
Leakage estimation using Kalman filtering in noninvasive mechanical ventilation.
Rodrigues, G G; Freitas, U S; Bounoiare, D; Aguirre, L A; Letellier, C
2013-05-01
Noninvasive mechanical ventilation is today often used to assist patient with chronic respiratory failure. One of the main reasons evoked to explain asynchrony events, discomfort, unwillingness to be treated, etc., is the occurrence of nonintentional leaks in the ventilation circuit, which are difficult to account for because they are not measured. This paper describes a solution to the problem of variable leakage estimation based on a Kalman filter driven by airflow and the pressure signals, both of which are available in the ventilation circuit. The filter was validated by showing that based on the attained leakage estimates, practically all the untriggered cycles can be explained.
Zhan, Yang; Guo, Shuixia; Kendrick, Keith M; Feng, Jianfeng
2009-04-01
Novel approaches to effectively reduce noise in data recorded from multi-trial physiology experiments have been investigated using two-dimensional filtering methods, adaptive Wiener filtering and reduced update Kalman filtering. Test data based on signal and noise model consisting of different conditions of signal components mixed with noise have been considered with filtering effects evaluated using analysis of frequency coherence and of time-dependent coherence. Various situations that may affect the filtering results have been explored and reveal that Wiener and Kalman filtering can considerably improve the coherence values between two channels of multi-trial data and suppress uncorrelated components. We have extended our approach to experimental data: multi-electrode array (MEA) local field potential (LFPs) recordings from the inferotemporal cortex of sheep and LFP vs. electromyogram (LFP-EMG) recording data during resting tremor in Parkinson's disease patients. Finally general procedures for implementation of these filtering techniques are described.
Use of an Extended Kalman Filter
1990-09-01
following dynamics: xk =x( .,)-T (2-4) Yk--i T (2-2) where: * x : Actual coordinate in X * y : Actual coordinate in Y " y-., :Previous position in X...represents a non linear relafionship L the measurements and the state variables. The actual measurement equation is as follows: Zk=tanFl (Xk-X’a) 14V 27.(yk-Y...its job, the filter needs an ,,riori knowledge of the state estimate 2£Afk1) , its error covariance matrix Pc(k-1) and also the actual observation zk
Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
NASA Technical Reports Server (NTRS)
Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin
2014-01-01
This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
VLBI real-time analysis by Kalman Filtering
NASA Astrophysics Data System (ADS)
Karbon, Maria; Soja, Benedikt; Nilson, Tobias; Heinkelmann, Robert; Liu, Li; Lu, Ciuxian; Xu, Minghui; Raposo-Pulido, Virginia; Mora-Diaz, Julian; Schuh, Harald
2014-05-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques. It provides the full set of Earth Orientation Parameter (EOP) and is unique for observing long term Universal Time (UT1) and precession/nutation. Currently the VLBI products are delivered with a delay of about two weeks from the moment of the observation. However, the need for near-real time estimates of the parameters is increasing, e.g. for satellite based navigation and positioning or for enabling precise tracking of interplanetary spacecraft. The goal is thus to reduce the time span between observation and the final result to less than one day. This can be archived by replacing the classical least squares method with an adaptive Kalman filter. We have developed a Kalman filter for VLBI data analysis. This method has the advantage that it is simultaneously possible to estimate stationary parameters, e.g. station positions, and to model the highly variable stochastic behavior of non-stationary parameters like clocks or atmospheric parameters. The filter is able to perform without any human interaction, making it a completely autonomous tool. In this work we describe the filter and discuss its application for EOP determination and prediction. We discuss the implementation of the stochastic models to statistically account for unpredictable changes in EOP. Furthermore, additional data like results from other techniques can be included to improve the performance. For example, atmospheric angular momentum calculated from numerical weather models can be introduced to supplement the short-term prediction of UT1 and polar motion. This Kalman filter will be extended and embedded in the newly developed Vienna VLBI Software (VieVS) as a completely autonomous tool enabling the VLBI analysis in near real-time and providing all the parameters of interest with the highest possible accuracy.
History matching production data using the ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Gu, Yaqing
In this dissertation, the ensemble Kalman filter (EnKF) is refined for applications to the problem of history matching. This method assimilates data sequentially whenever data are acquired. It is a Monte Carlo approach, in which an ensemble of models is used. The correlations between model variables and theoretical data are computed directly from the ensemble. Multiple history-matched models will be obtained after the initial ensemble is conditioned to all production data. The final models can be used to assess the uncertainty in future reservoir performance. The computational cost for generating the multiple history-matched models is approximately the simulation runs for all the ensemble models plus the overhead time for matrix computations. The plausibility of the EnKF as an alternative method for history matching to reservoir applications is shown by two waterflood problems. The effectiveness of the EnKF is more thoroughly demonstrated with a more realistic reservoir model, PUNQ-S3. The EnKF takes both model parameters and state variables as well as calculated data into its state vectors. When new observations are assimilated, all variables in the state vectors are adjusted simultaneously. For linear dynamic systems, the system governing equations are honored by the updated model parameters and state variables. For non-linear dynamic systems, however, it may be impossible to update the state variables to be consistent with the updated model parameters without resolving the non-linear forward problem. Wen and Chen suggested adding a "conforming step" at each measurement time to compute the state variables with the updated model parameters by re-initializing the dynamic equations at the previous measurement time. We demonstrate through both linear and non-linear examples that the results of the conforming method are incorrect. We propose the ensemble Randomized Maximum Likelihood filter (EnRMLF) as a modification to the traditional EnKF to handle the non
Tropospheric delays derived from Kalman-filtered VLBI observations
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Balidakis, Kyriakos; Lu, Cuixian; Anderson, James; Glaser, Susanne; Liu, Li; Mora-Diaz, Julian A.; Raposo-Pulido, Virginia; Xu, Minghui; Heinkelmann, Robert; Schuh, Harald
2015-04-01
One of the most important error sources in the products of space geodetic techniques is the troposphere. Currently, it is not possible to model the rapid variations in the path delay caused by water vapor with sufficient accuracy, thus it is necessary to estimate these delays in the data analysis. Very long baseline interferometry (VLBI) is well suited to determine wet delays with high accuracy and precision. Compared to GNSS, the analysis does not need to deal with effects related to code biases, multipath, satellite orbit mismodeling, or antenna phase center variations that are inherent in GNSS processing. VLBI data are usually analyzed by estimating geodetic parameters in a least squares adjustment. However, once the VLBI Global Observing System (VGOS) will have become operational, algorithms providing real-time capability, for instance a Kalman filter, should be preferable for data analysis. Even today, certain advantages of such a filter, for example, allowing stochastic modeling of geodetic parameters, warrant its application. The estimation of tropospheric wet delays, in particular, greatly benefits from the stochastic approach of the filter. In this work we have investigated the benefits of applying a Kalman filter in the VLBI data analysis for the determination of tropospheric parameters. The VLBI datasets considered are the CONT campaigns, which demonstrate state-of-the-art capabilities of the VLBI system. They are unique in following a continuous observation schedule over 15 days and in having data recorded at higher bandwidth than usual. The large amount of observations leads to a very high quality of geodetic products. CONT campaigns are held every three years; we have analyzed all CONT campaigns between 2002 and 2014 for this study. In our implementation of a Kalman filter in the VLBI software VieVS@GFZ, the zenith wet delays (ZWD) are modeled as random walk processes. We have compared the resulting time series to corresponding ones obtained from
Moment estimation for chemically reacting systems by extended Kalman filtering.
Ruess, J; Milias-Argeitis, A; Summers, S; Lygeros, J
2011-10-28
In stochastic models of chemically reacting systems that contain bimolecular reactions, the dynamics of the moments of order up to n of the species populations do not form a closed system, in the sense that their time-derivatives depend on moments of order n + 1. To close the dynamics, the moments of order n + 1 are generally approximated by nonlinear functions of the lower order moments. If the molecule counts of some of the species have a high probability of becoming zero, such approximations may lead to imprecise results and stochastic simulation is the only viable alternative for system analysis. Stochastic simulation can produce exact realizations of chemically reacting systems, but tends to become computationally expensive, especially for stiff systems that involve reactions at different time scales. Further, in some systems, important stochastic events can be very rare and many simulations are necessary to obtain accurate estimates. The computational cost of stochastic simulation can then be prohibitively large. In this paper, we propose a novel method for estimating the moments of chemically reacting systems. The method is based on closing the moment dynamics by replacing the moments of order n + 1 by estimates calculated from a small number of stochastic simulation runs. The resulting stochastic system is then used in an extended Kalman filter, where estimates of the moments of order up to n, obtained from the same simulation, serve as outputs of the system. While the initial motivation for the method was improving over the performance of stochastic simulation and moment closure methods, we also demonstrate that it can be used in an experimental setting to estimate moments of species that cannot be measured directly from time course measurements of the moments of other species.
Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1986-01-01
The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.
Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter
NASA Technical Reports Server (NTRS)
Verhaegen, M. H.
1989-01-01
This paper corrects an unclear statement of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that the habitual, incorrect implementation of the Kalman filter has been the major cause of its insensitivity to the so-called loss-of-symmetry phenomenon.
Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter
NASA Technical Reports Server (NTRS)
Verhaegen, M. H.
1987-01-01
This paper corrects an unclear treatment of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that habitual, incorrect implementation of the Kalman filter has been the major cause of its sensitivity to the so-called loss-of-symmetry phenomenon.
Determination of High-Speed Multiple Threat Using Kalman Filter Analysis of Maritime Movement
2015-06-01
HIGH-SPEED MULTIPLE THREAT USING KALMAN FILTER ANALYSIS OF MARITIME MOVEMENT by Joseph L. Carnes June 2015 Thesis Advisor: David A. Garren...USING KALMAN FILTER ANALYSIS OF MARITIME MOVEMENT 5. FUNDING NUMBERS 6. AUTHOR(S) Joseph L. Carnes 7. PERFORMING ORGANIZATION NAME(S) AND...feeding data into the Kalman filtering algorithm, which is used in the tracking of moving targets based on simulated radar position measurements
A Probabilistic Collocation Based Iterative Kalman Filter for Landfill Data Assimilation
NASA Astrophysics Data System (ADS)
Qiang, Z.; Zeng, L.; Wu, L.
2016-12-01
Due to the strong spatial heterogeneity of landfill, uncertainty is ubiquitous in gas transport process in landfill. To accurately characterize the landfill properties, the ensemble Kalman filter (EnKF) has been employed to assimilate the measurements, e.g., the gas pressure. As a Monte Carlo (MC) based method, the EnKF usually requires a large ensemble size, which poses a high computational cost for large scale problems. In this work, we propose a probabilistic collocation based iterative Kalman filter (PCIKF) to estimate permeability in a liquid-gas coupling model. This method employs polynomial chaos expansion (PCE) to represent and propagate the uncertainties of model parameters and states, and an iterative form of Kalman filter to assimilate the current gas pressure data. To further reduce the computation cost, the functional ANOVA (analysis of variance) decomposition is conducted, and only the first order ANOVA components are remained for PCE. Illustrated with numerical case studies, this proposed method shows significant superiority in computation efficiency compared with the traditional MC based iterative EnKF. The developed method has promising potential in reliable prediction and management of landfill gas production.
An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking
NASA Astrophysics Data System (ADS)
Raihan A. V, Dilshad; Chakravorty, Suman
2017-04-01
Optimal and consistent estimation of the state of space objects is pivotal to surveillance and tracking applications. However, probabilistic estimation of space objects is made difficult by the non-Gaussianity and nonlinearity associated with orbital mechanics. In this paper, we present an unscented Kalman-particle hybrid filtering framework for recursive Bayesian estimation of space objects. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for estimation when measurements are available. When the target is outside the field of view (FOV) of the sensor, it updates the state probability density function (PDF) via a sequential Monte Carlo method. The hybrid filter addresses the problem of particle depletion through a suitably designed filter transition scheme. To assess the performance of the hybrid filtering approach, we consider two test cases of space objects that are assumed to undergo full three dimensional orbital motion under the effects of J 2 and atmospheric drag perturbations. It is demonstrated that the hybrid filters can furnish fast, accurate and consistent estimates outperforming standard UKF and particle filter (PF) implementations.
Information and Entropy Flow in the Kalman?Bucy Filter
NASA Astrophysics Data System (ADS)
Mitter, Sanjoy K.; Newton, Nigel J.
2005-01-01
We investigate the information theoretic properties of Kalman-Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract `universe' comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman-Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauer's Principle.
NASA Astrophysics Data System (ADS)
Li, Judith Yue; Kokkinaki, Amalia; Ghorbanidehno, Hojat; Darve, Eric F.; Kitanidis, Peter K.
2015-12-01
Reservoir monitoring aims to provide snapshots of reservoir conditions and their uncertainties to assist operation management and risk analysis. These snapshots may contain millions of state variables, e.g., pressures and saturations, which can be estimated by assimilating data in real time using the Kalman filter (KF). However, the KF has a computational cost that scales quadratically with the number of unknowns, m, due to the cost of computing and storing the covariance and Jacobian matrices, along with their products. The compressed state Kalman filter (CSKF) adapts the KF for solving large-scale monitoring problems. The CSKF uses N preselected orthogonal bases to compute an accurate rank-N approximation of the covariance that is close to the optimal spectral approximation given by SVD. The CSKF has a computational cost that scales linearly in m and uses an efficient matrix-free approach that propagates uncertainties using N + 1 forward model evaluations, where N≪m. Here we present a generalized CSKF algorithm for nonlinear state estimation problems such as CO2 monitoring. For simultaneous estimation of multiple types of state variables, the algorithm allows selecting bases that represent the variability of each state type. Through synthetic numerical experiments of CO2 monitoring, we show that the CSKF can reproduce the Kalman gain accurately even for large compression ratios (m/N). For a given computational cost, the CSKF uses a robust and flexible compression scheme that gives more reliable uncertainty estimates than the ensemble Kalman filter, which may display loss of ensemble variability leading to suboptimal uncertainty estimates.
A cascaded two-step Kalman filter for estimation of human body segment orientation using MEMS-IMU.
Zihajehzadeh, S; Loh, D; Lee, M; Hoskinson, R; Park, E J
2014-01-01
Orientation of human body segments is an important quantity in many biomechanical analyses. To get robust and drift-free 3-D orientation, raw data from miniature body worn MEMS-based inertial measurement units (IMU) should be blended in a Kalman filter. Aiming at less computational cost, this work presents a novel cascaded two-step Kalman filter orientation estimation algorithm. Tilt angles are estimated in the first step of the proposed cascaded Kalman filter. The estimated tilt angles are passed to the second step of the filter for yaw angle calculation. The orientation results are benchmarked against the ones from a highly accurate tactical grade IMU. Experimental results reveal that the proposed algorithm provides robust orientation estimation in both kinematically and magnetically disturbed conditions.
Luo, Yingting; Zhu, Yunmin; Luo, Dandan; Zhou, Jie; Song, Enbin; Wang, Donghua
2008-01-01
This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices. PMID:27873977
Enhancement of Spanish Oesophageal Speech vowels using coherent subband modulator Kalman filtering.
Ishaq, Rizwan; Zapirain, Begoña García
2016-01-01
This paper proposes an Oesophageal Speech (OES) enhancement method, based on Kalman filtering. The Kalman filter is applied to modulators of OES frequency subbands instead of the fullband signal. The OES frequency subbands are decomposed into modulators and carriers components using coherent demodulation. In comparison with fullband Kalman filtering and pole stabilization, the proposed technique shows better results. The system performance is evaluated objectively and subjectively using the Harmonic to Noise Ratio (HNR) and Mean Opinion Score (MOS) respectively. Results have shown that Kalman filter in subband modulators processing is robust and efficient, improving the HNR by 4 to 5 dB for all Spanish vowels.
Luo, Yingting; Zhu, Yunmin; Luo, Dandan; Zhou, Jie; Song, Enbin; Wang, Donghua
2008-12-08
This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.
Ensemble Kalman filters for dynamical systems with unresolved turbulence
Grooms, Ian; Lee, Yoonsang; Majda, Andrew J.
2014-09-15
Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarse-resolution models are intended to predict the large-scale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the large-scale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein small-scale statistics can be used to estimate both the resolved and unresolved components of the solution. The one-dimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the non-Gaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in two-thirds of the climatological variance being carried by the unresolved small scales. Because the unresolved scales contain so much energy, filters that ignore the representation error fail utterly to provide meaningful estimates of the system state. Inclusion of a time-independent climatological estimate of the representation error in a standard framework leads to inaccurate estimates of the large-scale part of the signal; accurate estimates of the large scales are only achieved by using stochastic superparameterization to provide evolving, large-scale dependent predictions of the small-scale statistics. Again, because the unresolved scales contain so much energy
Rotation speed measurement for turbine governor: Torsion filtering by using Kalman filter
Houry, M.P.; Bourles, H.
1996-01-01
The rotation speed of a turbogenerator is disturbed by its shaft torsion. Obtaining a filtered measure of this speed is a problem of a great practical importance for turbine governor. A solution to this problem is explained using Kalman`s theory. The principles of the design, simulations and tests on the Electricite de France Micro-Network laboratory are presented showing several improvements over the current filter. Moreover, the described solution could be used profitably in all applications where it is necessary to substantially reduce a signal at given frequencies without causing too great a phase shift in the pass-band.
Applying Kalman filtering to investigate tropospheric effects in VLBI
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Heinkelmann, Robert; Liu, Li; Lu, Cuixian; Andres Mora-Diaz, Julian; Raposo-Pulido, Virginia; Xu, Minghui; Schuh, Harald
2014-05-01
Very Long Baseline Interferometry (VLBI) currently provides results, e.g., estimates of the tropospheric delays, with a delay of more than two weeks. In the future, with the coming VLBI2010 Global Observing System (VGOS) and increased usage of electronic data transfer, it is planned that the time between observations and results is decreased. This may, for instance, allow the integration of VLBI-derived tropospheric delays into numerical weather prediction models. Therefore, future VLBI analysis software packages need to be able to process the observational data autonomously in near real-time. For this purpose, we have extended the Vienna VLBI Software (VieVS) by a Kalman filter module. This presentation describes the filter and discusses its application for tropospheric studies. Instead of estimating zenith wet delays as piece-wise linear functions in a least-squares adjustment, the Kalman filter allows for more sophisticated stochastic modeling. We start with a random walk process to model the time-dependent behavior of the zenith wet delays. Other possible approaches include the stochastic model described by turbulence theory, e.g. the model by Treuhaft and Lanyi (1987). Different variance-covariance matrices of the prediction error, depending on the time of the year and the geographic latitude, have been tested. In winter and closer to the poles, lower variances and covariances are appropriate. The horizontal variations in tropospheric delays have been investigated by comparing three different strategies: assumption of a horizontally stratified troposphere, using north and south gradients modeled, e.g., as Gauss-Markov processes, and applying a turbulence model assuming correlations between observations in different azimuths. By conducting Monte-Carlo simulations of current standard VLBI networks and of future VGOS networks, the different tropospheric modeling strategies are investigated. For this purpose, we use the simulator module of VieVS which takes into
Kalman filtering to suppress spurious signals in Adaptive Optics control
Poyneer, L; Veran, J P
2010-03-29
In many scenarios, an Adaptive Optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.
Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables
NASA Technical Reports Server (NTRS)
Sedlak, Joseph E.; Harman, Richard
2004-01-01
There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.
Kalman filtering to suppress spurious signals in adaptive optics control.
Poyneer, Lisa A; Véran, Jean-Pierre
2010-11-01
In many scenarios, an adaptive optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common-path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so-called "curse of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF could be even more computationally expensive than EnKF. Motivated by most recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to eliminate the inconsistency between model parameters and states. The performance of RAPCKF is tested with numerical cases of unsaturated flow models. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.
Incremental activation detection for real-time fMRI series using robust Kalman filter.
Li, Liang; Yan, Bin; Tong, Li; Wang, Linyuan; Li, Jianxin
2014-01-01
Real-time functional magnetic resonance imaging (rt-fMRI) is a technique that enables us to observe human brain activations in real time. However, some unexpected noises that emerged in fMRI data collecting, such as acute swallowing, head moving and human manipulations, will cause much confusion and unrobustness for the activation analysis. In this paper, a new activation detection method for rt-fMRI data is proposed based on robust Kalman filter. The idea is to add a variation to the extended kalman filter to handle the additional sparse measurement noise and a sparse noise term to the measurement update step. Hence, the robust Kalman filter is designed to improve the robustness for the outliers and can be computed separately for each voxel. The algorithm can compute activation maps on each scan within a repetition time, which meets the requirement for real-time analysis. Experimental results show that this new algorithm can bring out high performance in robustness and in real-time activation detection.
NASA Astrophysics Data System (ADS)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called "curse of dimensionality". Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the "restart" scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost.
A Self-Tuning Kalman Filter for Autonomous Spacecraft Navigation
NASA Technical Reports Server (NTRS)
Truong, Son H.
1998-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also
A Self-Tuning Kalman Filter for Autonomous Spacecraft Navigation
NASA Technical Reports Server (NTRS)
Truong, Son H.
1998-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation
Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng
2016-01-01
A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm. PMID:27657069
Consensus+Innovations Distributed Kalman Filter With Optimized Gains
NASA Astrophysics Data System (ADS)
Das, Subhro; Moura, Jose M. F.
2017-01-01
In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a pre-specified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that, the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.
Nonlinear stability and ergodicity of ensemble based Kalman filters
NASA Astrophysics Data System (ADS)
Tong, Xin T.; Majda, Andrew J.; Kelly, David
2016-02-01
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and oil reservoir simulation, very little is known about the long-time behavior of these methods and why they are effective when applied with modest ensemble sizes in large dimensional turbulent dynamical systems. By following the basic principles of energy dissipation and controllability of filters, this paper establishes a simple, systematic and rigorous framework for the nonlinear analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the dynamical properties of boundedness and geometric ergodicity. The time uniform boundedness guarantees that the filter estimate will not diverge to machine infinity in finite time, which is a potential threat for EnKF and ESQF known as the catastrophic filter divergence. Geometric ergodicity ensures in addition that the filter has a unique invariant measure and that initialization errors will dissipate exponentially in time. We establish these results by introducing a natural notion of observable energy dissipation. The time uniform bound is achieved through a simple Lyapunov function argument, this result applies to systems with complete observations and strong kinetic energy dissipation, but also to concrete examples with incomplete observations. With the Lyapunov function argument established, the geometric ergodicity is obtained by verifying the controllability of the filter processes; in particular, such analysis for ESQF relies on a careful multivariate perturbation analysis of the covariance eigen-structure.
Friction coefficient estimation using an unscented Kalman filter
NASA Astrophysics Data System (ADS)
Zhao, Yunshi; Liang, Bo; Iwnicki, Simon
2014-05-01
The friction coefficient between a railway wheel and rail surface is a crucial factor in maintaining high acceleration and braking performance of railway vehicles; therefore, monitoring this friction coefficient is important. Due to the difficulty in directly measuring the friction coefficient, the creep force or creepage, indirect methods using state observers are used more frequently. This paper presents an approach using an unscented kalman filter to estimate the creep force and creepage and the friction coefficient from traction motor behaviours. A scaled roller rig is designed and a series of experiments is carried out to evaluate the estimator performance.
Automatic Certification of Kalman Filters for Reliable Code Generation
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd; Schumann, Johann; Richardson, Julian
2005-01-01
AUTOFILTER is a tool for automatically deriving Kalman filter code from high-level declarative specifications of state estimation problems. It can generate code with a range of algorithmic characteristics and for several target platforms. The tool has been designed with reliability of the generated code in mind and is able to automatically certify that the code it generates is free from various error classes. Since documentation is an important part of software assurance, AUTOFILTER can also automatically generate various human-readable documents, containing both design and safety related information. We discuss how these features address software assurance standards such as DO-178B.
Automatic Certification of Kalman Filters for Reliable Code Generation
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd; Schumann, Johann; Richardson, Julian
2005-01-01
AUTOFILTER is a tool for automatically deriving Kalman filter code from high-level declarative specifications of state estimation problems. It can generate code with a range of algorithmic characteristics and for several target platforms. The tool has been designed with reliability of the generated code in mind and is able to automatically certify that the code it generates is free from various error classes. Since documentation is an important part of software assurance, AUTOFILTER can also automatically generate various human-readable documents, containing both design and safety related information. We discuss how these features address software assurance standards such as DO-178B.
Optimal subband Kalman filter for normal and oesophageal speech enhancement.
Ishaq, Rizwan; García Zapirain, Begoña
2014-01-01
This paper presents the single channel speech enhancement system using subband Kalman filtering by estimating optimal Autoregressive (AR) coefficients and variance for speech and noise, using Weighted Linear Prediction (WLP) and Noise Weighting Function (NWF). The system is applied for normal and Oesophageal speech signals. The method is evaluated by Perceptual Evaluation of Speech Quality (PESQ) score and Signal to Noise Ratio (SNR) improvement for normal speech and Harmonic to Noise Ratio (HNR) for Oesophageal Speech (OES). Compared with previous systems, the normal speech indicates 30% increase in PESQ score, 4 dB SNR improvement and OES shows 3 dB HNR improvement.
Weighted Average Consensus-Based Unscented Kalman Filtering.
Li, Wangyan; Wei, Guoliang; Han, Fei; Liu, Yurong
2016-02-01
In this paper, we are devoted to investigate the consensus-based distributed state estimation problems for a class of sensor networks within the unscented Kalman filter (UKF) framework. The communication status among sensors is represented by a connected undirected graph. Moreover, a weighted average consensus-based UKF algorithm is developed for the purpose of estimating the true state of interest, and its estimation error is bounded in mean square which has been proven in the following section. Finally, the effectiveness of the proposed consensus-based UKF algorithm is validated through a simulation example.
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
NASA Technical Reports Server (NTRS)
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
NASA Technical Reports Server (NTRS)
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
Suppression of adjacent-channel and cochannel FM interference via extended Kalman filtering
Bradley, J.N.
1991-11-01
A method is discussed for the problem of demodulating an FM signal in the presence of an adjacent-channel or cochannel interferer. State-space descriptions of the underlying message processes and the measurement process are presented which are then incorporated in an extended Kalman filter framework. The extended filter was necessary due to the nonlinearity of the measurement equation. The results of computer simulations are presented which demonstrate the system performance for various selections of the modulation index and signal separation. The derived system is contrasted to the previous state of the art in this area which involved maximum likelihood estimation. 5 refs.
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.
NASA Technical Reports Server (NTRS)
Klein, V.; Schiess, J. R.
1977-01-01
An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-11-11
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-01-01
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted “useful” data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Garg, Sanjay
2011-01-01
applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.
Hierarchical Bayes Ensemble Kalman Filter for geophysical data assimilation
NASA Astrophysics Data System (ADS)
Tsyrulnikov, Michael; Rakitko, Alexander
2016-04-01
In the Ensemble Kalman Filter (EnKF), the forecast error covariance matrix B is estimated from a sample (ensemble), which inevitably implies a degree of uncertainty. This uncertainty is especially large in high dimensions, where the affordable ensemble size is orders of magnitude less than the dimensionality of the system. Common remedies include ad-hoc devices like variance inflation and covariance localization. The goal of this study is to optimize the account for the inherent uncertainty of the B matrix in EnKF. Following the idea by Myrseth and Omre (2010), we explicitly admit that the B matrix is unknown and random and estimate it along with the state (x) in an optimal hierarchical Bayes analysis scheme. We separate forecast errors into predictability errors (i.e. forecast errors due to uncertainties in the initial data) and model errors (forecast errors due to imperfections in the forecast model) and include the two respective components P and Q of the B matrix into the extended control vector (x,P,Q). Similarly, we break the traditional forecast ensemble into the predictability-error related ensemble and model-error related ensemble. The reason for the separation of model errors from predictability errors is the fundamental difference between the two sources of error. Model error are external (i.e. do not depend on the filter's performance) whereas predictability errors are internal to a filter (i.e. are determined by the filter's behavior). At the analysis step, we specify Inverse Wishart based priors for the random matrices P and Q and conditionally Gaussian prior for the state x. Then, we update the prior distribution of (x,P,Q) using both observation and ensemble data, so that ensemble members are used as generalized observations and ordinary observations are allowed to influence the covariances. We show that for linear dynamics and linear observation operators, conditional Gaussianity of the state is preserved in the course of filtering. At the forecast
Low-dimensional recurrent neural network-based Kalman filter for speech enhancement.
Xia, Youshen; Wang, Jun
2015-07-01
This paper proposes a new recurrent neural network-based Kalman filter for speech enhancement, based on a noise-constrained least squares estimate. The parameters of speech signal modeled as autoregressive process are first estimated by using the proposed recurrent neural network and the speech signal is then recovered from Kalman filtering. The proposed recurrent neural network is globally asymptomatically stable to the noise-constrained estimate. Because the noise-constrained estimate has a robust performance against non-Gaussian noise, the proposed recurrent neural network-based speech enhancement algorithm can minimize the estimation error of Kalman filter parameters in non-Gaussian noise. Furthermore, having a low-dimensional model feature, the proposed neural network-based speech enhancement algorithm has a much faster speed than two existing recurrent neural networks-based speech enhancement algorithms. Simulation results show that the proposed recurrent neural network-based speech enhancement algorithm can produce a good performance with fast computation and noise reduction.
NASA Astrophysics Data System (ADS)
Bourgeois, Brian S.; Elmore, Paul A.; Avera, William E.; Zambo, Samantha J.
2016-07-01
This paper examines and contrasts two estimation methods, Kalman filtering and linear smoothing, for creating interpolated data products from bathymetry measurements. Using targeted examples, we demonstrate previously obscured behavior showing the dependence of linear smoothers on the spatial arrangement of the measurements, yielding markedly different estimation results than the Kalman filter. For bathymetry data, we have modified the variance estimates from both the Kalman filter and linear smoothers to obtain comparable estimators for dense data. These comparable estimators produce uncertainty estimates that have statistically insignificant differences via hypothesis testing. Achieving comparable estimation is accomplished by applying the "propagated uncertainty" concept and a numerical realization of Tobler's principle to the measurement data prior to the computation of the estimate. We show new mathematical derivations for these modifications. In addition, we show test results with (a) synthetic data and (b) gridded bathymetry in the area of the Scripps and La Jolla Canyons. Our tenfold cross-validation for case (b) shows that the modified equations create comparable uncertainty for both gridding algorithms with null hypothesis acceptance rates of greater than 99.95% of the data points. In contrast, bilinear interpolation has 10 times the amount of rejection. We then discuss how the uncertainty estimators are, in principle, applicable to interpolate geophysical data other than bathymetry.
ERP Estimation using a Kalman Filter in VLBI
NASA Astrophysics Data System (ADS)
Karbon, M.; Soja, B.; Nilsson, T.; Heinkelmann, R.; Liu, L.; Lu, C.; Mora-Diaz, J. A.; Raposo-Pulido, V.; Xu, M.; Schuh, H.
2014-12-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques, providing the full set of Earth Orientation Parameters (EOP), and it is unique for observing long term Universal Time (UT1). For applications such as satellite-based navigation and positioning, accurate and continuous ERP obtained in near real-time are essential. They also allow the precise tracking of interplanetary spacecraft. One of the goals of VGOS (VLBI Global Observing System) is to provide such near real-time ERP. With the launch of this next generation VLBI system, the International VLBI Service for Geodesy and Astrometry (IVS) increased its efforts not only to reach 1 mm accuracy on a global scale but also to reduce the time span between the collection of VLBI observations and the availability of the final results substantially. Project VLBI-ART contributes to these objectives by implementing an elaborate Kalman filter, which represents a perfect tool for analyzing VLBI data in quasi real-time. The goal is to implement it in the GFZ version of the Vienna VLBI Software (VieVS) as a completely automated tool, i.e., with no need for human interaction. Here we present the methodology and first results of Kalman filtered EOP from VLBI data.
Multimodal Degradation Prognostics Based on Switching Kalman Filter Ensemble.
Lim, Pin; Goh, Chi Keong; Tan, Kay Chen; Dutta, Partha
2017-01-01
For accurate prognostics, users have to determine the current health of the system and predict future degradation pattern of the system. An increasingly popular approach toward tackling prognostic problems involves the use of switching models to represent various degradation phases, which the system undergoes. Such approaches have the advantage of determining the exact degradation phase of the system and being able to handle nonlinear degradation models through piecewise linear approximation. However, limitations of such existing methods include, limited applicability due to the discretization of predicted remaining useful life, insufficient robustness due to the use of single models and others. This paper circumvents these limitations by proposing a hybrid of ensemble methods with switching methods. The proposed method first implements a switching Kalman filter (SKF) to classify between various linear degradation phases, then predict the future propagation of fault dimension using appropriate Kalman filters for each phase. This proposed method achieves both continuous and discrete prediction values representing the remaining life and degradation phase of the system, respectively. The proposed framework is shown via a case study on benchmark simulated aeroengine data sets. The evaluation of the proposed framework shows that the proposed method achieves better accuracy and robustness against noise compared with other methods reported in the literature. The results also indicate the effectiveness of the SKF in detecting the switching point between various degradation modes.
Direct and accelerated parameter mapping using the unscented Kalman filter.
Zhao, Li; Feng, Xue; Meyer, Craig H
2016-05-01
To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.
Kalman Filtering USNO's GPS Observations for Improved Time Transfer Predictions
NASA Technical Reports Server (NTRS)
Hutsell, Steven T.
1996-01-01
The Global Positioning System (GPS) Master Control Station (MCS) performs the Coordinated Universal Time (UTC) time transfer mission by uploading and broadcasting predictions of the GPS-UTC offset in subframe 4 of the GS navigation message. These predictions are based on only two successive daily data points obtained from the US Naval Observatory (USNO). USNO produces these daily smoothed data points by performing a least-squares fit on roughly 38 hours worth of data from roughly 160 successive 13-minute tracks of GPS satellites. Though sufficient for helping to maintain a time transfer error specification of 28 ns (1 Sigma), the MCS's prediction algorithm does not make the best use of the available data from from USNO, and produces data that can degrade quickly over extended prediction spans. This paper investigates how, by applying Kalman filtering to the same available tracking data, the MCS could improve its estimate of GPS-UTC, and in particular, the GPS-UTC A(sub 1) term. By refining the A(sub 1) (frequency) estimate for GPS-UTC predictions, error in GPS time transfer could drop significantly. Additional, the risk of future spikes in GPS's time transfer error could similarly be minimized, by employing robust Kalman filtering for GPS-UTC predictions.
Skew redundant MEMS IMU calibration using a Kalman filter
NASA Astrophysics Data System (ADS)
Jafari, M.; Sahebjameyan, M.; Moshiri, B.; Najafabadi, T. A.
2015-10-01
In this paper, a novel calibration procedure for skew redundant inertial measurement units (SRIMUs) based on micro-electro mechanical systems (MEMS) is proposed. A general model of the SRIMU measurements is derived which contains the effects of bias, scale factor error and misalignments. For more accuracy, the effect of lever arms of the accelerometers to the center of the table are modeled and compensated in the calibration procedure. Two separate Kalman filters (KFs) are proposed to perform the estimation of error parameters for gyroscopes and accelerometers. The predictive error minimization (PEM) stochastic modeling method is used to simultaneously model the effect of bias instability and random walk noise on the calibration Kalman filters to diminish the biased estimations. The proposed procedure is simulated numerically and has expected experimental results. The calibration maneuvers are applied using a two-axis angle turntable in a way that the persistency of excitation (PE) condition for parameter estimation is met. For this purpose, a trapezoidal calibration profile is utilized to excite different deterministic error parameters of the accelerometers and a pulse profile is used for the gyroscopes. Furthermore, to evaluate the performance of the proposed KF calibration method, a conventional least squares (LS) calibration procedure is derived for the SRIMUs and the simulation and experimental results compare the functionality of the two proposed methods with each other.
Estimation of geothermal reservoir properties using the Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Marquart, Gabriele; Vogt, Christian; Widera, André
2013-04-01
Information about the distribution of permeability, temperature, and heat flow in the subsurface are of primary importance for the exploitation of geothermal reservoirs. The Ensemble Kalman Filter is a powerful tool to estimate these properties if temporal observations at a few drill holes in the reservoir are available. These observations can be temperature (BHT), hydraulic head during pumping tests, and chemical concentrations of tracer experiments. The Ensemble Kalman Filter is a recursive Bayesian method based on a Monte Carlo implementation to incorporate observations in an ensemble of reservoir simulations considering the probability of the model state and the likelihood of the observation. Assimilating data forces the simulation of the system to adjust the reservoir properties in the way to the match the data. Here we demonstrate the application of the EnKF for estimating reservoir permeability for different combinations of observations and number of observation sites in a synthetic test case and apply the method to the tracer experiment of 2005 of the Soultz-sous-Forêts reservoir.
Time transfer using geostationary satellites: Implementation of a Kalman filter
NASA Technical Reports Server (NTRS)
Meyer, F.
1994-01-01
Since 1988, various experiments have shown that the TV signals transmitted by direct TV satellites may easily be used to perform time transfers at the level of a few tens of nanoseconds, the main source of error being the uncertainty on the satellite position. We first present the two methods used in our experiment to reduce the effects of the satellite residual motion: the first one consists in estimating the longitude variations of the satellite and then using this information to improve other measurements. This allows reducing the uncertainty to values between 9 and 50 nanoseconds according to the position of the involved stations. In the second method we determine the satellite position by using the data collected by three calibrated stations. Time transfer between each of these stations and a fourth one has been shown to be achievable at the precision level of ten nanoseconds. A new approach based on the use of a Kalman filter is proposed in order to take into account the dynamics of the geostationary satellite. The precisions on orbital elements and clock differences and rates determination given by the first simulated applications of the Kalman filter are presented and compared to those obtained by the other methods.
Reconstruction of spacecraft rotational motion using a Kalman filter
NASA Astrophysics Data System (ADS)
Pankratov, V. A.; Sazonov, V. V.
2016-05-01
Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.
NASA Astrophysics Data System (ADS)
Peng, Jing; Wu, Falin; Zhu, Ming; Wang, Feixue; Zhang, Kefei
In this paper, an improved GPS/RFID integration method based on Sequential Iterated Reduced Sigma Point Kalman Filter (SIRSPKF) is proposed for vehicle navigation applications. It is applied to improve the accuracy, reliability and availability of satellite positioning in the areas where the satellite visibility is limited. An RFID system is employed to assist the GPS system in achieving high accuracy positioning. Further, to reduce the measurement noise and decrease the computational complexity caused by the integrated GPS/RFID, SIRSPKF is investigated as the dominant filter for the proposed integration. Performances and computational complexities of different integration scenarios with different filters are compared in this paper. A field experiment shows that both accuracy and availability of positioning can be improved significantly by this low-cost GPS/RFID integration method with the reduced computational load.
NASA Technical Reports Server (NTRS)
Lam, Quang; Chipman, Richard; Sunkel, John
1991-01-01
Two algorithms, extended Kalman filter and neuro-filter, are formulated to perform mass property identification for the Space Station Freedom. Control moment gyros that are part of the Station's basic momentum management system are chosen to provide input excitation in the form of applied torques. These torques together with the measured angular body rate responses are supplied to the filters. From these data, both algorithms are shown to accurately identify the station mass properties when excitation levels are high and balanced between axes. The neuro-filter, however, is shown to be more robust and to perform well even with weakly persistent, unbalanced signals contaminated with noise.
Improved Kalman filter method for measurement noise reduction in multi sensor RFID systems.
Eom, Ki Hwan; Lee, Seung Joon; Kyung, Yeo Sun; Lee, Chang Won; Kim, Min Chul; Jung, Kyung Kwon
2011-01-01
Recently, the range of available radio frequency identification (RFID) tags has been widened to include smart RFID tags which can monitor their varying surroundings. One of the most important factors for better performance of smart RFID system is accurate measurement from various sensors. In the multi-sensing environment, some noisy signals are obtained because of the changing surroundings. We propose in this paper an improved Kalman filter method to reduce noise and obtain correct data. Performance of Kalman filter is determined by a measurement and system noise covariance which are usually called the R and Q variables in the Kalman filter algorithm. Choosing a correct R and Q variable is one of the most important design factors for better performance of the Kalman filter. For this reason, we proposed an improved Kalman filter to advance an ability of noise reduction of the Kalman filter. The measurement noise covariance was only considered because the system architecture is simple and can be adjusted by the neural network. With this method, more accurate data can be obtained with smart RFID tags. In a simulation the proposed improved Kalman filter has 40.1%, 60.4% and 87.5% less mean squared error (MSE) than the conventional Kalman filter method for a temperature sensor, humidity sensor and oxygen sensor, respectively. The performance of the proposed method was also verified with some experiments.
Kalman filter for statistical monitoring of forest cover across sub-continental regions
Raymond L. Czaplewski
1991-01-01
The Kalman filter is a multivariate generalization of the composite estimator which recursively combines a current direct estimate with a past estimate that is updated for expected change over time with a prediction model. The Kalman filter can estimate proportions of different cover types for sub-continental regions each year. A random sample of high-resolution...
An Improved Unscented Kalman Filter Based Decoder for Cortical Brain-Machine Interfaces
Li, Simin; Li, Jie; Li, Zheng
2016-01-01
Brain-machine interfaces (BMIs) seek to connect brains with machines or computers directly, for application in areas such as prosthesis control. For this application, the accuracy of the decoding of movement intentions is crucial. We aim to improve accuracy by designing a better encoding model of primary motor cortical activity during hand movements and combining this with decoder engineering refinements, resulting in a new unscented Kalman filter based decoder, UKF2, which improves upon our previous unscented Kalman filter decoder, UKF1. The new encoding model includes novel acceleration magnitude, position-velocity interaction, and target-cursor-distance features (the decoder does not require target position as input, it is decoded). We add a novel probabilistic velocity threshold to better determine the user's intent to move. We combine these improvements with several other refinements suggested by others in the field. Data from two Rhesus monkeys indicate that the UKF2 generates offline reconstructions of hand movements (mean CC 0.851) significantly more accurately than the UKF1 (0.833) and the popular position-velocity Kalman filter (0.812). The encoding model of the UKF2 could predict the instantaneous firing rate of neurons (mean CC 0.210), given kinematic variables and past spiking, better than the encoding models of these two decoders (UKF1: 0.138, p-v Kalman: 0.098). In closed-loop experiments where each monkey controlled a computer cursor with each decoder in turn, the UKF2 facilitated faster task completion (mean 1.56 s vs. 2.05 s) and higher Fitts's Law bit rate (mean 0.738 bit/s vs. 0.584 bit/s) than the UKF1. These results suggest that the modeling and decoder engineering refinements of the UKF2 improve decoding performance. We believe they can be used to enhance other decoders as well. PMID:28066170
An Improved Unscented Kalman Filter Based Decoder for Cortical Brain-Machine Interfaces.
Li, Simin; Li, Jie; Li, Zheng
2016-01-01
Brain-machine interfaces (BMIs) seek to connect brains with machines or computers directly, for application in areas such as prosthesis control. For this application, the accuracy of the decoding of movement intentions is crucial. We aim to improve accuracy by designing a better encoding model of primary motor cortical activity during hand movements and combining this with decoder engineering refinements, resulting in a new unscented Kalman filter based decoder, UKF2, which improves upon our previous unscented Kalman filter decoder, UKF1. The new encoding model includes novel acceleration magnitude, position-velocity interaction, and target-cursor-distance features (the decoder does not require target position as input, it is decoded). We add a novel probabilistic velocity threshold to better determine the user's intent to move. We combine these improvements with several other refinements suggested by others in the field. Data from two Rhesus monkeys indicate that the UKF2 generates offline reconstructions of hand movements (mean CC 0.851) significantly more accurately than the UKF1 (0.833) and the popular position-velocity Kalman filter (0.812). The encoding model of the UKF2 could predict the instantaneous firing rate of neurons (mean CC 0.210), given kinematic variables and past spiking, better than the encoding models of these two decoders (UKF1: 0.138, p-v Kalman: 0.098). In closed-loop experiments where each monkey controlled a computer cursor with each decoder in turn, the UKF2 facilitated faster task completion (mean 1.56 s vs. 2.05 s) and higher Fitts's Law bit rate (mean 0.738 bit/s vs. 0.584 bit/s) than the UKF1. These results suggest that the modeling and decoder engineering refinements of the UKF2 improve decoding performance. We believe they can be used to enhance other decoders as well.
Application of Kalman Filtering Techniques for Microseismic Event Detection
NASA Astrophysics Data System (ADS)
Baziw, E.; Weir-Jones, I.
- Microseismic monitoring systems are generally installed in areas of induced seismicity caused by human activity. Induced seismicity results from changes in the state of stress which may occur as a result of excavation within the rock mass in mining (i.e., rockbursts), and changes in hydrostatic pressures and rock temperatures (e.g., during fluid injection or extraction) in oil exploitation, dam construction or fluid disposal. Microseismic monitoring systems determine event locations and important source parameters such as attenuation, seismic moment, source radius, static stress drop, peak particle velocity and seismic energy. An essential part of the operation of a microseismic monitoring system is the reliable detection of microseismic events. In the absence of reliable, automated picking techniques, operators rely upon manual picking. This is time-consuming, costly and, in the presence of background noise, very prone to error. The techniques described in this paper not only permit the reliable identification of events in cluttered signal environments they have also enabled the authors to develop reliable automated event picking procedures. This opens the way to use microseismic monitoring as a cost-effective production/operations procedure. It has been the experience of the authors that in certain noisy environments, the seismic monitoring system may trigger on and subsequently acquire substantial quantities of erroneous data, due to the high energy content of the ambient noise. Digital filtering techniques need to be applied on the microseismic data so that the ambient noise is removed and event detection simplified. The monitoring of seismic acoustic emissions is a continuous, real-time process and it is desirable to implement digital filters which can also be designed in the time domain and in real-time such as the Kalman Filter. This paper presents a real-time Kalman Filter which removes the statistically describable background noise from the recorded
An extended Kalman filter for spinning spacecraft attitude estimation
NASA Technical Reports Server (NTRS)
Baker, David F.
1991-01-01
An extended Kalman filter for real-time ground attitude estimation of a gyro-less spinning spacecraft was developed and tested. The filter state vector includes the angular momentum direction, phase angle, inertial nutation angle, and inertial and body nutation rates. The filter solves for the nutating three-axis attitude and accounts for effects due to principle axes offset from the body axes. The attitude is propagated using the kinematics of a rigid body symmetric about the principle spin axis; disturbance torques are assumed to be small. Filter updates consist only of the measured angles between celestial objects (Sun, Earth, etc.) and the nominal spin axis, and the times these angles were measured. Both simulated data and real data from the Dynamics Explorer -A (DE-A) spacecraft were used to test the filter; the results are presented. Convergence was achieved rapidly from a wide range of a priori state estimates, and sub-degree accuracy was attained. Systematic errors affecting the solution accuracy are discussed, as are the results of an attempt to solve for sensor measurement angle biases in the state vector.
Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Miller, Brad A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Miller, Brad A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Miller, Bard A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
NASA Technical Reports Server (NTRS)
Snow, Frank; Harman, Richard; Garrick, Joseph
1988-01-01
The Gamma Ray Observatory (GRO) spacecraft needs a highly accurate attitude knowledge to achieve its mission objectives. Utilizing the fixed-head star trackers (FHSTs) for observations and gyroscopes for attitude propagation, the discrete Kalman Filter processes the attitude data to obtain an onboard accuracy of 86 arc seconds (3 sigma). A combination of linear analysis and simulations using the GRO Software Simulator (GROSS) are employed to investigate the Kalman filter for stability and the effects of corrupted observations (misalignment, noise), incomplete dynamic modeling, and nonlinear errors on Kalman filter. In the simulations, on-board attitude is compared with true attitude, the sensitivity of attitude error to model errors is graphed, and a statistical analysis is performed on the residuals of the Kalman Filter. In this paper, the modeling and sensor errors that degrade the Kalman filter solution beyond mission requirements are studied, and methods are offered to identify the source of these errors.
[Application of kalman filtering based on wavelet transform in ICP-AES].
Qin, Xia; Shen, Lan-sun
2002-12-01
Kalman filtering is a recursive algorithm, which has been proposed as an attractive alternative to correct overlapping interferences in ICP-AES. However, the noise in ICP-AES contaminates the signal arising from the analyte and hence limits the accuracy of kalman filtering. Wavelet transform is a powerful technique in signal denoising due to its multi-resolution characteristics. In this paper, first, the effect of noise on kalman filtering is discussed. Then we apply the wavelet-transform-based soft-thresholding as the pre-processing of kalman filtering. The simulation results show that the kalman filtering based on wavelet transform can effectively reduce the noise and increase the accuracy of the analysis.
Particle and Kalman filtering for state estimation and control of DC motors.
Rigatos, Gerasimos G
2009-01-01
State estimation is a major problem in industrial systems. To this end, Gaussian and nonparametric filters have been developed. In this paper the Kalman Filter, which assumes Gaussian measurement noise, is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a DC motor is used. The reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor. In simulation tests it was observed that for a large number of particles the Particle Filter could succeed in accurately estimating the motor's state vector, but at the same time it required higher computational effort.
Kalman Filters in Improving the Signal to Noise Ratio of Full Tensor Gravity Gradiometry Data
NASA Astrophysics Data System (ADS)
Sepehrmanesh, M.; Ravat, D.
2014-12-01
We have applied several extensions and optimal smoothing approaches of the Kalman filter, one of the best known recursive data processing techniques, on the Full Tensor Gradiometry (FTG) data acquired by Bell Geospace over the Vinton salt dome located in southwest Louisiana. We used the filter to improve the signal-to-noise ratio of gravity gradiometry components. We tested the standard Kalman filter and Fading memory and Constrained Kalman filter extensions with Fixed-lag and Forward-Backward smoothing methods to maintain symmetry. Our most meaningful results were obtained through the Kalman filter with the constraint of Laplace's equation combined with the Forward-Backward filter operations. Laplace's equation constraint was incorporated using two separate strategies: Model reduction and Perfect constraint (or Perfect measurement). In general, Kalman filter processed data have greater dynamic range than previously filtered data and also have the ability to extract signal from noisy data without having to remove a band of wavenumbers. In addition, our constrained Kalman filter also has the ability to force the Laplace's equation constraint. These characteristics enable the Kalman filter to investigate short wavelength signals associated with near-surface lateral density variations. In analyzing two dimensional maps for geologic variations, our workflow includes leveling and decorrugation, both procedures necessary for data processed along profiles. Several previously mapped near-subsurface geologic features like faults and their continuity in the Vinton dome area are more readily apparent in our Kalman filter processed components. Since the processed data generally agree with the previously mapped and interpreted structures, the interpretation could be extended to previously unmapped areas. The use of Kalman filtering in combination with Laplace's equation in applications such as gravity and magnetic gradiometry could be useful in determining more precisely the
Estimating ice-affected streamflow by extended Kalman filtering
Holtschlag, D.J.; Grewal, M.S.
1998-01-01
An extended Kalman filter was developed to automate the real-time estimation of ice-affected streamflow on the basis of routine measurements of stream stage and air temperature and on the relation between stage and streamflow during open-water (ice-free) conditions. The filter accommodates three dynamic modes of ice effects: sudden formation/ablation, stable ice conditions, and eventual elimination. The utility of the filter was evaluated by applying it to historical data from two long-term streamflow-gauging stations, St. John River at Dickey, Maine and Platte River at North Bend, Nebr. Results indicate that the filter was stable and that parameters converged for both stations, producing streamflow estimates that are highly correlated with published values. For the Maine station, logarithms of estimated streamflows are within 8% of the logarithms of published values 87.2% of the time during periods of ice effects and within 15% 96.6% of the time. Similarly, for the Nebraska station, logarithms of estimated streamflows are within 8% of the logarithms of published values 90.7% of the time and within 15% 97.7% of the time. In addition, the correlation between temporal updates and published streamflows on days of direct measurements at the Maine station was 0.777 and 0.998 for ice-affected and open-water periods, respectively; for the Nebraska station, corresponding correlations were 0.864 and 0.997.
Using Kalman filters to reduce noise from RFID location system.
Abreu, Pedro Henriques; Xavier, José; Silva, Daniel Castro; Reis, Luís Paulo; Petry, Marcelo
2014-01-01
Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes-linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11-13% of improvement).
Using Kalman Filters to Reduce Noise from RFID Location System
Xavier, José; Reis, Luís Paulo; Petry, Marcelo
2014-01-01
Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes—linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11–13% of improvement). PMID:24592186
Constraining the Ensemble Kalman Filter for improved streamflow forecasting
NASA Astrophysics Data System (ADS)
Maxwell, Deborah; Jackson, Bethanna; McGregor, James
2016-04-01
Data assimilation techniques such as the Kalman Filter and its variants are often applied to hydrological models with minimal state volume/capacity constraints. Flux constraints are rarely, if ever, applied. Consequently, model states can be adjusted beyond physically reasonable limits, compromising the integrity of model output. In this presentation, we investigate the effect of constraining the Ensemble Kalman Filter (EnKF) on forecast performance. An EnKF implementation with no constraints is compared to model output with no assimilation, followed by a 'typical' hydrological implementation (in which mass constraints are enforced to ensure non-negativity and capacity thresholds of model states are not exceeded), and then a more tightly constrained implementation where flux as well as mass constraints are imposed to limit the rate of water movement within a state. A three year period (2008-2010) with no significant data gaps and representative of the range of flows observed over the fuller 1976-2010 record was selected for analysis. Over this period, the standard implementation of the EnKF (no constraints) contained eight hydrological events where (multiple) physically inconsistent state adjustments were made. All were selected for analysis. Overall, neither the unconstrained nor the "typically" mass-constrained forecasts were significantly better than the non-filtered forecasts; in fact several were significantly degraded. Flux constraints (in conjunction with mass constraints) significantly improved the forecast performance of six events relative to all other implementations, while the remaining two events showed no significant difference in performance. We conclude that placing flux as well as mass constraints on the data assimilation framework encourages physically consistent state updating and results in more accurate and reliable forward predictions of streamflow for robust decision-making. We also experiment with the observation error, and find that this
Kalman Filter for Mass Property and Thrust Identification (MMS)
NASA Technical Reports Server (NTRS)
Queen, Steven
2015-01-01
The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories, elliptically orbiting the Earth in a tetrahedron formation. For the operational success of the mission, on-board systems must be able to deliver high-precision orbital adjustment maneuvers. On MMS, this is accomplished using feedback from on-board star sensors in tandem with accelerometers whose measurements are dynamically corrected for errors associated with a spinning platform. In order to determine the required corrections to the measured acceleration, precise estimates of attitude, rate, and mass-properties is necessary. To this end, both an on-board and ground-based Multiplicative Extended Kalman Filter (MEKF) were formulated and implemented in order to estimate the dynamic and quasi-static properties of the spacecraft.
Robust car tracking using Kalman filtering and Bayesian templates
NASA Astrophysics Data System (ADS)
Dellaert, Frank; Thorpe, Chuck E.
1998-01-01
We present a real-time model-based vision approach for detecting and tracking vehicles from a moving platform. It was developed in the context of the CMU Navlab project and is intended to provide the Navlabs with situational awareness in mixed traffic. Tracking is done by combining a simple image processing techniques with a 3D extended Kalman filter and a measurement equation that projects from the 3D model to image space. No ground plane assumption is made. The resulting system runs at frame rate or higher, and produces excellent estimates of road curvature, distance to and relative speed of a tracked vehicle. We have complemented the tracker with a novel machine learning based algorithm for car detection, the CANSS algorithm, which serves to initialize tracking.
Damping strapdown inertial navigation system based on a Kalman filter
NASA Astrophysics Data System (ADS)
Zhao, Lin; Li, Jiushun; Cheng, Jianhua; Hao, Yong
2016-11-01
A damping strapdown inertial navigation system (DSINS) can effectively suppress oscillation errors of strapdown inertial navigation systems (SINSs) and improve the navigation accuracy of SINSs. Aiming at overcoming the disadvantages of traditional damping methods, a DSINS, based on a Kalman filter (KF), is proposed in this paper. Using the measurement data of accelerometers and calculated navigation parameters during the navigation process, the expression of the observation equation is derived. The calculation process of the observation in both the internal damping state and the external damping state is presented. Finally, system oscillation errors are compensated by a KF. Simulation and test results show that, compared with traditional damping methods, the proposed method can reduce system overshoot errors and shorten the convergence time of oscillation errors effectively.
The development of a Kalman filter clock predictor
NASA Technical Reports Server (NTRS)
Davis, John A.; Greenhall, Charles A.; Boudjemaa, Redoane
2005-01-01
A Kalman filter based clock predictor is developed, and its performance evaluated using both simulated and real data. The clock predictor is shown to possess a neat to optimal Prediction Error Variance (PEV) when the underlying noise consists of one of the power law noise processes commonly encountered in time and frequency measurements. The predictor's performance is the presence of multiple noise processes is also examined. The relationship between the PEV obtained in the presence of multiple noise processes and those obtained for the individual component noise processes is examined. Comparisons are made with a simple linear clock predictor. The clock predictor is used to predict future values of the time offset between pairs of NPL's active hydrogen masers.
Estimation of noise parameters in dynamical system identification with Kalman filters.
Kwasniok, Frank
2012-09-01
A method is proposed for determining dynamical and observational noise parameters in state and parameter identification from time series using Kalman filters. The noise covariances are estimated in a secondary optimization by maximizing the predictive likelihood of the data. The approach is based on internal consistency; for the correct noise parameters, the uncertainty projected by the Kalman filter matches the actual predictive uncertainty. The method is able to disentangle dynamical and observational noise. The algorithm is demonstrated for the linear, extended, and unscented Kalman filters using an Ornstein-Uhlenbeck process, the noise-driven Lorenz system, and van der Pol oscillator as well as a paleoclimatic ice-core record as examples. The approach is also applicable to the ensemble Kalman filter and can be readily extended to non-Gaussian estimation frameworks such as Gaussian-sum filters and particle filters.
A constrained neural network Kalman filter for price estimation in high frequency financial data.
Bolland, P J; Connor, J T
1997-08-01
In this paper we present a neural network extended Kalman filter for modeling noisy financial time series. The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter. Conditions for the neural network weight matrix are provided to guarantee the stability of the filter. The extended Kalman filter presented is designed to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise. The erratic arrival of data (arrival noise) results in the neural network predictions being iterated into the future. Constraining the neural network to have a fixed point at the origin produces better iterated predictions and more stable results. The performance of constrained and unconstrained neural networks within the extended Kalman filter is demonstrated on "Quote" tick data from the $/DM exchange rate (1993-1995).
Determination and prediction of EOP using Kalman filtering
NASA Astrophysics Data System (ADS)
Karbon, Maria; Nilsson, Tobias; Schuh, Harald
2013-04-01
The necessity to observe and predict short term variations in the Earth's rotation in near real-time has increased significantly over the last decades, in particular in regard to satellite navigation and positioning and tracking of interplanetary spacecrafts. As the orientation of the Earth changes unpredictably in a rapid and irregular manner, the observation of extra-terrestrial objects from the Earth are affected by such variations and a precise knowledge of these changes is needed. Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques providing the full set of Earth Orientation Parameter (EOP) and it is unique for observing long term Universal Time (UT1) and nutation. Also other space geodetic techniques, such as Global Navigation Satellite Systems (GNSS) , Lunar Laser Ranging, and Satellite Laser Ranging, are able to determine the EOP as well. The challenge lies in the combination of these various EOP series as each technique is sensitive to a different subset or linear combination of the EOP also the precision of the determination differs between the techniques as well as the temporal density of the data. Within the project VLBI-Art an elaborate Kalman filter is developed to determine and predict EOP through combining data sets from various techniques by implementing stochastic models to account statistically for unpredictable changes in EOP. Furthermore, atmospheric angular momentum calculated from numerical weather models are introduced to supplement the short-term prediction of UT1 and polar motion, making use of the high correlation between these parameters. The potential of incorporating additional data like ring-laser gyroscope observations will be investigated. This Kalman filter will be extended and embedded in the newly developed Vienna VLBI Software (VieVS) as a completely automated tool enabling it to analyze VLBI in near real-time, providing all the parameter of interest with the highest possible
Upper Atmosphere Data Assimilation using an ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Matsuo, T.; Lee, I.; Anderson, J. L.
2013-12-01
We present an application of ensemble Kalman filtering (EnKF) to a general circulation model of the thermosphere and ionosphere. An EnKF assimilation procedure has been constructed using the Data Assimilation Research Testbed and the Thermoshere-Ionosphere Electrodynamics General Circulation Model, two sets of community software offered by NCAR. It is designed to incorporate thermosphere-ionosphere coupling self-consistently both in the analysis and forecast steps of filtering, so that thermospheric parameters can be inferred from ionospheric observations and vice versa. One of the important advantages of the EnKF is that its covariance is consistent with the time-dependent dynamics of the thermosphere and ionosphere. In spite of sampling error issues, cross-covariance between observations and unobserved state variables obtained from the ensemble is effective enough to constrain the thermospheric state from abundant observations of electron density, which in turn improves the overall specification of the ionosphere. We demonstrate these points using specific observations including (i) neutral mass densities obtained from the accelerometer experiment on board the CHAMP satellite, and (ii) electron density profiles obtained from the COSMIC/FORMOSAT-3 mission. Furthermore, we discuss some of the issues specific to upper atmospheric EnKF applications and the roles of auxiliary filtering algorithms, such as adaptive covariance inflation and localization of covariance, to cope with these issues.
Unscented Kalman filtering for single camera based motion and shape estimation.
Jwo, Dah-Jing; Tseng, Chien-Hao; Liu, Jen-Chu; Lee, Hsien-Der
2011-01-01
Accurate estimation of the motion and shape of a moving object is a challenging task due to great variety of noises present from sources such as electronic components and the influence of the external environment, etc. To alleviate the noise, the filtering/estimation approach can be used to reduce it in streaming video to obtain better estimation accuracy in feature points on the moving objects. To deal with the filtering problem in the appropriate nonlinear system, the extended Kalman filter (EKF), which neglects higher-order derivatives in the linearization process, has been very popular. The unscented Kalman filter (UKF), which uses a deterministic sampling approach to capture the mean and covariance estimates with a minimal set of sample points, is able to achieve at least the second order accuracy without Jacobians' computation involved. In this paper, the UKF is applied to the rigid body motion and shape dynamics to estimate feature points on moving objects. The performance evaluation is carried out through the numerical study. The results show that UKF demonstrates substantial improvement in accuracy estimation for implementing the estimation of motion and planar surface parameters of a single camera.
1993-07-30
Document No. WRDC-TR-89-1152. Los Gatos , CA, Feb 1990. 20. Wei, M. and K.P. Schwarz. "Testing a Decentralized Filter for GPS/INS Integration", IEEE...a LL * 4j 0 Q 0 0 joj- ------- 5.- ~uv B-29- .: ...... ........ - .. C CD CD cc~ LO) U)) U. w N cm JO1JJ SOIS 1eIGWfIII JBPOEU NV.L B-30 Appendix C
A SAS/IML program using the Kalman filter for estimating state space models.
Gu, Fei; Yung, Yiu-Fai
2013-03-01
To help disseminate the knowledge and software implementation of a state space model (SSM), this article provides a SAS/IML (SAS Institute, 2010) program for estimating the parameters of general linear Gaussian SSMs using the Kalman filter algorithm. In order to use this program, the user should have SAS installed on a computer and have a valid license for SAS/IML. Since the code is completely open, it is expected that this program can be used not only by applied researchers, but also by quantitative methodologists who are interested in improving their methods and promoting SSM as a research instrument.
Ohkubo, Jun
2015-10-01
An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.
Second-order discrete Kalman filtering equations for control-structure interaction simulations
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.
1991-01-01
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.
Zero Gyro Kalman Filtering in the presence of a Reaction Wheel Failure
NASA Technical Reports Server (NTRS)
Hur-Diaz, Sun; Wirzburger, John; Smith, Dan; Myslinski, Mike
2007-01-01
Typical implementation of Kalman filters for spacecraft attitude estimation involves the use of gyros for three-axis rate measurements. When there are less than three axes of information available, the accuracy of the Kalman filter depends highly on the accuracy of the dynamics model. This is particularly significant during the transient period when a reaction wheel with a high momentum fails, is taken off-line, and spins down. This paper looks at how a reaction wheel failure can affect the zero-gyro Kalman filter performance for the Hubble Space Telescope and what steps are taken to minimize its impact.
Zero Gyro Kalman Filtering in the Presence of a Reaction Wheel Failure
NASA Technical Reports Server (NTRS)
Hur-Diaz, Sun; Wirzburger, John; Smith, Dan; Myslinski, Mike
2007-01-01
Typical implementation of Kalman filters for spacecraft attitude estimation involves the use of gyros for three-axis rate measurements. When there are less than three axes of information available, the accuracy of the Kalman filter depends highly on the accuracy of the dynamics model. This is particularly significant during the transient period when a reaction wheel with a high momentum fails, is taken off-line, and spins down. This paper looks at how a reaction wheel failure can affect the zero-gyro Kalman filter performance for the Hubble Space Telescope and what steps are taken to minimize its impact.
Hesar, Hamed Danandeh; Mohebbi, Maryam
2017-05-01
In this paper, a model-based Bayesian filtering framework called the "marginalized particle-extended Kalman filter (MP-EKF) algorithm" is proposed for electrocardiogram (ECG) denoising. This algorithm does not have the extended Kalman filter (EKF) shortcoming in handling non-Gaussian nonstationary situations because of its nonlinear framework. In addition, it has less computational complexity compared with particle filter. This filter improves ECG denoising performance by implementing marginalized particle filter framework while reducing its computational complexity using EKF framework. An automatic particle weighting strategy is also proposed here that controls the reliance of our framework to the acquired measurements. We evaluated the proposed filter on several normal ECGs selected from MIT-BIH normal sinus rhythm database. To do so, artificial white Gaussian and colored noises as well as nonstationary real muscle artifact (MA) noise over a range of low SNRs from 10 to -5 dB were added to these normal ECG segments. The benchmark methods were the EKF and extended Kalman smoother (EKS) algorithms which are the first model-based Bayesian algorithms introduced in the field of ECG denoising. From SNR viewpoint, the experiments showed that in the presence of Gaussian white noise, the proposed framework outperforms the EKF and EKS algorithms in lower input SNRs where the measurements and state model are not reliable. Owing to its nonlinear framework and particle weighting strategy, the proposed algorithm attained better results at all input SNRs in non-Gaussian nonstationary situations (such as presence of pink noise, brown noise, and real MA). In addition, the impact of the proposed filtering method on the distortion of diagnostic features of the ECG was investigated and compared with EKF/EKS methods using an ECG diagnostic distortion measure called the "Multi-Scale Entropy Based Weighted Distortion Measure" or MSEWPRD. The results revealed that our proposed
SEPARATION OF OVERLAPPED ELECTROCHEMICAL PEAKS USING THE KALMAN FILTER
Brown, T. F.; Brown, S. D.
1981-01-01
A major limitation in the use of electrochemical techniques for the quantitative analysis of mixtures is the difficulty of resolving overlapped peaks. This problem is further complicated by the low signal-to-noise ratios often encountered in trace analysis and by the use of electrochemical techniques that produce broad, asymmetric waveforms. This paper demonstrates the use of the Kalman Filter for multi-component analysis of linear sweep voltammograms. Even with the broad, asymmetric LSV waveform, synthetic data runs show that a peak separation of as little as 2.5 mV is sufficient for peak deconvolution in the presence of random noise. Besides separating overlapped peaks, the methods also filters the noise from the signal and can be used to separate the capacitive current component from the faradaic current component. The method is validated further using the Cd(II)/In(III) and Cd(II)/In(III)/Pb(II) systems which show peak separations of 40 to 200 mV. The use of the techniques with two other voltammetric waveforms is also demonstrated.
Kalman filter approach to traffic modeling and prediction
NASA Astrophysics Data System (ADS)
Grindey, Gregory J.; Amin, S. M.; Rodin, Ervin Y.; Garcia-Ortiz, Asdrubal
1998-01-01
The objective of our work has been to develop and integrate prediction, control and optimization modules for use in highway traffic management. This is accomplished through the use of the Semantic Control paradigm, implementing a hybrid prediction/routing/control system, to model both macro-level as well a micro level. This paper addresses the design and operation of a Kalman filter that processes traffic sensor data in order to model and predict highway traffic volume. This data was given in the form of hourly traffic flow, and has been fit using a cubic spline method to allow observations at various time intervals. THe filter is augmented via the Method of Sage and Husa to identify the parameters of the system noise on-line, and to determine the dynamics of the traffic process iteratively to aid in the prediction of the future traffic. The results show a good ability to predict traffic flow at the sensors for several time periods in the future, as well as some noise rejection capabilities.
Kalman filtering techniques for focal plane electric field estimation.
Groff, Tyler D; Jeremy Kasdin, N
2013-01-01
For a coronagraph to detect faint exoplanets, it will require focal plane wavefront control techniques to continue reaching smaller angular separations and higher contrast levels. These correction algorithms are iterative and the control methods need an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. The best way to make such algorithms the least disruptive to science exposures is to reduce the number required to estimate the field. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field while stabilizing the suppression against poor signal-to-noise. In addition to a significant reduction in exposures, we discuss the relative merit of this algorithm to estimation schemes that do not incorporate prior state estimate history, particularly in regard to estimate error and covariance. Ultimately the filter will lead to an adaptive algorithm which can estimate physical parameters in the laboratory for robustness to variance in the optical train.
A Kalman filter to estimate altitude change during a fall.
Stevens, Michael C; Wei Lu; Changhong Wang; Redmond, Stephen J; Lovell, Nigel H
2016-08-01
Barometers have been incorporated into fall detectors in order to enhance the accuracy of fall detection algorithms, however they are power-hungry devices. We present an offline evaluation of a Kalman filter (KF) for estimating the pressure change during a fall that enables low-power operation of the barometer. The KF takes advantage of the fact that a semi-permeable air membrane on a waterproof fall detector enclosure causes a delay in the equilibrium between internal and external enclosure pressure, and this delay enables the barometer to be switched off until a free-fall is detected. We assessed the KF using data obtained from simulated falls and activities of daily living. The KF was able to differentiate between fall and non-fall activities, with the average measured pressure change during a fall of 8 Pa best determined using a delay in pressure equalization of 20 seconds. The KF detected a change in altitude faster than a simple moving average filter (MAF), reaching 66% of its final value before the MAF was able to initialize.
A practical scheme of the sigma-point Kalman filter for high-dimensional systems
NASA Astrophysics Data System (ADS)
Tang, Youmin; Deng, Ziwang; Manoj, K. K.; Chen, Dake
2014-03-01
applying a sigma-point Kalman filter (SPKF) to a high-dimensional system such as the oceanic general circulation model (OGCM), a major challenge is to reduce its heavy burden of storage memory and costly computation. In this study, we propose a new scheme for SPKF to address these issues. First, a reduced rank SPKF was introduced on the high-dimensional model state space using the truncated single value decomposition (TSVD) method (T-SPKF). Second, the relationship of SVDs between the model state space and a low-dimensional ensemble space is used to construct sigma points on the ensemble space (ET-SPKF). As such, this new scheme greatly reduces the demand of memory storage and computational cost and makes the SPKF method applicable to high-dimensional systems. Two numerical models are used to test and validate the ET-SPKF algorithm. The first model is the 40-variable Lorenz model, which has been a test bed of new assimilation algorithms. The second model is a realistic OGCM for the assimilation of actual observations, including Argo and in situ observations over the Pacific Ocean. The experiments show that ET-SPKF is computationally feasible for high-dimensional systems and capable of precise analyses. In particular, for realistic oceanic assimilations, the ET-SPKF algorithm can significantly improve oceanic analysis and improve ENSO prediction. A comparison between the ET-SPKF algorithm and EnKF (ensemble Kalman filter) is also tribally conducted using the OGCM and actual observations.
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-06-01
In order to improve the tracking accuracy, model estimation accuracy and quick response of multiple model maneuvering target tracking, the interacting multiple models five degree cubature Kalman filter (IMM5CKF) is proposed in this paper. In the proposed algorithm, the interacting multiple models (IMM) algorithm processes all the models through a Markov Chain to simultaneously enhance the model tracking accuracy of target tracking. Then a five degree cubature Kalman filter (5CKF) evaluates the surface integral by a higher but deterministic odd ordered spherical cubature rule to improve the tracking accuracy and the model switch sensitivity of the IMM algorithm. Finally, the simulation results demonstrate that the proposed algorithm exhibits quick and smooth switching when disposing different maneuver models, and it also performs better than the interacting multiple models cubature Kalman filter (IMMCKF), interacting multiple models unscented Kalman filter (IMMUKF), 5CKF and the optimal mode transition matrix IMM (OMTM-IMM).
Denève, Sophie; Duhamel, Jean-René; Pouget, Alexandre
2007-05-23
Several behavioral experiments suggest that the nervous system uses an internal model of the dynamics of the body to implement a close approximation to a Kalman filter. This filter can be used to perform a variety of tasks nearly optimally, such as predicting the sensory consequence of motor action, integrating sensory and body posture signals, and computing motor commands. We propose that the neural implementation of this Kalman filter involves recurrent basis function networks with attractor dynamics, a kind of architecture that can be readily mapped onto cortical circuits. In such networks, the tuning curves to variables such as arm velocity are remarkably noninvariant in the sense that the amplitude and width of the tuning curves of a given neuron can vary greatly depending on other variables such as the position of the arm or the reliability of the sensory feedback. This property could explain some puzzling properties of tuning curves in the motor and premotor cortex, and it leads to several new predictions.
Sadaghzadeh N, Nargess; Poshtan, Javad; Wagner, Achim; Nordheimer, Eugen; Badreddin, Essameddin
2014-03-01
Based on a cascaded Kalman-Particle Filtering, gyroscope drift and robot attitude estimation method is proposed in this paper. Due to noisy and erroneous measurements of MEMS gyroscope, it is combined with Photogrammetry based vision navigation scenario. Quaternions kinematics and robot angular velocity dynamics with augmented drift dynamics of gyroscope are employed as system state space model. Nonlinear attitude kinematics, drift and robot angular movement dynamics each in 3 dimensions result in a nonlinear high dimensional system. To reduce the complexity, we propose a decomposition of system to cascaded subsystems and then design separate cascaded observers. This design leads to an easier tuning and more precise debugging from the perspective of programming and such a setting is well suited for a cooperative modular system with noticeably reduced computation time. Kalman Filtering (KF) is employed for the linear and Gaussian subsystem consisting of angular velocity and drift dynamics together with gyroscope measurement. The estimated angular velocity is utilized as input of the second Particle Filtering (PF) based observer in two scenarios of stochastic and deterministic inputs. Simulation results are provided to show the efficiency of the proposed method. Moreover, the experimental results based on data from a 3D MEMS IMU and a 3D camera system are used to demonstrate the efficiency of the method.
Wang, Rui; Li, Yanxiao; Sun, Hui; Chen, Zengqiang
2017-07-11
The modern civil aircrafts use air ventilation pressurized cabins subject to the limited space. In order to monitor multiple contaminants and overcome the hypersensitivity of the single sensor, the paper constructs an output correction integrated sensor configuration using sensors with different measurement theories after comparing to other two different configurations. This proposed configuration works as a node in the contaminant distributed wireless sensor monitoring network. The corresponding measurement error models of integrated sensors are also proposed by using the Kalman consensus filter to estimate states and conduct data fusion in order to regulate the single sensor measurement results. The paper develops the sufficient proof of the Kalman consensus filter stability when considering the system and the observation noises and compares the mean estimation and the mean consensus errors between Kalman consensus filter and local Kalman filter. The numerical example analyses show the effectiveness of the algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Technical Reports Server (NTRS)
Kelly, D. A.; Fermelia, A.; Lee, G. K. F.
1990-01-01
An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.
NASA Technical Reports Server (NTRS)
Ledsham, W. H.; Staelin, D. H.
1978-01-01
An extended Kalman-Bucy filter has been implemented for atmospheric temperature profile retrievals from observations made using the Scanned Microwave Spectrometer (SCAMS) instrument carried on the Nimbus 6 satellite. This filter has the advantage that it requires neither stationary statistics in the underlying processes nor linear production of the observed variables from the variables to be estimated. This extended Kalman-Bucy filter has yielded significant performance improvement relative to multiple regression retrieval methods. A multi-spot extended Kalman-Bucy filter has also been developed in which the temperature profiles at a number of scan angles in a scanning instrument are retrieved simultaneously. These multi-spot retrievals are shown to outperform the single-spot Kalman retrievals.
Extended Kalman filtering applied to a two-axis robotic arm with flexible links
Lertpiriyasuwat, V.; Berg, M.C.; Buffinton, K.W.
2000-03-01
An industrial robot today uses measurements of its joint positions and models of its kinematics and dynamics to estimate and control its end-effector position. Substantially better end-effector position estimation and control performance would be obtainable if direct measurements of its end-effector position were also used. The subject of this paper is extended Kalman filtering for precise estimation of the position of the end-effector of a robot using, in addition to the usual measurements of the joint positions, direct measurements of the end-effector position. The estimation performances of extended Kalman filters are compared in applications to a planar two-axis robotic arm with very flexible links. The comparisons shed new light on the dependence of extended Kalman filter estimation performance on the quality of the model of the arm dynamics that the extended Kalman filter operates with.
Ghumare, Eshwar; Schrooten, Maarten; Vandenberghe, Rik; Dupont, Patrick
2015-08-01
Kalman filter approaches are widely applied to derive time varying effective connectivity from electroencephalographic (EEG) data. For multi-trial data, a classical Kalman filter (CKF) designed for the estimation of single trial data, can be implemented by trial-averaging the data or by averaging single trial estimates. A general linear Kalman filter (GLKF) provides an extension for multi-trial data. In this work, we studied the performance of the different Kalman filtering approaches for different values of signal-to-noise ratio (SNR), number of trials and number of EEG channels. We used a simulated model from which we calculated scalp recordings. From these recordings, we estimated cortical sources. Multivariate autoregressive model parameters and partial directed coherence was calculated for these estimated sources and compared with the ground-truth. The results showed an overall superior performance of GLKF except for low levels of SNR and number of trials.
A new approach to UTC calculation by means of the Kalman filter
NASA Astrophysics Data System (ADS)
Parisi, Federica; Panfilo, Gianna
2016-10-01
In this paper a new approach to Coordinated Universal Time (UTC) calculation is presented by means of the Kalman filter. An ensemble of atomic clocks participating in UTC is selected for analyzing and testing the potentiality of this new method.
Analysis of video-based microscopic particle trajectories using Kalman filtering.
Wu, Pei-Hsun; Agarwal, Ashutosh; Hess, Henry; Khargonekar, Pramod P; Tseng, Yiider
2010-06-16
The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes.
NASA Astrophysics Data System (ADS)
Erdal, Daniel; Cirpka, Olaf A.
2017-02-01
Groundwater resources management requires operational, regional-scale groundwater models accounting for dominant spatial variability of aquifer properties and spatiotemporal variability of groundwater recharge. We test the Ensemble Kalman filter (EnKF) to estimate transient hydraulic heads and groundwater recharge, as well as the hydraulic conductivity and specific-yield distributions of a virtual phreatic aquifer. To speed up computation time, we use a coarsened spatial grid in the filter simulations, and reconstruct head measurements at observation points by a local model in the vicinity of the piezometer as part of the observation operator. We show that the EnKF can adequately estimate both the mean and spatial patterns of hydraulic conductivity when assimilating daily values of hydraulic heads from a highly variable initial sample. The filter can also estimate temporally variable recharge to a satisfactory level, as long as the ensemble size is large enough. Constraining the parameters on concentrations of groundwater-age tracers (here: tritium) and transient hydraulic-head observations cannot reasonably be done by the EnKF because the concentrations depend on the recharge history over longer times while the head observations have much shorter temporal support. We thus use a different method, the Kalman Ensemble Generator (KEG), to precondition the initial ensemble of the EnKF on the groundwater-age tracer data and time-averaged hydraulic-head values. The preconditioned initial ensemble exhibits a smaller spread as well as improved means and spatial patterns. The preconditioning improves the EnKF particularly for smaller ensemble sizes, allowing operational data assimilation with reduced computational effort. In a validation scenario of delineating groundwater protection zones, the preconditioned filter performs clearly better than the filter using the original initial ensemble.
Tsunami Modeling and Prediction Using a Data Assimilation Technique with Kalman Filters
NASA Astrophysics Data System (ADS)
Barnier, G.; Dunham, E. M.
2016-12-01
Earthquake-induced tsunamis cause dramatic damages along densely populated coastlines. It is difficult to predict and anticipate tsunami waves in advance, but if the earthquake occurs far enough from the coast, there may be enough time to evacuate the zones at risk. Therefore, any real-time information on the tsunami wavefield (as it propagates towards the coast) is extremely valuable for early warning systems. After the 2011 Tohoku earthquake, a dense tsunami-monitoring network (S-net) based on cabled ocean-bottom pressure sensors has been deployed along the Pacific coast in Northeastern Japan. Maeda et al. (GRL, 2015) introduced a data assimilation technique to reconstruct the tsunami wavefield in real time by combining numerical solution of the shallow water wave equations with additional terms penalizing the numerical solution for not matching observations. The penalty or gain matrix is determined though optimal interpolation and is independent of time. Here we explore a related data assimilation approach using the Kalman filter method to evolve the gain matrix. While more computationally expensive, the Kalman filter approach potentially provides more accurate reconstructions. We test our method on a 1D tsunami model derived from the Kozdon and Dunham (EPSL, 2014) dynamic rupture simulations of the 2011 Tohoku earthquake. For appropriate choices of model and data covariance matrices, the method reconstructs the tsunami wavefield prior to wave arrival at the coast. We plan to compare the Kalman filter method to the optimal interpolation method developed by Maeda et al. (GRL, 2015) and then to implement the method for 2D.
Kalman Filtering and Smoothing in Fotonap for Orbit Determination Using GPS Measurements
1978-09-01
LEI L, KALMAN FILTERING AND SMOOTHING IN FOTONAP oFor Orbit Determination Using GPS Measurements September 1978 FINAL REPORT ETL-0161 OLD DOMINION...SYSTEMS, INC. Gaithersburg, Maryland 1.-i "T. I r n l 19 7 9 1979 F’ Ap o ".I ETL-0161 KALMAN FILTERING AND SMOOTHING IN FOTONAP For Orbit...h . U f w fkl AAMNYLTERING AND . SMOOTHING IN FOTON P FFor Orbit Determinatibn Using Contract Report GPS Measurements. L. ~ PERFORMING ORG. REPORT
McGibbon, C A; Palmer, T; Goldvasser, D; Krebs, D E
2001-04-30
A Kalman filter algorithm was implemented for automatic detection of blink artifacts in video-oculography (VOG) data, and a cubic spline used to patch the eliminated data. The algorithm was tested by randomly introducing artificial blinks into eye movement data and computing the errors introduced by the patches. We also computed visual vestibulo-ocular reflex (VVOR) gain and phase in healthy and vestibulopathic subjects during a locomotor task, before and after blink removal, to demonstrate the interpretive importance of eliminating blink artifacts. The error introduced by the patched data was small (0.50+/-0.32 degrees ) and within the resolution of head angle measurements. Comparison of gain and phase shift before and after removing blinks revealed that even when calculated values are within expected limits, coherence of the VVOR signal was significantly (p=0.003) lower prior to blink removal (0.51+/-0.37) compared to that after blink removal (0.92+/-0.08). Comparison of VVOR calculations between healthy and vestibulopathic subjects (after removal of blinks) revealed that vestibulopathic subjects had significantly decreased gains (p=0.018) and increased phase shifts (p=0.009): these results agree with data reported in literature. We conclude that the Kalman filter detection and cubic spline patching algorithms are useful tools for VOG and should enable reliable VVOR measurements during unconstrained, ecologically meaningful locomotor activities.
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
A Kalman filtering approach to robust synchronization of coupled neural oscillators
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos G.; Rigatou, Efthymia G.
2013-10-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of the coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie Derivatives. For such a model it becomes possible to design a state feedback controller that assures synchronization for the state variables of the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
NASA Astrophysics Data System (ADS)
Raitoharju, Matti; Nurminen, Henri; Piché, Robert
2015-12-01
Indoor positioning based on wireless local area network (WLAN) signals is often enhanced using pedestrian dead reckoning (PDR) based on an inertial measurement unit. The state evolution model in PDR is usually nonlinear. We present a new linear state evolution model for PDR. In simulated-data and real-data tests of tightly coupled WLAN-PDR positioning, the positioning accuracy with this linear model is better than with the traditional models when the initial heading is not known, which is a common situation. The proposed method is computationally light and is also suitable for smoothing. Furthermore, we present modifications to WLAN positioning based on Gaussian coverage areas and show how a Kalman filter using the proposed model can be used for integrity monitoring and (re)initialization of a particle filter.
Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.
Spacecraft Attitude Estimation Integrating the Q-Method into an Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Ainscough, Thomas G.
A new algorithm is proposed that smoothly integrates the nonlinear estimation of the attitude quaternion using Davenport's q-method and the estimation of non-attitude states within the framework of an extended Kalman filter. A modification to the q-method and associated covariance analysis is derived with the inclusion of an a priori attitude estimate. The non-attitude states are updated from the nonlinear attitude estimate based on linear optimal Kalman filter techniques. The proposed filter is compared to existing methods and is shown to be equivalent to second-order in the attitude update and exactly equivalent in the non-attitude state update with the Sequential Optimal Attitude Recursion filter. Monte Carlo analysis is used in numerical simulations to demonstrate the validity of the proposed approach. This filter successfully estimates the nonlinear attitude and non-attitude states in a single Kalman filter without the need for iterations.
A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.
Sabatini, Angelo Maria
2011-01-01
In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical.
Fuzzy Logic Based Autonomous Parallel Parking System with Kalman Filtering
NASA Astrophysics Data System (ADS)
Panomruttanarug, Benjamas; Higuchi, Kohji
This paper presents an emulation of fuzzy logic control schemes for an autonomous parallel parking system in a backward maneuver. There are four infrared sensors sending the distance data to a microcontroller for generating an obstacle-free parking path. Two of them mounted on the front and rear wheels on the parking side are used as the inputs to the fuzzy rules to calculate a proper steering angle while backing. The other two attached to the front and rear ends serve for avoiding collision with other cars along the parking space. At the end of parking processes, the vehicle will be in line with other parked cars and positioned in the middle of the free space. Fuzzy rules are designed based upon a wall following process. Performance of the infrared sensors is improved using Kalman filtering. The design method needs extra information from ultrasonic sensors. Starting from modeling the ultrasonic sensor in 1-D state space forms, one makes use of the infrared sensor as a measurement to update the predicted values. Experimental results demonstrate the effectiveness of sensor improvement.
Automated septum thickness measurement--a Kalman filter approach.
Snare, Sten Roar; Mjølstad, Ole Christian; Orderud, Fredrik; Dalen, Håvard; Torp, Hans
2012-11-01
Interventricular septum thickness in end-diastole (IVSd) is one of the key parameters in cardiology. This paper presents a fast algorithm, suitable for pocket-sized ultrasound devices, for measurement of IVSd using 2D B-mode parasternal long axis images. The algorithm is based on a deformable model of the septum and the mitral valve. The model shape is estimated using an extended Kalman filter. A feasibility study using 32 unselected recordings is presented. The recordings originate from a database consisting of subjects from a normal healthy population. Five patients with suspected hypertrophy were included in the study. Reference B-mode measurements were made by two cardiologists. A paired t-test revealed a non-significant mean difference, compared to the B-mode reference, of (mean±SD) 0.14±1.36 mm (p=0.532). Pearson's correlation coefficient was 0.79 (p<0.001). The results are comparable to the variability between the two cardiologists, which was found to be 1.29±1.23 mm (p<0.001). The results indicate that the method has potential as a tool for rapid assessment of IVSd. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Kalman Filter Based Railway Tracking from Mobile LIDAR Data
NASA Astrophysics Data System (ADS)
Jwa, Y.; Sonh, G.
2015-08-01
This study introduces a new method to reconstruct 3D model of railway tracks from a railway corridor scene captured by mobile LiDAR data. The proposed approach starts to approximate the orientation of railway track trajectory from LiDAR point clouds and extract a strip, which direction is orthogonal to the trajectory of railway track. Within the strip, a track region and its track points are detected based on the Bayesian decision process. Once the main track region is localized, rail head points are segmented based on the region growing approach from the detected track points and then initial track models are reconstructed using a third-degree polynomial function. Based on the initial modelling result, a potential track region with varying lengths is dynamically predicted and the model parameters are updated in the Kalman Filter framework. The key aspect is that the proposed approach is able to enhance the efficiency of the railway tracking process by reducing the complexity for detecting track points and reconstructing track models based on the use of the track model previously reconstructed. An evaluation of the proposed method is performed over an urban railway corridor area containing multiple railway track pairs.
Streamflow data assimilation in SWAT model using Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Sun, Leqiang; Nistor, Ioan; Seidou, Ousmane
2015-12-01
The Extended Kalman Filter (EKF) is coupled with the Soil and Water Assessment Tools (SWAT) model in the streamflow assimilation of the upstream Senegal River in West Africa. Given the large number of distributed variables in SWAT, only the average watershed scale variables are included in the state vector and the Hydrological Response Unit (HRU) scale variables are updated with the a posteriori/a priori ratio of their watershed scale counterparts. The Jacobian matrix is calculated numerically by perturbing the state variables. Both the soil moisture and CN2 are significantly updated in the wet season, yet they have opposite update patterns. A case study for a large flood forecast shows that for up to seven days, the streamflow forecast is moderately improved using the EKF-subsequent open loop scheme but significantly improved with a newly designed quasi-error update scheme. The former has better performances in the flood rising period while the latter has better performances in the recession period. For both schemes, the streamflow forecast is improved more significantly when the lead time is shorter.
Probabilistic video stabilization using Kalman filtering and mosaicing
NASA Astrophysics Data System (ADS)
Litvin, Andrey; Konrad, Janusz; Karl, William C.
2003-05-01
The removal of unwanted, parasitic vibrations in a video sequence induced by camera motion is an essential part of video acquisition in industrial, military and consumer applications. In this paper, we present a new image processing method to remove such vibrations and reconstruct a video sequence void of sudden camera movements. Our approach to separating unwanted vibrations from intentional camera motion is based on a probabilistic estimation framework. We treat estimated parameters of interframe camera motion as noisy observations of the intentional camera motion parameters. We construct a physics-based state-space model of these interframe motion parameters and use recursive Kalman filtering to perform stabilized camera position estimation. A six-parameter affine model is used to describe the interframe transformation, allowing quite accurate description of typical scene changes due to camera motion. The model parameters are estimated using a p-norm-based multi-resolution approach. This approach is robust to model mismatch and to object motion within the scene (which are treated as outliers). We use mosaicking in order to reconstruct undefined areas that result from motion compensation applied to each video frame. Registration between distant frames is performed efficiently by cascading interframe affine transformation parameters. We compare our method's performance with that of a commercial product on real-life video sequences, and show a significant improvement in stabilization quality for our method.
Discrete Kalman Filter based Sensor Fusion for Robust Accessibility Interfaces
NASA Astrophysics Data System (ADS)
Ghersi, I.; Mariño, M.; Miralles, M. T.
2016-04-01
Human-machine interfaces have evolved, benefiting from the growing access to devices with superior, embedded signal-processing capabilities, as well as through new sensors that allow the estimation of movements and gestures, resulting in increasingly intuitive interfaces. In this context, sensor fusion for the estimation of the spatial orientation of body segments allows to achieve more robust solutions, overcoming specific disadvantages derived from the use of isolated sensors, such as the sensitivity of magnetic-field sensors to external influences, when used in uncontrolled environments. In this work, a method for the combination of image-processing data and angular-velocity registers from a 3D MEMS gyroscope, through a Discrete-time Kalman Filter, is proposed and deployed as an alternate user interface for mobile devices, in which an on-screen pointer is controlled with head movements. Results concerning general performance of the method are presented, as well as a comparative analysis, under a dedicated test application, with results from a previous version of this system, in which the relative-orientation information was acquired directly from MEMS sensors (3D magnetometer-accelerometer). These results show an improved response for this new version of the pointer, both in terms of precision and response time, while keeping many of the benefits that were highlighted for its predecessor, giving place to a complementary method for signal acquisition that can be used as an alternative-input device, as well as for accessibility solutions.
Kalman filter implementation for small satellites using constraint GPS data
NASA Astrophysics Data System (ADS)
Wesam, Elmahy M.; Zhang, Xiang; Lu, Zhengliang; Liao, Wenhe
2017-06-01
Due to the increased need for autonomy, an Extended Kalman Filter (EKF) has been designed to autonomously estimate the orbit using GPS data. A propagation step models the satellite dynamics as a two body with J2 (second zonal effect) perturbations being suitable for orbits in altitudes higher than 600 km. An onboard GPS receiver provides continuous measurement inputs. The continuity of measurements decreases the errors of the orbit determination algorithm. Power restrictions are imposed on small satellites in general and nanosatellites in particular. In cubesats, the GPS is forced to be shut down most of the mission’s life time. GPS is turned on when experiments like atmospheric ones are carried out and meter level accuracy for positioning is required. This accuracy can’t be obtained by other autonomous sensors like magnetometer and sun sensor as they provide kilometer level accuracy. Through simulation using Matlab and satellite tool kit (STK) the position accuracy is analyzed after imposing constrained conditions suitable for small satellites and a very tight one suitable for nanosatellite missions.
Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction.
Muruganantham, Arrchana; Tan, Kay Chen; Vadakkepat, Prahlad
2016-12-01
Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.
Extended Kalman filter for multiwavelength differential absorption lidar
NASA Astrophysics Data System (ADS)
Warren, Russell E.; Vanderbeek, Richard G.
2001-08-01
Our earlier study described an approach for estimating the path-integrated concentration, CL, of a set of vapor materials using time series data from topographic backscatter lidar with frequency-agile lasers. That methodology assumed the availability of background data samples collected before the release of the vapors of interest to estimate statistical parameters such as the mean topographic backscatter return and the transmitter energy mean and variance as a function of wavelength. The background data were then used in an extended Kalman filter approach for estimating the CL components as a function of time. That approach worked well for data that showed negligible drift in the mean parameters over the data collection time. In practice, however, the transmitter energy and background return can drift, producing substantial bias in the estimates. In this paper we generalize the approach to a more complete state model that includes the mean transmitter energy and background return in addition to the CL vapor set. This generalization allows the algorithm to track slow drift in those parameters and provides generally improved estimates. Results of the new algorithm are compared with those of a two-wavelength classical DIAL estimator on synthetic and field test data.
IASI Radiance Data Assimilation in Local Ensemble Transform Kalman Filter
NASA Astrophysics Data System (ADS)
Cho, K.; Hyoung-Wook, C.; Jo, Y.
2016-12-01
Korea institute of Atmospheric Prediction Systems (KIAPS) is developing NWP model with data assimilation systems. Local Ensemble Transform Kalman Filter (LETKF) system, one of the data assimilation systems, has been developed for KIAPS Integrated Model (KIM) based on cubed-sphere grid and has successfully assimilated real data. LETKF data assimilation system has been extended to 4D- LETKF which considers time-evolving error covariance within assimilation window and IASI radiance data assimilation using KPOP (KIAPS package for observation processing) with RTTOV (Radiative Transfer for TOVS). The LETKF system is implementing semi operational prediction including conventional (sonde, aircraft) observation and AMSU-A (Advanced Microwave Sounding Unit-A) radiance data from April. Recently, the semi operational prediction system updated radiance observations including GPS-RO, AMV, IASI (Infrared Atmospheric Sounding Interferometer) data at July. A set of simulation of KIM with ne30np4 and 50 vertical levels (of top 0.3hPa) were carried out for short range forecast (10days) within semi operation prediction LETKF system with ensemble forecast 50 members. In order to only IASI impact, our experiments used only conventional and IAIS radiance data to same semi operational prediction set. We carried out sensitivity test for IAIS thinning method (3D and 4D). IASI observation number was increased by temporal (4D) thinning and the improvement of IASI radiance data impact on the forecast skill of model will expect.
Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation
NASA Technical Reports Server (NTRS)
Hutsell, Steven T.
1996-01-01
The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.
A steady-state Kalman filter for assimilating data from a single polar orbiting satellite
NASA Technical Reports Server (NTRS)
Banfield, Don; Ingersoll, Andrew P.; Keppenne, Christian L.
1995-01-01
A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed 'truth' into another run termed 'prediction'. At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.
Durantin, Gautier; Scannella, Sébastien; Gateau, Thibault; Delorme, Arnaud; Dehais, Frédéric
2016-01-01
Working memory (WM) is a key executive function for operating aircraft, especially when pilots have to recall series of air traffic control instructions. There is a need to implement tools to monitor WM as its limitation may jeopardize flight safety. An innovative way to address this issue is to adopt a Neuroergonomics approach that merges knowledge and methods from Human Factors, System Engineering, and Neuroscience. A challenge of great importance for Neuroergonomics is to implement efficient brain imaging techniques to measure the brain at work and to design Brain Computer Interfaces (BCI). We used functional near infrared spectroscopy as it has been already successfully tested to measure WM capacity in complex environment with air traffic controllers (ATC), pilots, or unmanned vehicle operators. However, the extraction of relevant features from the raw signal in ecological environment is still a critical issue due to the complexity of implementing real-time signal processing techniques without a priori knowledge. We proposed to implement the Kalman filtering approach, a signal processing technique that is efficient when the dynamics of the signal can be modeled. We based our approach on the Boynton model of hemodynamic response. We conducted a first experiment with nine participants involving a basic WM task to estimate the noise covariances of the Kalman filter. We then conducted a more ecological experiment in our flight simulator with 18 pilots who interacted with ATC instructions (two levels of difficulty). The data was processed with the same Kalman filter settings implemented in the first experiment. This filter was benchmarked with a classical pass-band IIR filter and a Moving Average Convergence Divergence (MACD) filter. Statistical analysis revealed that the Kalman filter was the most efficient to separate the two levels of load, by increasing the observed effect size in prefrontal areas involved in WM. In addition, the use of a Kalman filter increased
Durantin, Gautier; Scannella, Sébastien; Gateau, Thibault; Delorme, Arnaud; Dehais, Frédéric
2015-01-01
Working memory (WM) is a key executive function for operating aircraft, especially when pilots have to recall series of air traffic control instructions. There is a need to implement tools to monitor WM as its limitation may jeopardize flight safety. An innovative way to address this issue is to adopt a Neuroergonomics approach that merges knowledge and methods from Human Factors, System Engineering, and Neuroscience. A challenge of great importance for Neuroergonomics is to implement efficient brain imaging techniques to measure the brain at work and to design Brain Computer Interfaces (BCI). We used functional near infrared spectroscopy as it has been already successfully tested to measure WM capacity in complex environment with air traffic controllers (ATC), pilots, or unmanned vehicle operators. However, the extraction of relevant features from the raw signal in ecological environment is still a critical issue due to the complexity of implementing real-time signal processing techniques without a priori knowledge. We proposed to implement the Kalman filtering approach, a signal processing technique that is efficient when the dynamics of the signal can be modeled. We based our approach on the Boynton model of hemodynamic response. We conducted a first experiment with nine participants involving a basic WM task to estimate the noise covariances of the Kalman filter. We then conducted a more ecological experiment in our flight simulator with 18 pilots who interacted with ATC instructions (two levels of difficulty). The data was processed with the same Kalman filter settings implemented in the first experiment. This filter was benchmarked with a classical pass-band IIR filter and a Moving Average Convergence Divergence (MACD) filter. Statistical analysis revealed that the Kalman filter was the most efficient to separate the two levels of load, by increasing the observed effect size in prefrontal areas involved in WM. In addition, the use of a Kalman filter increased
Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering.
Fraanje, Rufus; Rice, Justin; Verhaegen, Michel; Doelman, Niek
2010-11-01
Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order.
NASA Astrophysics Data System (ADS)
Hirpa, F. A.; Gebremichael, M.; Hopson, T. M.; Wojick, R.
2011-12-01
We present results of data assimilation of ground discharge observation and remotely sensed soil moisture observations into Sacramento Soil Moisture Accounting (SACSMA) model in a small watershed (1593 km2) in Minnesota, the Unites States. Specifically, we perform assimilation experiments with Ensemble Kalman Filter (EnKF) and Particle Filter (PF) in order to improve streamflow forecast accuracy at six hourly time step. The EnKF updates the soil moisture states in the SACSMA from the relative errors of the model and observations, while the PF adjust the weights of the state ensemble members based on the likelihood of the forecast. Results of the improvements of each filter over the reference model (without data assimilation) will be presented. Finally, the EnKF and PF are coupled together to further improve the streamflow forecast accuracy.
Gyro Drift Correction for An Indirect Kalman Filter Based Sensor Fusion Driver.
Lee, Chan-Gun; Dao, Nhu-Ngoc; Jang, Seonmin; Kim, Deokhwan; Kim, Yonghun; Cho, Sungrae
2016-06-11
Sensor fusion techniques have made a significant contribution to the success of the recently emerging mobile applications era because a variety of mobile applications operate based on multi-sensing information from the surrounding environment, such as navigation systems, fitness trackers, interactive virtual reality games, etc. For these applications, the accuracy of sensing information plays an important role to improve the user experience (UX) quality, especially with gyroscopes and accelerometers. Therefore, in this paper, we proposed a novel mechanism to resolve the gyro drift problem, which negatively affects the accuracy of orientation computations in the indirect Kalman filter based sensor fusion. Our mechanism focuses on addressing the issues of external feedback loops and non-gyro error elements contained in the state vectors of an indirect Kalman filter. Moreover, the mechanism is implemented in the device-driver layer, providing lower process latency and transparency capabilities for the upper applications. These advances are relevant to millions of legacy applications since utilizing our mechanism does not require the existing applications to be re-programmed. The experimental results show that the root mean square errors (RMSE) before and after applying our mechanism are significantly reduced from 6.3 × 10(-1) to 5.3 × 10(-7), respectively.
A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows
NASA Astrophysics Data System (ADS)
Meldi, M.; Poux, A.
2017-10-01
A Kalman filter based sequential estimator is presented in this work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state integrating available observation in the CFD model, naturally preserving a zero-divergence condition for the velocity field. Because of the prohibitive costs associated with a complete Kalman Filter application, two model reduction strategies have been proposed and assessed. These strategies dramatically reduce the increase in computational costs of the model, which can be quantified in an augmentation of 10%- 15% with respect to the classical numerical simulation. In addition, an extended analysis of the behavior of the numerical model covariance Q has been performed. Optimized values are strongly linked to the truncation error of the discretization procedure. The estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity, including turbulent flow configurations. The results show that the augmented flow successfully improves the prediction of the physical quantities investigated, even when the observation is provided in a limited region of the physical domain. In addition, the present work suggests that these Data Assimilation techniques, which are at an embryonic stage of development in CFD, may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation.
Advanced Kalman Filter for Real-Time Responsiveness in Complex Systems
Welch, Gregory Francis
2014-06-10
Complex engineering systems pose fundamental challenges in real-time operations and control because they are highly dynamic systems consisting of a large number of elements with severe nonlinearities and discontinuities. Today’s tools for real-time complex system operations are mostly based on steady state models, unable to capture the dynamic nature and too slow to prevent system failures. We developed advanced Kalman filtering techniques and the formulation of dynamic state estimation using Kalman filtering techniques to capture complex system dynamics in aiding real-time operations and control. In this work, we looked at complex system issues including severe nonlinearity of system equations, discontinuities caused by system controls and network switches, sparse measurements in space and time, and real-time requirements of power grid operations. We sought to bridge the disciplinary boundaries between Computer Science and Power Systems Engineering, by introducing methods that leverage both existing and new techniques. While our methods were developed in the context of electrical power systems, they should generalize to other large-scale scientific and engineering applications.
Gyro Drift Correction for An Indirect Kalman Filter Based Sensor Fusion Driver
Lee, Chan-Gun; Dao, Nhu-Ngoc; Jang, Seonmin; Kim, Deokhwan; Kim, Yonghun; Cho, Sungrae
2016-01-01
Sensor fusion techniques have made a significant contribution to the success of the recently emerging mobile applications era because a variety of mobile applications operate based on multi-sensing information from the surrounding environment, such as navigation systems, fitness trackers, interactive virtual reality games, etc. For these applications, the accuracy of sensing information plays an important role to improve the user experience (UX) quality, especially with gyroscopes and accelerometers. Therefore, in this paper, we proposed a novel mechanism to resolve the gyro drift problem, which negatively affects the accuracy of orientation computations in the indirect Kalman filter based sensor fusion. Our mechanism focuses on addressing the issues of external feedback loops and non-gyro error elements contained in the state vectors of an indirect Kalman filter. Moreover, the mechanism is implemented in the device-driver layer, providing lower process latency and transparency capabilities for the upper applications. These advances are relevant to millions of legacy applications since utilizing our mechanism does not require the existing applications to be re-programmed. The experimental results show that the root mean square errors (RMSE) before and after applying our mechanism are significantly reduced from 6.3×10-1 to 5.3×10-7, respectively. PMID:27294941
Extended Kalman filter based structural damage detection for MR damper controlled structures
NASA Astrophysics Data System (ADS)
Jin, Chenhao; Jang, Shinae; Sun, Xiaorong; Jiang, Zhaoshuo; Christenson, Richard
2016-04-01
The Magneto-rheological (MR) dampers have been widely used in many building and bridge structures against earthquake and wind loadings due to its advantages including mechanical simplicity, high dynamic range, low power requirements, large force capacity, and robustness. However, research about structural damage detection methods for MR damper controlled structures is limited. This paper aims to develop a real-time structural damage detection method for MR damper controlled structures. A novel state space model of MR damper controlled structure is first built by combining the structure's equation of motion and MR damper's hyperbolic tangent model. In this way, the state parameters of both the structure and MR damper are added in the state vector of the state space model. Extended Kalman filter is then used to provide prediction for state variables from measurement data. The two techniques are synergistically combined to identify parameters and track the changes of both structure and MR damper in real time. The proposed method is tested using response data of a three-floor MR damper controlled linear building structure under earthquake excitation. The testing results show that the adaptive extended Kalman filter based approach is capable to estimate not only structural parameters such as stiffness and damping of each floor, but also the parameters of MR damper, so that more insights and understanding of the damage can be obtained. The developed method also demonstrates high damage detection accuracy and light computation, as well as the potential to implement in a structural health monitoring system.
NASA Astrophysics Data System (ADS)
Li, Linqian; Feng, Yiqiao; Zhang, Wenbo; Cui, Nan; Xu, Hengying; Tang, Xianfeng; Xi, Lixia; Zhang, Xiaoguang
2017-07-01
A joint carrier recovery scheme for polarization division multiplexing (PDM) coherent optical transmission system is proposed and demonstrated, in which the extended Kalman filter (EKF) is exploited to estimate and equalize the carrier frequency offset (CFO) and carrier phase noise (CPN) simultaneously. The proposed method is implemented and verified in the PDM-QPSK system and the PDM-16QAM system with the comparisons to conventional improved Mth-power (IMP) algorithm for CFO estimation, blind phase search (BPS) algorithm or Viterbi-Viterbi (V-V) algorithm for CPN recovery. It is demonstrated that the proposed scheme shows high CFO estimation accuracy, with absolute mean estimation error below 1.5 MHz. Meanwhile, the proposed method has the CFO tolerance of [±3 GHz] for PDM-QPSK system and [±0.9 GHz] for PDM-16QAM system. Compare with IMP/BPS and IMP/V-V, the proposed scheme can enhance the linewidth symbol duration product from 3 × 10-4 (IMP/BPS) and 2 × 10-4 (IMP/V-V) to 1 × 10-3 for PDM-QPSK, and from 1 × 10-4 (IMP/BPS) to 3 × 10-4 for PDM-16QAM, respectively, at the 1 dB optical signal-to-noise ratio (OSNR) penalty. The proposed Kalman filter also shows a fast convergence with only 100 symbols and much lower computational complexity.
Motion based markerless gait analysis using standard events of gait and ensemble Kalman filtering.
Vishnoi, Nalini; Mitra, Anish; Duric, Zoran; Gerber, Naomi Lynn
2014-01-01
We present a novel approach to gait analysis using ensemble Kalman filtering which permits markerless determination of segmental movement. We use image flow analysis to reliably compute temporal and kinematic measures including the translational velocity of the torso and rotational velocities of the lower leg segments. Detecting the instances where velocity changes direction also determines the standard events of a gait cycle (double-support, toe-off, mid-swing and heel-strike). In order to determine the kinematics of lower limbs, we model the synergies between the lower limb motions (thigh-shank, shank-foot) by building a nonlinear dynamical system using CMUs 3D motion capture database. This information is fed into the ensemble Kalman Filter framework to estimate the unobserved limb (upper leg and foot) motion from the measured lower leg rotational velocity. Our approach does not require calibrated cameras or special markers to capture movement. We have tested our method on different gait sequences collected from the sagttal plane and presented the estimated kinematics overlaid on the original image frames. We have also validated our approach by manually labeling the videos and comparing our results against them.
NASA Astrophysics Data System (ADS)
Ni, Jiang Q.; Ho, Ka L.; Tse, Kai W.
1998-08-01
Conventional synthesis filters in subband systems lose their optimality when additive noise (due, for example, to signal quantization) disturbs the subband components. The multichannel representation of subband signals is combined with the statistical model of input signal to derive the multirate state-space model for the filter bank system with additive subband noises. Thus the signal reconstruction problem in subband systems can be formulated as the process of optimal state estimation in the equivalent multirate state-space model. Incorporated with the vector dynamic model, a 2D multirate state-space model suitable for 2D Kalman filtering is developed. The performance of the proposed 2D multirate Kalman filter can be further improved through adaptive segmentation of the object plane. The object plane is partitioned into disjoint regions based on their spatial activity, and different vector dynamical models are used to characterize the nonstationary object- plane distributions. Finally, computer simulations with the proposed 2D multirate Kalman filter give favorable results.
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2005-01-01
In-flight sensor fault detection and isolation (FDI) is critical to maintaining reliable engine operation during flight. The aircraft engine control system, which computes control commands on the basis of sensor measurements, operates the propulsion systems at the demanded conditions. Any undetected sensor faults, therefore, may cause the control system to drive the engine into an undesirable operating condition. It is critical to detect and isolate failed sensors as soon as possible so that such scenarios can be avoided. A challenging issue in developing reliable sensor FDI systems is to make them robust to changes in engine operating characteristics due to degradation with usage and other faults that can occur during flight. A sensor FDI system that cannot appropriately account for such scenarios may result in false alarms, missed detections, or misclassifications when such faults do occur. To address this issue, an enhanced bank of Kalman filters was developed, and its performance and robustness were demonstrated in a simulation environment. The bank of filters is composed of m + 1 Kalman filters, where m is the number of sensors being used by the control system and, thus, in need of monitoring. Each Kalman filter is designed on the basis of a unique fault hypothesis so that it will be able to maintain its performance if a particular fault scenario, hypothesized by that particular filter, takes place.
On the evaluation of uncertainties for state estimation with the Kalman filter
NASA Astrophysics Data System (ADS)
Eichstädt, S.; Makarava, N.; Elster, C.
2016-12-01
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous areas. It provides sequentially calculated estimates of the system states along with a corresponding covariance matrix. For nonlinear systems, the extended Kalman filter is often used. This is derived from the Kalman filter by linearization around the current estimate. A key issue in metrology is the evaluation of the uncertainty associated with the Kalman filter state estimates. The ‘Guide to the Expression of Uncertainty in Measurement’ (GUM) and its supplements serve as the de facto standard for uncertainty evaluation in metrology. We explore the relationship between the covariance matrix produced by the Kalman filter and a GUM-compliant uncertainty analysis. In addition, the results of a Bayesian analysis are considered. For the case of linear systems with known system matrices, we show that all three approaches are compatible. When the system matrices are not precisely known, however, or when the system is nonlinear, this equivalence breaks down and different results can then be reached. For precisely known nonlinear systems, though, the result of the extended Kalman filter still corresponds to the linearized uncertainty propagation of the GUM. The extended Kalman filter can suffer from linearization and convergence errors. These disadvantages can be avoided to some extent by applying Monte Carlo procedures, and we propose such a method which is GUM-compliant and can also be applied online during the estimation. We illustrate all procedures in terms of a 2D dynamic system and compare the results with those obtained by particle filtering, which has been proposed for the approximate calculation of a Bayesian solution. Finally, we give some recommendations based on our findings.
Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey
2015-12-01
The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.
A Kalman filter algorithm for terminal-area navigation with sensors of moderate accuracy
NASA Technical Reports Server (NTRS)
Cicolani, L. S.; Kanning, G.; Schmidt, S. F.
1983-01-01
Translational state estimation in terminal area operations, using a set of commonly available position, air data, nd acceleration sensors, is described. Kalman filtering is applied to obtain maximum estimation occuracy from the sensors but feasibility in real-time computations requires a variety of approximations and devices aimed at minimizing the required computation time with only negligible loss of accuracy. Accuracy behavior throughout the terminal area, its relation to sensor accuracy, its effect on trajectory tracking errors and control activity in an automatic flight control system, and its adequacy in terms of existing criteria for various terminal area operations are examined. The principal investigative tool is a simulation of the system. Previously announced in STAR as N83-29193
Estimation of intra-operative brain shift based on constrained Kalman filter.
Shakarami, M; Suratgar, A A; Talebi, H A
2015-03-01
In this study, the problem of estimation of brain shift is addressed by which the accuracy of neuronavigation systems can be improved. To this end, the actual brain shift is considered as a Gaussian random vector with a known mean and an unknown covariance. Then, brain surface imaging is employed together with solutions of linear elastic model and the best estimation is found using constrained Kalman filter (CKF). Moreover, a recursive method (RCKF) is presented, the computational cost of which in the operating room is significantly lower than CKF, because it is not required to compute inverse of any large matrix. Finally, the theory is verified by the simulation results, which show the superiority of the proposed method as compared to one existing method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Simultaneous estimation of phase derivative and phase using parallel Kalman filter implementation
NASA Astrophysics Data System (ADS)
Kulkarni, Rishikesh; Rastogi, Pramod
2016-06-01
This paper proposes a technique for the simultaneous estimation of interference phase derivative and phase from a complex interferogram recorded in an optical interferometric setup. The complex interferogram is represented as a spatially varying autoregressive process in a given row or column at a time. The phase derivative is estimated from the poles of the transfer function representation of the autoregressive process. The poles are computed using the spatially varying autoregressive coefficients which are estimated by a computationally efficient Rauch-Tung-Striebel smoothing algorithm. The estimated phase derivative is used as a control input to a state space model designed for the phase estimation at each pixel. The unscented Kalman filter is utilized to deal with the nonlinear measurement process for the accurate estimation of the unwrapped phase. Numerical and experimental results substantiate the ability of the proposed method in handling noisy phase fringe patterns.
EEG-fMRI fusion of paradigm-free activity using Kalman filtering.
Deneux, Thomas; Faugeras, Olivier
2010-04-01
We address here the use of EEG and fMRI, and their combination, in order to estimate the full spatiotemporal patterns of activity on the cortical surface in the absence of any particular assumptions on this activity such as stimulation times. For handling such a high-dimension inverse problem, we propose the use of (1) a global forward model of how these measures are functions of the "neural activity" of a large number of sources distributed on the cortical surface, formalized as a dynamical system, and (2) adaptive filters, as a natural solution to solve this inverse problem iteratively along the temporal dimension. This estimation framework relies on realistic physiological models, uses EEG and fMRI in a symmetric manner, and takes into account both their temporal and spatial information. We use the Kalman filter and smoother to perform such an estimation on realistic artificial data and demonstrate that the algorithm can handle the high dimensionality of these data and that it succeeds in solving this inverse problem, combining efficiently the information provided by the two modalities (this information being naturally predominantly temporal for EEG and spatial for fMRI). It performs particularly well in reconstructing a random temporally and spatially smooth activity spread over the cortex. The Kalman filter and smoother show some limitations, however, which call for the development of more specific adaptive filters. First, they do not cope well with the strong nonlinearity in the model that is necessary for an adequate description of the relation between cortical electric activities and the metabolic demand responsible for fMRI signals. Second, they fail to estimate a sparse activity (i.e., presenting sharp peaks at specific locations and times). Finally their computational cost remains high. We use schematic examples to explain these limitations and propose further developments of our method to overcome them.
On-Orbit Multi-Field Wavefront Control with a Kalman Filter
NASA Technical Reports Server (NTRS)
Lou, John; Sigrist, Norbert; Basinger, Scott; Redding, David
2008-01-01
A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system
Extended Kalman filtering for continuous volumetric MR-temperature imaging.
Denis de Senneville, Baudouin; Roujol, Sébastien; Hey, Silke; Moonen, Chrit; Ries, Mario
2013-04-01
Real time magnetic resonance (MR) thermometry has evolved into the method of choice for the guidance of high-intensity focused ultrasound (HIFU) interventions. For this role, MR-thermometry should preferably have a high temporal and spatial resolution and allow observing the temperature over the entire targeted area and its vicinity with a high accuracy. In addition, the precision of real time MR-thermometry for therapy guidance is generally limited by the available signal-to-noise ratio (SNR) and the influence of physiological noise. MR-guided HIFU would benefit of the large coverage volumetric temperature maps, including characterization of volumetric heating trajectories as well as near- and far-field heating. In this paper, continuous volumetric MR-temperature monitoring was obtained as follows. The targeted area was continuously scanned during the heating process by a multi-slice sequence. Measured data and a priori knowledge of 3-D data derived from a forecast based on a physical model were combined using an extended Kalman filter (EKF). The proposed reconstruction improved the temperature measurement resolution and precision while maintaining guaranteed output accuracy. The method was evaluated experimentally ex vivo on a phantom, and in vivo on a porcine kidney, using HIFU heating. On the in vivo experiment, it allowed the reconstruction from a spatio-temporally under-sampled data set (with an update rate for each voxel of 1.143 s) to a 3-D dataset covering a field of view of 142.5×285×54 mm(3) with a voxel size of 3×3×6 mm(3) and a temporal resolution of 0.127 s. The method also provided noise reduction, while having a minimal impact on accuracy and latency.
Identification of hydrological model parameter variation using ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Deng, Chao; Liu, Pan; Guo, Shenglian; Li, Zejun; Wang, Dingbao
2016-12-01
Hydrological model parameters play an important role in the ability of model prediction. In a stationary context, parameters of hydrological models are treated as constants; however, model parameters may vary with time under climate change and anthropogenic activities. The technique of ensemble Kalman filter (EnKF) is proposed to identify the temporal variation of parameters for a two-parameter monthly water balance model (TWBM) by assimilating the runoff observations. Through a synthetic experiment, the proposed method is evaluated with time-invariant (i.e., constant) parameters and different types of parameter variations, including trend, abrupt change and periodicity. Various levels of observation uncertainty are designed to examine the performance of the EnKF. The results show that the EnKF can successfully capture the temporal variations of the model parameters. The application to the Wudinghe basin shows that the water storage capacity (SC) of the TWBM model has an apparent increasing trend during the period from 1958 to 2000. The identified temporal variation of SC is explained by land use and land cover changes due to soil and water conservation measures. In contrast, the application to the Tongtianhe basin shows that the estimated SC has no significant variation during the simulation period of 1982-2013, corresponding to the relatively stationary catchment properties. The evapotranspiration parameter (C) has temporal variations while no obvious change patterns exist. The proposed method provides an effective tool for quantifying the temporal variations of the model parameters, thereby improving the accuracy and reliability of model simulations and forecasts.
Data-worth analysis through probabilistic collocation-based Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Dai, Cheng; Xue, Liang; Zhang, Dongxiao; Guadagnini, Alberto
2016-09-01
We propose a new and computationally efficient data-worth analysis and quantification framework keyed to the characterization of target state variables in groundwater systems. We focus on dynamically evolving plumes of dissolved chemicals migrating in randomly heterogeneous aquifers. An accurate prediction of the detailed features of solute plumes requires collecting a substantial amount of data. Otherwise, constraints dictated by the availability of financial resources and ease of access to the aquifer system suggest the importance of assessing the expected value of data before these are actually collected. Data-worth analysis is targeted to the quantification of the impact of new potential measurements on the expected reduction of predictive uncertainty based on a given process model. Integration of the Ensemble Kalman Filter method within a data-worth analysis framework enables us to assess data worth sequentially, which is a key desirable feature for monitoring scheme design in a contaminant transport scenario. However, it is remarkably challenging because of the (typically) high computational cost involved, considering that repeated solutions of the inverse problem are required. As a computationally efficient scheme, we embed in the data-worth analysis framework a modified version of the Probabilistic Collocation Method-based Ensemble Kalman Filter proposed by Zeng et al. (2011) so that we take advantage of the ability to assimilate data sequentially in time through a surrogate model constructed via the polynomial chaos expansion. We illustrate our approach on a set of synthetic scenarios involving solute migrating in a two-dimensional random permeability field. Our results demonstrate the computational efficiency of our approach and its ability to quantify the impact of the design of the monitoring network on the reduction of uncertainty associated with the characterization of a migrating contaminant plume.
NASA Astrophysics Data System (ADS)
Hirpa, F. A.; Gebremichael, M.; LEE, H.; Hopson, T. M.
2012-12-01
Hydrologic data assimilation techniques provide a means to improve river discharge forecasts through updating hydrologic model states and correcting the atmospheric forcing data via optimally combining model outputs with observations. The performance of the assimilation procedure, however, depends on the data assimilation techniques used and the amount of uncertainty in the data sets. To investigate the effects of these, we comparatively evaluate three data assimilation techniques, including ensemble Kalman filter (EnKF), particle filter (PF) and variational (VAR) technique, which assimilate discharge and synthetic soil moisture data at various uncertainty levels into the Sacramento Soil Moisture accounting (SAC-SMA) model used by the National Weather Service (NWS) for river forecasting in The United States. The study basin is Greens Bayou watershed with area of 178 km2 in eastern Texas. In the presentation, we summarize the results of the comparisons, and discuss the challenges of applying each technique for hydrologic applications.
The extended Kalman filter for forecast of algal bloom dynamics.
Mao, J Q; Lee, Joseph H W; Choi, K W
2009-09-01
A deterministic ecosystem model is combined with an extended Kalman filter (EKF) to produce short term forecasts of algal bloom and dissolved oxygen dynamics in a marine fish culture zone (FCZ). The weakly flushed FCZ is modelled as a well-mixed system; the tidal exchange with the outer bay is lumped into a flushing rate that is numerically determined from a three-dimensional hydrodynamic model. The ecosystem model incorporates phytoplankton growth kinetics, nutrient uptake, photosynthetic production, nutrient sources from organic fish farm loads, and nutrient exchange with a sediment bed layer. High frequency field observations of chlorophyll, dissolved oxygen (DO) and hydro-meteorological parameters (sampling interval Deltat=1 day, 2h, 1h, respectively) and bi-weekly nutrient data are assimilated into the model to produce the combined state estimate accounting for the uncertainties. In addition to the water quality state variables, the EKF incorporates dynamic estimation of algal growth rate and settling velocity. The effectiveness of the EKF data assimilation is studied for a wide range of sampling intervals and prediction lead-times. The chlorophyll and dissolved oxygen estimated by the EKF are compared with field data of seven algal bloom events observed at Lamma Island, Hong Kong. The results show that the EKF estimate well captures the nonlinear error evolution in time; the chlorophyll level can be satisfactorily predicted by the filtered model estimate with a mean absolute error of around 1-2 microg/L. Predictions with 1-2 day lead-time are highly correlated with the observations (r=0.7-0.9); the correlation stays at a high level for a lead-time of 3 days (r=0.6-0.7). Estimated algal growth and settling rates are in accord with field observations; the more frequent DO data can compensate for less frequent algal biomass measurements. The present study is the first time the EKF is successfully applied to forecast an entire algal bloom cycle, suggesting the
A Kalman filter for combining high frequency Earth rotation parameters from VLBI and GNSS
NASA Astrophysics Data System (ADS)
Nilsson, T.; Karbon, M.; Schuh, H.
2013-08-01
We present a Kalman filter for combination of sub-diurnal Earth Rotation Parameters (ERP) estimated from different techniques. We test this filter by combining ERP estimated from VLBI and GPS for the CONT08 campaign. We find that the Kalman filter works and give reasonable results. The combined solution is dominated by the GPS data since the ERP from this technique have much lower formal errors. However VLBI is important for providing the absolute value of dUT1 since GPS is only sensitive to the time derivative of dUT1, i.e. the length of day.
Control of underactuated robotic systems with the use of the derivative-free nonlinear Kalman filter
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos G.; Siano, Pierluigi
2013-10-01
The Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system can not be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is is shown that one can estimate simultaneously external disturbances terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty.
Theoretical Bit Error Rate Performance of the Kalman Filter Excisor for FM Interference
1992-12-01
un filtre de Kalman as- servi numeriquement par verrouillage de phase et s’avere quasi-optimum quant a la demodulation d’une interference de type MF...Puisqu’on presuppose que l’interftrence est plus forte le signal ou que le bruit, le filtre de Kalman se verrouille sur l’interfdrence et permet...AD-A263 018 THEORETICAL BIT ERROR RATE PERFORMANCE OF THE KALMAN FILTER EXCISOR FOR FM INTERFERENCE by Brian RKominchuk APR 19 1993 DEFENCE RESEARCH
Estimation of Sonobuoy Position Relative to an Aircraft Using Extended Kalman Filters
1979-09-01
SECURITY CLASS. (a# this swot ) Naval Postgraduate School Ucasfe Monterey, California 93940 UnDcl assi F AIeNDONRDG SCHEDULE 1B. DISTRIBUTION...22 C. TEE SIX-STATE SYSTEM-----------------23 I). TEE TWO-STATE SYSTEM- ---------------- IV. ANAYLSIS ---------------------------- Z A. THE...simplifing techniques used in Kalman filters include precomputed gains. Although forfeiting the optimal Kalman gains, this has the advantage of reducing
Esteban, Segundo; Girón-Sierra, Jose M; Polo, Óscar R; Angulo, Manuel
2016-10-31
Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework.
Esteban, Segundo; Girón-Sierra, Jose M.; Polo, Óscar R.; Angulo, Manuel
2016-01-01
Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework. PMID:27809250
RumEnKF: running very large Ensembles Kalman Filter by forgetting what you just did.
NASA Astrophysics Data System (ADS)
Hut, R.; Amisigo, B. A.; Steele-Dunne, S. C.; Van De Giesen, N.
2014-12-01
The eWaterCycle project works towards running an operational hyper-resolution hydrological global model, assimilating incoming satellite data in real time, and making 14 day predictions of floods and droughts. A problem encountered in the eWatercycle project is that the computer memory needed to store a single ensemble member becomes so large that storing enough ensembles to run the EnKF is impossible, even when using mitigating strategies such as covariance inflation or localization. Reduction of Used Memory Ensemble Kalman Filtering (RumEnKF) is introduced as a variant on the Ensemble Kalman Filter (EnKF). RumEnKF differs from EnKF in that it does not store the entire ensemble, but rather only saves the first two moments of the ensemble distribution. In this way, the number of ensemble members that can be calculated is less dependent on available memory, and mainly on available computing power (CPU). RumEnKF is developed to make optimal use of current generation super computer architecture, where the number of available floating point operations (flops) increases more rapidly than the available memory and where inter-node communication can quickly become a bottleneck. In this presentation, two simple models are used (auto-regressive and Lorenz) to show that RumEnKF performs similar to the EnKF. Furthermore, it is also shown that increasing the ensemble size has a similar impact on the estimation error from the two algorithms In this preliminary results, RumEnKF reduces the used memory compared to the EnKF when the number of ensemble members is greater than half the number of state variables. Future research will focus on strategies to further reduce the memory burden of running non-linear data assimilation on very large models.
Target tracking by distributed autonomous vessels using the derivative-free nonlinear Kalman filter
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Siano, Pierluigi; Raffo, Guilerme
2015-12-01
In this paper a distributed control problem for unmanned surface vessels (USVs) is formulated as follows: there are N USVs which pursue another vessel (moving target). At each time instant each USV can obtain measurements of the target's cartesian coordinates. The objective is to make the USVs converge in a synchronized manner towards the target, while avoiding collisions between them and avoiding collisions with obstacles in their motion plane. A distributed control law is developed for the USVs which enables not only convergence of the USVs to the goal position, but also makes possible to maintain the cohesion of the USVs fleet. Moreover, distributed filtering is performed, so as to obtain an estimate of the target vessel's state vector. This provides the desirable state vector to be tracked by each one of the USVs. To this end, a new distributed nonlinear filtering method of improved accuracy and computation speed is introduced. This filtering approach, under the name Derivative-free distributed nonlinear Kalman Filter is based on differential flatness theory and on an exact linearization of the target vessel's dynamic/kinematic model.
Enhanced Kalman Filtering for a 2D CFD NS Wind Farm Flow Model
NASA Astrophysics Data System (ADS)
Doekemeijer, B. M.; van Wingerden, J. W.; Boersma, S.; Pao, L. Y.
2016-09-01
Wind turbines are often grouped together for financial reasons, but due to wake development this usually results in decreased turbine lifetimes and power capture, and thereby an increased levelized cost of energy (LCOE). Wind farm control aims to minimize this cost by operating turbines at their optimal control settings. Most state-of-the-art control algorithms are open-loop and rely on low fidelity, static flow models. Closed-loop control relying on a dynamic model and state observer has real potential to further decrease wind's LCOE, but is often too computationally expensive for practical use. In this paper two time-efficient Kalman filter (KF) variants are outlined incorporating the medium fidelity, dynamic flow model “WindFarmSimulator” (WFSim). This model relies on a discretized set of Navier-Stokes equations in two dimensions to predict the flow in wind farms at low computational cost. The filters implemented are an Ensemble KF and an Approximate KF. Simulations in which a high fidelity simulation model represents the true wind farm show that these filters are 101 —102 times faster than a regular KF with comparable or better performance, correcting for wake dynamics that are not modeled in WFSim (noticeably, wake meandering and turbine hub effects). This is a first big step towards real-time closed-loop control for wind farms.
NASA Technical Reports Server (NTRS)
Fukumori, Ichiro; Malanotte-Rizzoli, Paola
1995-01-01
A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.
A Reduced Extended Kalman Filter Method For Data Assimilation And Parameter Optimization
NASA Astrophysics Data System (ADS)
Kao, C. J.
2007-12-01
This work is an extension of our two recent papers [Kao et al., Data assimilation with an extended Kalman filter for an impact-produced shock-wave study, J. Comp. Phys., 196 (2004), 705-723, and Kao et al., Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter, J. Comp. Phys., 214 (2006), 725-737 ] about the applications of the extended Kalman filter (EKF) to data assimilation in predictive codes. We have shown through the above two studies that the EKF method successfully estimates the evolving model state variables as well as model parameters of a shock-wave system by merging single-point pressure data into an Euler-equations computer code. We here intend to introduce a reduced EKF for the same purposes in terms of data assimilation and parameter optimization, but with a much smaller computational cost so that the applications of EKF to multi-dimensional realistic problems can be made possible. One of the distinctive features of EKF is that, as the system evolves forward in time, the EKF algorithm tracks the time-dependent error-covariance matrix of the model's state variables and parameters based on a consistent tangent-linear approximation of the model dynamics. When data becomes available at one instant in time, the update of the model state variables and parameters is achieved through a functional form of the linear merger of the model prediction and the data, subjective to the minimization of the trace of the error-covariance matrix of the model state variables and parameters. It, however, has been a concern that the calculation for the time evolution of the error-covariance matrix in applying EKF is computationally demanding and prohibitively expensive for real multi-dimensional problems. Several simplified approaches of EKF have been proposed to reduce the computational burden. This current study was actually motivated by Dee's work [Dee, P. D., 1991: Simplification of the
Hongda Wang; Chiu-Sing Choy
2016-08-01
The ability of correlation integral for automatic seizure detection using scalp EEG data has been re-examined in this paper. To facilitate the detection performance and overcome the shortcoming of correlation integral, nonlinear adaptive denoising and Kalman filter have been adopted for pre-processing and post-processing. The three-stage algorithm has achieved 84.6% sensitivity and 0.087/h false detection rate, which are comparable to many machine learning based methods, but at much lower computational cost. Since this algorithm is tested with long-term scalp EEG, it has the potential to achieve higher performance with intracranial EEG. The clinical value of this algorithm includes providing a pre-judgement to assist the doctor's diagnosis procedure and acting as a reliable warning system in a wearable device for epilepsy patients.
NASA Technical Reports Server (NTRS)
Auger, Ludovic; Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.
A Kalman-filtering approach to high dynamic range imaging for measurement applications.
Dedrick, Eric; Lau, Daniel
2012-02-01
High dynamic range imaging (HDRI) methods in computational photography address situations where the dynamic range of a scene exceeds what can be captured by an image sensor in a single exposure. HDRI techniques have also been used to construct radiance maps in measurement applications; unfortunately, the design and evaluation of HDRI algorithms for use in these applications have received little attention. In this paper, we develop a novel HDRI technique based on pixel-by-pixel Kalman filtering and evaluate its performance using objective metrics that this paper also introduces. In the presented experiments, this new technique achieves as much as 9.4-dB improvement in signal-to-noise ratio and can achieve as much as a 29% improvement in radiometric accuracy over a classic method.
NASA Technical Reports Server (NTRS)
Park, K. C.; Alvin, K. F.; Belvin, W. Keith
1991-01-01
A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.
Monitoring hydraulic fractures: state estimation using an extended Kalman filter
NASA Astrophysics Data System (ADS)
Alves Rochinha, Fernando; Peirce, Anthony
2010-02-01
There is considerable interest in using remote elastostatic deformations to identify the evolving geometry of underground fractures that are forced to propagate by the injection of high pressure viscous fluids. These so-called hydraulic fractures are used to increase the permeability in oil and gas reservoirs as well as to pre-fracture ore-bodies for enhanced mineral extraction. The undesirable intrusion of these hydraulic fractures into environmentally sensitive areas or into regions in mines which might pose safety hazards has stimulated the search for techniques to enable the evolving hydraulic fracture geometries to be monitored. Previous approaches to this problem have involved the inversion of the elastostatic data at isolated time steps in the time series provided by tiltmeter measurements of the displacement gradient field at selected points in the elastic medium. At each time step, parameters in simple static models of the fracture (e.g. a single displacement discontinuity) are identified. The approach adopted in this paper is not to regard the sequence of sampled elastostatic data as independent, but rather to treat the data as linked by the coupled elastic-lubrication equations that govern the propagation of the evolving hydraulic fracture. We combine the Extended Kalman Filter (EKF) with features of a recently developed implicit numerical scheme to solve the coupled free boundary problem in order to form a novel algorithm to identify the evolving fracture geometry. Numerical experiments demonstrate that, despite excluding significant physical processes in the forward numerical model, the EKF-numerical algorithm is able to compensate for the un-modeled dynamics by using the information fed back from tiltmeter data. Indeed the proposed algorithm is able to provide reasonably faithful estimates of the fracture geometry, which are shown to converge to the actual hydraulic fracture geometry as the number of tiltmeters is increased. Since the location of
The Joint Adaptive Kalman Filter (JAKF) for Vehicle Motion State Estimation
Gao, Siwei; Liu, Yanheng; Wang, Jian; Deng, Weiwen; Oh, Heekuck
2016-01-01
This paper proposes a multi-sensory Joint Adaptive Kalman Filter (JAKF) through extending innovation-based adaptive estimation (IAE) to estimate the motion state of the moving vehicles ahead. JAKF views Lidar and Radar data as the source of the local filters, which aims to adaptively adjust the measurement noise variance-covariance (V-C) matrix ‘R’ and the system noise V-C matrix ‘Q’. Then, the global filter uses R to calculate the information allocation factor ‘β’ for data fusion. Finally, the global filter completes optimal data fusion and feeds back to the local filters to improve the measurement accuracy of the local filters. Extensive simulation and experimental results show that the JAKF has better adaptive ability and fault tolerance. JAKF enables one to bridge the gap of the accuracy difference of various sensors to improve the integral filtering effectivity. If any sensor breaks down, the filtered results of JAKF still can maintain a stable convergence rate. Moreover, the JAKF outperforms the conventional Kalman filter (CKF) and the innovation-based adaptive Kalman filter (IAKF) with respect to the accuracy of displacement, velocity, and acceleration, respectively. PMID:27438835
The Joint Adaptive Kalman Filter (JAKF) for Vehicle Motion State Estimation.
Gao, Siwei; Liu, Yanheng; Wang, Jian; Deng, Weiwen; Oh, Heekuck
2016-07-16
This paper proposes a multi-sensory Joint Adaptive Kalman Filter (JAKF) through extending innovation-based adaptive estimation (IAE) to estimate the motion state of the moving vehicles ahead. JAKF views Lidar and Radar data as the source of the local filters, which aims to adaptively adjust the measurement noise variance-covariance (V-C) matrix 'R' and the system noise V-C matrix 'Q'. Then, the global filter uses R to calculate the information allocation factor 'β' for data fusion. Finally, the global filter completes optimal data fusion and feeds back to the local filters to improve the measurement accuracy of the local filters. Extensive simulation and experimental results show that the JAKF has better adaptive ability and fault tolerance. JAKF enables one to bridge the gap of the accuracy difference of various sensors to improve the integral filtering effectivity. If any sensor breaks down, the filtered results of JAKF still can maintain a stable convergence rate. Moreover, the JAKF outperforms the conventional Kalman filter (CKF) and the innovation-based adaptive Kalman filter (IAKF) with respect to the accuracy of displacement, velocity, and acceleration, respectively.
Event-triggered Kalman-consensus filter for two-target tracking sensor networks.
Su, Housheng; Li, Zhenghao; Ye, Yanyan
2017-06-24
This paper is concerned with the problem of event-triggered Kalman-consensus filter for two-target tracking sensor networks. According to the event-triggered protocol and the mean-square analysis, a suboptimal Kalman gain matrix is derived and a suboptimal event-triggered distributed filter is obtained. Based on the Kalman-consensus filter protocol, all sensors which only depend on its neighbors' information can track their corresponding targets. Furthermore, utilizing Lyapunov method and matrix theory, some sufficient conditions are presented for ensuring the stability of the system. Finally, a simulation example is presented to verify the effectiveness of the proposed event-triggered protocol. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Schütte, Dirk; Hassen, S. Z. Sayed; Karvinen, Kai S.; Boyson, Toby K.; Kallapur, Abhijit G.; Song, Hongbin; Petersen, Ian R.; Huntington, Elanor H.; Heurs, Michèle
2016-01-01
We propose and demonstrate a new autolocking scheme using a three-mirror ring cavity consisting of a linear quadratic regulator and a time-varying Kalman filter. Our technique does not require a frequency scan to acquire resonance. We utilize the singular perturbation method to simplify our system dynamics and to permit the application of linear control techniques. The error signal combined with the transmitted power is used to estimate the cavity detuning. This estimate is used by a linear time-varying Kalman filter which enables the implementation of an optimal controller. The experimental results validate the controller design, and we demonstrate improved robustness to disturbances and a faster locking time than a traditional proportional-integral controller. More important, the time-varying Kalman filtering approach automatically reacquires lock for large detunings, where the error signal leaves its linear capture range, a feat which linear time-invariant controllers cannot achieve.
Gauterin, Eckhard; Kammerer, Philipp; Kühn, Martin; Schulte, Horst
2016-05-01
Advanced model-based control of wind turbines requires knowledge of the states and the wind speed. This paper benchmarks a nonlinear Takagi-Sugeno observer for wind speed estimation with enhanced Kalman Filter techniques: The performance and robustness towards model-structure uncertainties of the Takagi-Sugeno observer, a Linear, Extended and Unscented Kalman Filter are assessed. Hence the Takagi-Sugeno observer and enhanced Kalman Filter techniques are compared based on reduced-order models of a reference wind turbine with different modelling details. The objective is the systematic comparison with different design assumptions and requirements and the numerical evaluation of the reconstruction quality of the wind speed. Exemplified by a feedforward loop employing the reconstructed wind speed, the benefit of wind speed estimation within wind turbine control is illustrated.
A Hybrid Extended Kalman Filter as an Observer for a Pot-Electro-Magnetic Actuator
NASA Astrophysics Data System (ADS)
Schmidt, Simon; Mercorelli, Paolo
2017-01-01
This paper deals with an application in which a hybrid extended Kalman Filter (HEKF) is used to estimate state variables in a U-shaped electro-magnetic actuator to be used in mechanical systems. In this context a hybrid Kalman Filter is the one which switches between different models. The paper proposes a hybrid model for an extended Kalman Filter to be used as an observer to estimate the state and to control the force of the actuator. Applications include position, velocity and force control in automotive, engine and manufacturing systems. This work is focused on the estimation of state variables of the actuator. Simulated results show the effectiveness of the proposed approach.
Infrared species tomography of a transient flow field using Kalman filtering.
Daun, Kyle J; Waslander, Steven L; Tulloch, Brandon B
2011-02-20
In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.
On-line classification and prediction of eye movements by multiple-model Kalman filtering.
Kohlbecher, Stefan; Schneider, Erich
2009-05-01
An extensible multiple-model Kalman filter framework for eye tracking and video-oculography (VOG) applications is proposed. The Kalman filter predicts future states of a system on the basis of a mathematical model and previous measurements. The predicted values are then compared against the current measurements. In a correcting step, the predicted state is enhanced by the measurements. In this work, the Kalman filter is used for smoothing the VOG data, for on-line classification of eye movements, as well as for predictive real-time control of a gaze-driven head-mounted camera (EyeSeeCam). With multiple models running in parallel, it was possible to distinguish between fixations, slow-phase eye movements, and saccades. Under the assumption that each class of eye movement follows a distinct model, one can decide which types of eye movement occurred by evaluating the probability for each model.
Identification and tracking of harmonic sources in a power system using a Kalman filter
Ma, H.; Girgis, A.A.
1996-07-01
In this paper, two problems have been addressed on harmonic sources identification: the optimal locations of a limited number of harmonic meters and the optimal dynamic estimates of harmonic source locations and their injections in unbalanced three-phase power systems. A Kalman filtering is used to attack these problems. System error covariance analysis by the Kalman filter associated with a harmonic injection estimate determines the optimal arrangement of limited harmonic meters. Based on the optimally-arranged harmonic metering locations, the Kalman filter then yields the optimal dynamic estimates of harmonic injections with a few noisy harmonic measurements. The method is dynamic and has the capability of identifying, analyzing and tracking each harmonic injection at all buses in unbalanced three-phase power systems. Actual recorded harmonic measurements and simulated data in a power distribution system are provided to prove the efficiency of this approach.
Observation impact in a convective-scale localized ensemble transform Kalman filter
NASA Astrophysics Data System (ADS)
Sommer, Matthias; Weissmann, Martin
2014-05-01
In operational weather forecasting, knowledge about observation impact, i.e. the contribution of specific observations to forecast error reduction, is crucial to refine the observing and data assimilation system. However, assessing this quantity by direct computation (data denial experiments) is usually not feasible because of the high computational cost. This has motivated the derivation of approximated forms of observation impact. If an adjoint model is available, established methods exist that give a reliable estimate. On the other hand, in an ensemble-based environment, a recently developed algorithm [1] uses the analysis and forecast deviations to approximate observation impact. This has now for the first time been implemented in the convective-scale limited-area model COSMO and has been thoroughly verified with data-denial experiments [2]. It has been found that the difference to data denial is not significant (less than 10%) and accuracy can be expected to improve further when considering longer test periods. The peculiarities for an application on this scale include a strongly non-linear behavior and a typically small localization length. While the former can be expected to be reasonably addressed by the ensemble algorithm, the latter imposes constraints for an appropriate choice of lead time. It could also be shown that valuable information, such as the detection of disadvantageous observations can be gained. This presentation shows the feasibility and distinctive features of the method for a convective-scale setup, gives examples from a pre-operational application at Deutscher Wetterdienst, and discusses the sensitivity to lead time, localization and verification norm. References: [1] E. Kalnay, Y. Ota, T. Miyoshi, and J. Liu. A simpler formulation of forecast sensitivity to observations: application to ensemble Kalman filters. Tellus A 64, 2012. [2] M. Sommer and M. Weissmann. Observation impact in a convective-scale localized ensemble transform Kalman
NASA Astrophysics Data System (ADS)
Ablyazimov, T. O.; Zyzak, M. V.; Ivanov, V. V.; Kisel, P. I.
2015-05-01
One of the main goals in the Compressed Baryonic Matter (CBM) experiment (GSI, Germany) is to find parameters of charged particle trajectories. An online full event reconstruction is planned to be carried out in this experiment, thus demanding fast algorithms be developed, which make the most of the capabilities of modern CPU and GPU architectures. This paper presents the results of an analysis of the Kalman filter-based track reconstruction for charged particles implemented by using various code parallelization methods. A multicore server located at the Laboratory of Information Technologies, Joint Institute for Nuclear Research (LIT JINR), with two CPU Intel Xeon X5660 processors and a GPU Nvidia GTX 480 video card is used.
Hanson, Jeremy M.; De Bono, Bryan; Levesque, Jeffrey P.; Mauel, Michael E.; Maurer, David A.; Navratil, Gerald A.; Pedersen, Thomas Sunn; Shiraki, Daisuke; James, Royce W.
2009-05-15
The simulation and experimental optimization of a Kalman filter feedback control algorithm for n=1 tokamak external kink modes are reported. In order to achieve the highest plasma pressure limits in ITER, resistive wall mode stabilization is required [T. C. Hender et al., Nucl. Fusion 47, S128 (2007)] and feedback algorithms will need to distinguish the mode from noise due to other magnetohydrodynamic activity. The Kalman filter contains an internal model that captures the dynamics of a rotating, growing n=1 mode. This model is actively compared with real-time measurements to produce an optimal estimate for the mode's amplitude and phase. On the High Beta Tokamak-Extended Pulse experiment [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)], the Kalman filter algorithm is implemented using a set of digital, field-programmable gate array controllers with 10 {mu}s latencies. Signals from an array of 20 poloidal sensor coils are used to measure the n=1 mode, and the feedback control is applied using 40 poloidally and toroidally localized control coils. The feedback system with the Kalman filter is able to suppress the external kink mode over a broad range of phase angles between the sensed mode and applied control field. Scans of filter parameters show good agreement between simulation and experiment, and feedback suppression and excitation of the kink mode are enhanced in experiments when a filter made using optimal parameters from the scans is used.
Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Raffo, Guilerme
2015-12-01
The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.
Use of Kalman filter methods in analysis of in-pile LMFBR accident simulations
Meek, C.C.; Doerner, R.C.
1983-01-01
Kalman filter methodology has been applied to inpile liquid-metal fast breeder reactor simulation experiments to obtain estimates of the fuel-clad thermal gap conductance. A transient lumped parameter model of the experiment is developed. An optimal estimate of the state vector chosen to characterize the experiment is obtained through the use of the Kalman filter. From this estimate, the fuel-clad thermal gap conductance is calculated as a function of time into the test and axial position along the length of the fuel pin.
Extended Kalman Filter Based Neural Networks Controller For Hot Strip Rolling mill
NASA Astrophysics Data System (ADS)
Moussaoui, A. K.; Abbassi, H. A.; Bouazza, S.
2008-06-01
The present paper deals with the application of an Extended Kalman filter based adaptive Neural-Network control scheme to improve the performance of a hot strip rolling mill. The suggested Neural Network model was implemented using Bayesian Evidence based training algorithm. The control input was estimated iteratively by an on-line extended Kalman filter updating scheme basing on the inversion of the learned neural networks model. The performance of the controller is evaluated using an accurate model estimated from real rolling mill input/output data, and the usefulness of the suggested method is proved.
Extended Kalman Filter Based Neural Networks Controller For Hot Strip Rolling mill
Moussaoui, A. K.; Abbassi, H. A.; Bouazza, S.
2008-06-12
The present paper deals with the application of an Extended Kalman filter based adaptive Neural-Network control scheme to improve the performance of a hot strip rolling mill. The suggested Neural Network model was implemented using Bayesian Evidence based training algorithm. The control input was estimated iteratively by an on-line extended Kalman filter updating scheme basing on the inversion of the learned neural networks model. The performance of the controller is evaluated using an accurate model estimated from real rolling mill input/output data, and the usefulness of the suggested method is proved.
A Self-Tuning Kalman Filter for Autonomous Navigation using the Global Positioning System (GPS)
NASA Technical Reports Server (NTRS)
Truong, S. H.
1999-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.
A Self-Tuning Kalman Filter for Autonomous Navigation Using the Global Positioning System (GPS)
NASA Technical Reports Server (NTRS)
Truong, Son H.
1999-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS (Global Positioning Systems) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.
A Self-Tuning Kalman Filter for Autonomous Navigation using the Global Positioning System (GPS)
NASA Technical Reports Server (NTRS)
Truong, S. H.
1999-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.
A Self-Tuning Kalman Filter for Autonomous Navigation Using the Global Positioning System (GPS)
NASA Technical Reports Server (NTRS)
Truong, Son H.
1999-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS (Global Positioning Systems) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.
The application of dummy noise adaptive Kalman filter in underwater navigation
NASA Astrophysics Data System (ADS)
Li, Song; Zhang, Chun-Hua; Luan, Jingde
2011-10-01
The track of underwater target is easy to be affected by the various by the various factors, which will cause poor performance in Kalman filter with the error in the state and measure model. In order to solve the situation, a method is provided with dummy noise compensative technology. Dummy noise is added to state and measure model artificially, and then the question can be solved by the adaptive Kalman filter with unknown time-changed statistical character. The simulation result of underwater navigation proves the algorithm is effective.
2009-07-01
ensembles for probabilistic forecasts of hurricanes . 1. Introduction Landfalling hurricanes are among the deadliest and costliest natural hazards. Over...Cloud-Resolving Hurricane Initialization and Prediction through Assimilation of Doppler Radar Observations with an Ensemble Kalman Filter FUQING...Doppler radar radial velocity observations for cloud-resolving hurricane analysis, initialization, and prediction with an ensemble Kalman filter (EnKF
Brückner, Hans-Peter; Spindeldreier, Christian; Blume, Holger
2013-01-01
A common approach for high accuracy sensor fusion based on 9D inertial measurement unit data is Kalman filtering. State of the art floating-point filter algorithms differ in their computational complexity nevertheless, real-time operation on a low-power microcontroller at high sampling rates is not possible. This work presents algorithmic modifications to reduce the computational demands of a two-step minimum order Kalman filter. Furthermore, the required bit-width of a fixed-point filter version is explored. For evaluation real-world data captured using an Xsens MTx inertial sensor is used. Changes in computational latency and orientation estimation accuracy due to the proposed algorithmic modifications and fixed-point number representation are evaluated in detail on a variety of processing platforms enabling on-board processing on wearable sensor platforms.
NASA Astrophysics Data System (ADS)
Meng, Yang; Gao, Shesheng; Zhong, Yongmin; Hu, Gaoge; Subic, Aleksandar
2016-03-01
The use of the direct filtering approach for INS/GNSS integrated navigation introduces nonlinearity into the system state equation. As the unscented Kalman filter (UKF) is a promising method for nonlinear problems, an obvious solution is to incorporate the UKF concept in the direct filtering approach to address the nonlinearity involved in INS/GNSS integrated navigation. However, the performance of the standard UKF is dependent on the accurate statistical characterizations of system noise. If the noise distributions of inertial instruments and GNSS receivers are not appropriately described, the standard UKF will produce deteriorated or even divergent navigation solutions. This paper presents an adaptive UKF with noise statistic estimator to overcome the limitation of the standard UKF. According to the covariance matching technique, the innovation and residual sequences are used to determine the covariance matrices of the process and measurement noises. The proposed algorithm can estimate and adjust the system noise statistics online, and thus enhance the adaptive capability of the standard UKF. Simulation and experimental results demonstrate that the performance of the proposed algorithm is significantly superior to that of the standard UKF and adaptive-robust UKF under the condition without accurate knowledge on system noise, leading to improved navigation precision.
Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering
Havlicek, Martin; Friston, Karl J.; Jan, Jiri; Brazdil, Milan; Calhoun, Vince D.
2011-01-01
This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain. PMID:21396454
Szczęsna, Agnieszka; Pruszowski, Przemysław
2016-01-01
Inertial orientation tracking is still an area of active research, especially in the context of out-door, real-time, human motion capture. Existing systems either propose loosely coupled tracking approaches where each segment is considered independently, taking the resulting drawbacks into account, or tightly coupled solutions that are limited to a fixed chain with few segments. Such solutions have no flexibility to change the skeleton structure, are dedicated to a specific set of joints, and have high computational complexity. This paper describes the proposal of a new model-based extended quaternion Kalman filter that allows for estimation of orientation based on outputs from the inertial measurements unit sensors. The filter considers interdependencies resulting from the construction of the kinematic chain so that the orientation estimation is more accurate. The proposed solution is a universal filter that does not predetermine the degree of freedom at the connections between segments of the model. To validation the motion of 3-segments single link pendulum captured by optical motion capture system is used. The next step in the research will be to use this method for inertial motion capture with a human skeleton model.
Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Scheid, R. E., Jr.
1987-01-01
This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Scheid, R. E., Jr.
1987-01-01
This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
Bounded-observation Kalman filtering of correlation in multivariate neural recordings.
Kafashan, MohammadMehdi; Palanca, Ben J; Ching, ShiNung
2014-01-01
A persistent question in multivariate neural signal processing is how best to characterize the statistical association between brain regions known as functional connectivity. Of the many metrics available for determining such association, the standard Pearson correlation coefficient (i.e., the zero-lag cross-correlation) remains widely used, particularly in neuroimaging. Generally, the cross-correlation is computed over an entire trial or recording session, with the assumption of within-trial stationarity. Increasingly, however, the length and complexity of neural data requires characterizing transient effects and/or non-stationarity in the temporal evolution of the correlation. That is, to estimate dynamics in the association between brain regions. Here, we present a simple, data-driven Kalman filter-based approach to tracking correlation dynamics. The filter explicitly accounts for the bounded nature of correlation measurements through the inclusion of a Fisher transform in the measurement equation. An output linearization facilitates a straightforward implementation of the standard recursive filter equations, including admittance of covariance identification via an autoregressive least squares method. We demonstrate the efficacy and utility of the approach in an example of multivariate neural functional magnetic resonance imaging data.
Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering.
Havlicek, Martin; Friston, Karl J; Jan, Jiri; Brazdil, Milan; Calhoun, Vince D
2011-06-15
This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.
Kalman Filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry.
Zhang, Yuxin; Chen, Shuo; Deng, Kexin; Chen, Bingyao; Wei, Xing; Yang, Jiafei; Wang, Shi; Ying, Kui
2017-01-01
To develop a self-adaptive and fast thermometry method by combining the original hybrid magnetic resonance thermometry method and the bio heat transfer equation (BHTE) model. The proposed Kalman filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry, abbreviated as KalBHT hybrid method, introduced the BHTE model to synthesize a window on the regularization term of the hybrid algorithm, which leads to a self-adaptive regularization both spatially and temporally with change of temperature. Further, to decrease the sensitivity to accuracy of the BHTE model, Kalman filter is utilized to update the window at each iteration time. To investigate the effect of the proposed model, computer heating simulation, phantom microwave heating experiment and dynamic in-vivo model validation of liver and thoracic tumor were conducted in this study. The heating simulation indicates that the KalBHT hybrid algorithm achieves more accurate results without adjusting λ to a proper value in comparison to the hybrid algorithm. The results of the phantom heating experiment illustrate that the proposed model is able to follow temperature changes in the presence of motion and the temperature estimated also shows less noise in the background and surrounding the hot spot. The dynamic in-vivo model validation with heating simulation demonstrates that the proposed model has a higher convergence rate, more robustness to susceptibility problem surrounding the hot spot and more accuracy of temperature estimation. In the healthy liver experiment with heating simulation, the RMSE of the hot spot of the proposed model is reduced to about 50% compared to the RMSE of the original hybrid model and the convergence time becomes only about one fifth of the hybrid model. The proposed model is able to improve the accuracy of the original hybrid algorithm and accelerate the convergence rate of MR temperature estimation.
Structural damage detection using extended Kalman filter combined with statistical process control
NASA Astrophysics Data System (ADS)
Jin, Chenhao; Jang, Shinae; Sun, Xiaorong
2015-04-01
Traditional modal-based methods, which identify damage based upon changes in vibration characteristics of the structure on a global basis, have received considerable attention in the past decades. However, the effectiveness of the modalbased methods is dependent on the type of damage and the accuracy of the structural model, and these methods may also have difficulties when applied to complex structures. The extended Kalman filter (EKF) algorithm which has the capability to estimate parameters and catch abrupt changes, is currently used in continuous and automatic structural damage detection to overcome disadvantages of traditional methods. Structural parameters are typically slow-changing variables under effects of operational and environmental conditions, thus it would be difficult to observe the structural damage and quantify the damage in real-time with EKF only. In this paper, a Statistical Process Control (SPC) is combined with EFK method in order to overcome this difficulty. Based on historical measurements of damage-sensitive feathers involved in the state-space dynamic models, extended Kalman filter (EKF) algorithm is used to produce real-time estimations of these features as well as standard derivations, which can then be used to form control ranges for SPC to detect any abnormality of the selected features. Moreover, confidence levels of the detection can be adjusted by choosing different times of sigma and number of adjacent out-of-range points. The proposed method is tested using simulated data of a three floors linear building in different damage scenarios, and numerical results demonstrate high damage detection accuracy and light computation of this presented method.
The Unscented Kalman Filter estimates the plasma insulin from glucose measurement.
Eberle, Claudia; Ament, Christoph
2011-01-01
Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.
GPS/UWB/MEMS-IMU tightly coupled navigation with improved robust Kalman filter
NASA Astrophysics Data System (ADS)
Li, Zengke; Chang, Guobin; Gao, Jingxiang; Wang, Jian; Hernandez, Alberto
2016-12-01
The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been very intensively developed and widely applied in multiple areas. To further enhance the reliability and availability of GPS/INS integrated navigation in GPS challenging environment, range observation through ultra-wideband (UWB) is introduced in GPS/INS tightly coupled navigation. An improved robust Kalman filter is proposed and used to resist the influence of gross error from UWB observation in GPS/UWB/IMU tightly coupled navigation. The variance of the squared Mahalanobis distance in moving window is calculated, which brings as new judgement factor for gross errors in order to decrease the rate of false outlier identification. A simulation analysis shows that the improved robust Kalman filter is able to correctly identify gross errors and the rate of false judgment as zero. In order to validate the new robust filter, a real experiment is conducted. The results indicate that the improved robust Kalman filter used in GPS/UWB/INS tightly coupled navigation is able to remove the harmful effect of gross error in UWB observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all the simulated small and large gross errors added to UWB distance observation are successfully identified.
NASA Technical Reports Server (NTRS)
Kanning, G.; Cicolani, L. S.; Schmidt, S. F.
1983-01-01
Translational state estimation in terminal area operations, using a set of commonly available position, air data, and acceleration sensors, is described. Kalman filtering is applied to obtain maximum estimation accuracy from the sensors but feasibility in real-time computations requires a variety of approximations and devices aimed at minimizing the required computation time with only negligible loss of accuracy. Accuracy behavior throughout the terminal area, its relation to sensor accuracy, its effect on trajectory tracking errors and control activity in an automatic flight control system, and its adequacy in terms of existing criteria for various terminal area operations are examined. The principal investigative tool is a simulation of the system.
Acoustic tomography of the atmosphere using iterated unscented Kalman filter
NASA Astrophysics Data System (ADS)
Kolouri, Soheil
Tomography approaches are of great interests because of their non-intrusive nature and their ability to generate a significantly larger amount of data in comparison to the in-situ measurement method. Acoustic tomography is an approach which reconstructs the unknown parameters that affect the propagation of acoustic rays in a field of interest by studying the temporal characteristics of the propagation. Acoustic tomography has been used in several different disciplines such as biomedical imaging, oceanographic studies and atmospheric studies. The focus of this thesis is to study acoustic tomography of the atmosphere in order to reconstruct the temperature and wind velocity fields in the atmospheric surface layer using the travel-times collected from several pairs of transmitter and receiver sensors distributed in the field. Our work consists of three main parts. The first part of this thesis is dedicated to reviewing the existing methods for acoustic tomography of the atmosphere, namely statistical inversion (SI), time dependent statistical inversion (TDSI), simultaneous iterative reconstruction technique (SIRT), and sparse recovery framework. The properties of these methods are then explained extensively and their shortcomings are also mentioned. In the second part of this thesis, a new acoustic tomography method based on Unscented Kalman Filter (UKF) is introduced in order to address some of the shortcomings of the existing methods. Using the UKF, the problem is cast as a state estimation problem in which the temperature and wind velocity fields are the desired states to be reconstructed. The field is discretized into several grids in which the temperature and wind velocity fields are assumed to be constant. Different models, namely random walk, first order 3-D autoregressive (AR) model, and 1-D temporal AR model are used to capture the state evolution in time-space. Given the time of arrival (TOA) equation for acoustic propagation as the observation equation, the
Robust recovery of human motion from video using Kalman filters and virtual humans.
Cerveri, P; Pedotti, A; Ferrigno, G
2003-08-01
In sport science, as in clinical gait analysis, optoelectronic motion capture systems based on passive markers are widely used to recover human movement. By processing the corresponding image points, as recorded by multiple cameras, the human kinematics is resolved through multistage processing involving spatial reconstruction, trajectory tracking, joint angle determination, and derivative computation. Key problems with this approach are that marker data can be indistinct, occluded or missing from certain cameras, that phantom markers may be present, and that both 3D reconstruction and tracking may fail. In this paper, we present a novel technique, based on state space filters, that directly estimates the kinematical variables of a virtual mannequin (biomechanical model) from 2D measurements, that is, without requiring 3D reconstruction and tracking. Using Kalman filters, the configuration of the model in terms of joint angles, first and second order derivatives is automatically updated in order to minimize the distances, as measured on TV-cameras, between the 2D measured markers placed on the subject and the corresponding back-projected virtual markers located on the model. The Jacobian and Hessian matrices of the nonlinear observation function are computed through a multidimensional extension of Stirling's interpolation formula. Extensive experiments on simulated and real data confirmed the reliability of the developed system that is robust against false matching and severe marker occlusions. In addition, we show how the proposed technique can be extended to account for skin artifacts and model inaccuracy.
NASA Astrophysics Data System (ADS)
Guadagnini, A.; Panzeri, M.; Riva, M.; Neuman, S. P.
2013-12-01
We embed stochastic groundwater flow moment equations (MEs) in the Ensemble Kalman Filter (EnKF) in a way that obviates the need for Monte Carlo (MC) simulation. The MEs yield approximate conditional ensemble means and covariances of hydraulic heads and fluxes in randomly heterogeneous media. Embedding these in EnKF allows updating of conductivity and head predictors as new data become available without the need for MC. The approach is well suited for cases in which real-time measurements allow sequential (as opposed to simultaneous) updating of flow parameters. We discuss and compare the accuracies and computational efficiencies of our newly proposed ME-based EnKF approach and the traditional MC-based EnKF approach for the case of a pumping well in a two-dimensional randomly heterogeneous aquifer. We analyze a number of settings and investigate the impact on parameters estimates of (a) the number of head measurements assimilated, (b) the error variance associated with head and log conductivity measurements and (c) the initial hydraulic head field. We demonstrate the computational feasibility and accuracy of our methodology and show that hydraulic conductivity estimates are more sensitive to early than to later head values, improving with increased assimilation frequency at early time. Our approach mitigates issues of filter inbreeding and spurious covariances often plaguing standard EnKF.
Application of the Kalman Filter for Faster Strong Coupling of Cardiovascular Simulations.
Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya
2016-07-01
In this paper, we propose a method for reducing the computational cost of strong coupling for multiscale cardiovascular simulation models. In such a model, individual model modules of myocardial cell, left ventricular structural dynamics, and circulatory hemodynamics are coupled. The strong coupling method enables stable and accurate calculation, but requires iterative calculations which are computationally expensive. The iterative calculations can be reduced, if accurate initial approximations are made available by predictors. The proposed method uses the Kalman filter to estimate accurate predictions by filtering out noise included in past values. The performance of the proposed method was assessed with an application to a previously published multiscale cardiovascular model. The proposed method reduced the number of iterations by 90% and 62% compared with no prediction and Lagrange extrapolation, respectively. Even when the parameters were varied and number of elements of the left ventricular finite-element model increased, the number of iterations required by the proposed method was significantly lower than that without prediction. These results indicate the robustness, scalability, and validity of the proposed method.
NASA Astrophysics Data System (ADS)
Medina, H.; Romano, N.; Chirico, G. B.
2014-07-01
This study presents a dual Kalman filter (DSUKF - dual standard-unscented Kalman filter) for retrieving states and parameters controlling the soil water dynamics in a homogeneous soil column, by assimilating near-surface state observations. The DSUKF couples a standard Kalman filter for retrieving the states of a linear solver of the Richards equation, and an unscented Kalman filter for retrieving the parameters of the soil hydraulic functions, which are defined according to the van Genuchten-Mualem closed-form model. The accuracy and the computational expense of the DSUKF are compared with those of the dual ensemble Kalman filter (DEnKF) implemented with a nonlinear solver of the Richards equation. Both the DSUKF and the DEnKF are applied with two alternative state-space formulations of the Richards equation, respectively differentiated by the type of variable employed for representing the states: either the soil water content (θ) or the soil water matric pressure head (h). The comparison analyses are conducted with reference to synthetic time series of the true states, noise corrupted observations, and synthetic time series of the meteorological forcing. The performance of the retrieval algorithms are examined accounting for the effects exerted on the output by the input parameters, the observation depth and assimilation frequency, as well as by the relationship between retrieved states and assimilated variables. The uncertainty of the states retrieved with DSUKF is considerably reduced, for any initial wrong parameterization, with similar accuracy but less computational effort than the DEnKF, when this is implemented with ensembles of 25 members. For ensemble sizes of the same order of those involved in the DSUKF, the DEnKF fails to provide reliable posterior estimates of states and parameters. The retrieval performance of the soil hydraulic parameters is strongly affected by several factors, such as the initial guess of the unknown parameters, the wet or dry
Kalman Filter Models for Extrapolations in Dose-Response Experiments and Accelerated Life-Tests.
1988-09-09
Kalman-Filter models with Gaussian innovations provide a useful and easy to implement tool for inference from dose - response experiments and...proposed dose - response relationship. This is in contrast to the currently used approaches wherein there is an implicit commitment to the validity of
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
ERIC Educational Resources Information Center
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
The use of the Kalman filter in the automated segmentation of EIT lung images.
Zifan, A; Liatsis, P; Chapman, B E
2013-06-01
In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging.
Assimilating Remotely Sensed Surface Soil Moisture into SWAT using Ensemble Kalman Filter
USDA-ARS?s Scientific Manuscript database
In this study, a 1-D Ensemble Kalman Filter has been used to update the soil moisture states of the Soil and Water Assessment Tool (SWAT) model. Experiments were conducted for the Cobb Creek Watershed in southeastern Oklahoma for 2006-2008. Assimilation of in situ data proved limited success in the ...
Impact and point prediction using a neural extended Kalman filter with multiple sensors
NASA Astrophysics Data System (ADS)
Stubberud, Stephen C.; Kramer, Kathleen A.
2007-04-01
The neural extended Kalman filter is an adaptive estimation technique that has been shown to learn on-line the maneuver model of the trajectory of a target. This improved motion model can be used to better predict the location of a target at given point in time, especially when the target, such as a mortar shell, has limited maneuvering capabilities. In this paper, the neural extended Kalman filter is used to predict, with multiple-sensor-systems provided measurement reports, impact point and impact time of a ballistic-like projectile when the drag on the shell was not accurately modeled in the motion model. In previous work, the neural extended Kalman filter was shown to work well with a single sensor with a uniform sample rate. Multiple sensors can incorporate two major differences into the problem. The first difference is that of the multiple aspect angles and uncertainty that are used in the model adaptation. The second difference is that of a non-uniform update rate of the measurements to the tracking system. While most tracking systems can easily handle this difference, the adaptation of the neural network training parameters can be deleteriously affected by these variations. The first of these two differences, potential concerns to the neural extended Kalman filter's implementation, is investigated in this effort. In this effort, performance of this adaptive and predictive scheme with multiple sensors in a three dimensional space is shown to provide a quality impact estimate.
CONSISTENT USE OF THE KALMAN FILTER IN CHEMICAL TRANSPORT MODELS (CTMS) FOR DEDUCING EMISSIONS
Past research has shown that emissions can be deduced using observed concentrations of a chemical, a Chemical Transport Model (CTM), and the Kalman filter in an inverse modeling application. An expression was derived for the relationship between the "observable" (i.e., the con...
USDA-ARS?s Scientific Manuscript database
Recent advances in hydrologic data assimilation have demonstrated the value of remotely sensed surface soil moisture in improving forecasts of key hydrologic variables such as root-zone soil moisture and surface runoff. In hydrologic data assimilation, the ensemble Kalman filter (EnKF) provides a ro...
NASA Technical Reports Server (NTRS)
Lisano, M. E.
2003-01-01
This paper describes the design and initial test results of an extended Kalman filter that has been developed at Jet Propulsion Laboratory (JPL) for post-flight reconstruction of the trajectory and attitude history of a spacecraft entering a planetary atmosphere and descending upon a parachute.
CONSISTENT USE OF THE KALMAN FILTER IN CHEMICAL TRANSPORT MODELS (CTMS) FOR DEDUCING EMISSIONS
Past research has shown that emissions can be deduced using observed concentrations of a chemical, a Chemical Transport Model (CTM), and the Kalman filter in an inverse modeling application. An expression was derived for the relationship between the "observable" (i.e., the con...
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
ERIC Educational Resources Information Center
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
Estimation of Kalman filter model parameters from an ensemble of tests
NASA Technical Reports Server (NTRS)
Gibbs, B. P.; Haley, D. R.; Levine, W.; Porter, D. W.; Vahlberg, C. J.
1980-01-01
A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented. In addition, the problem of estimating time constants and process noise levels is addressed. Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered.
Kalman filter for statistical monitoring of forest cover across sub-continental regions [Symposium
Raymond L. Czaplewski
1991-01-01
The Kalman filter is a generalization of the composite estimator. The univariate composite estimate combines 2 prior estimates of population parameter with a weighted average where the scalar weight is inversely proportional to the variances. The composite estimator is a minimum variance estimator that requires no distributional assumptions other than estimates of the...
Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel
2015-10-01
A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).
USDA-ARS?s Scientific Manuscript database
Hydrologic data assimilation has become an important tool for improving hydrologic model predictions by utilizing observations from ground, aircraft, and satellite sensors. Among existing data assimilation methods, the ensemble Kalman filter (EnKF) provides a robust framework for optimally updating ...
Raymond L. Czaplewski
2015-01-01
Wall-to-wall remotely sensed data are increasingly available to monitor landscape dynamics over large geographic areas. However, statistical monitoring programs that use post-stratification cannot fully utilize those sensor data. The Kalman filter (KF) is an alternative statistical estimator. I develop a new KF algorithm that is numerically robust with large numbers of...
Wang, Li-Qi; Ge, Hui-Fang; Li, Gui-Bin; Yu, Dian-Yu; Hu, Li-Zhi; Jiang, Lian-Zhou
2014-04-01
Combining classical Kalman filter with NIR analysis technology, a new method of characteristic wavelength variable selection, namely Kalman filtering method, is presented. The principle of Kalman filter for selecting optimal wavelength variable was analyzed. The wavelength selection algorithm was designed and applied to NIR detection of soybean oil acid value. First, the PLS (partial leastsquares) models were established by using different absorption bands of oil. The 4 472-5 000 cm(-1) characteristic band of oil acid value, including 132 wavelengths, was selected preliminarily. Then the Kalman filter was used to select characteristic wavelengths further. The PLS calibration model was established using selected 22 characteristic wavelength variables, the determination coefficient R2 of prediction set and RMSEP (root mean squared error of prediction) are 0.970 8 and 0.125 4 respectively, equivalent to that of 132 wavelengths, however, the number of wavelength variables was reduced to 16.67%. This algorithm is deterministic iteration, without complex parameters setting and randomicity of variable selection, and its physical significance was well defined. The modeling using a few selected characteristic wavelength variables which affected modeling effect heavily, instead of total spectrum, can make the complexity of model decreased, meanwhile the robustness of model improved. The research offered important reference for developing special oil near infrared spectroscopy analysis instruments on next step.
Kalman filtering naturally accounts for visually guided and predictive smooth pursuit dynamics.
Orban de Xivry, Jean-Jacques; Coppe, Sébastien; Blohm, Gunnar; Lefèvre, Philippe
2013-10-30
The brain makes use of noisy sensory inputs to produce eye, head, or arm motion. In most instances, the brain combines this sensory information with predictions about future events. Here, we propose that Kalman filtering can account for the dynamics of both visually guided and predictive motor behaviors within one simple unifying mechanism. Our model relies on two Kalman filters: (1) one processing visual information about retinal input; and (2) one maintaining a dynamic internal memory of target motion. The outputs of both Kalman filters are then combined in a statistically optimal manner, i.e., weighted with respect to their reliability. The model was tested on data from several smooth pursuit experiments and reproduced all major characteristics of visually guided and predictive smooth pursuit. This contrasts with the common belief that anticipatory pursuit, pursuit maintenance during target blanking, and zero-lag pursuit of sinusoidally moving targets all result from different control systems. This is the first instance of a model integrating all aspects of pursuit dynamics within one coherent and simple model and without switching between different parallel mechanisms. Our model suggests that the brain circuitry generating a pursuit command might be simpler than previously believed and only implement the functional equivalents of two Kalman filters whose outputs are optimally combined. It provides a general framework of how the brain can combine continuous sensory information with a dynamic internal memory and transform it into motor commands.
Kalman-filter model for determining block and trickle SNM losses
Barlow, R.E.; Durst, M.J.; Smiriga, N.G.
1982-07-01
This paper describes an integrated decision procedure for deciding whether a diversion of SNM has occurred. Two possible types of diversion are considered: a block loss during a single time period and a cumulative trickle loss over several time periods. The methodology used is based on a compound Kalman filter model. Numerical examples illustrate our approach.
Integration of Differential GPS and Inertial Navigation using a Complementary Kalman Filter
1993-09-01
Global Positioning System or GPS . However, GPS updates only come once per second. INS...autoland problem. The remaining sensor is the Global Positioning System ( GPS ). This is the newest and most accurate radio navigation aid available. GPS ...Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP Kalman filtering, Differential Global Position System ,
Applications of Kalman filtering to real-time trace gas concentration measurements
NASA Technical Reports Server (NTRS)
Leleux, D. P.; Claps, R.; Chen, W.; Tittel, F. K.; Harman, T. L.
2002-01-01
A Kalman filtering technique is applied to the simultaneous detection of NH3 and CO2 with a diode-laser-based sensor operating at 1.53 micrometers. This technique is developed for improving the sensitivity and precision of trace gas concentration levels based on direct overtone laser absorption spectroscopy in the presence of various sensor noise sources. Filter performance is demonstrated to be adaptive to real-time noise and data statistics. Additionally, filter operation is successfully performed with dynamic ranges differing by three orders of magnitude. Details of Kalman filter theory applied to the acquired spectroscopic data are discussed. The effectiveness of this technique is evaluated by performing NH3 and CO2 concentration measurements and utilizing it to monitor varying ammonia and carbon dioxide levels in a bioreactor for water reprocessing, located at the NASA-Johnson Space Center. Results indicate a sensitivity enhancement of six times, in terms of improved minimum detectable absorption by the gas sensor.
Applications of Kalman filtering to real-time trace gas concentration measurements
NASA Technical Reports Server (NTRS)
Leleux, D. P.; Claps, R.; Chen, W.; Tittel, F. K.; Harman, T. L.
2002-01-01
A Kalman filtering technique is applied to the simultaneous detection of NH3 and CO2 with a diode-laser-based sensor operating at 1.53 micrometers. This technique is developed for improving the sensitivity and precision of trace gas concentration levels based on direct overtone laser absorption spectroscopy in the presence of various sensor noise sources. Filter performance is demonstrated to be adaptive to real-time noise and data statistics. Additionally, filter operation is successfully performed with dynamic ranges differing by three orders of magnitude. Details of Kalman filter theory applied to the acquired spectroscopic data are discussed. The effectiveness of this technique is evaluated by performing NH3 and CO2 concentration measurements and utilizing it to monitor varying ammonia and carbon dioxide levels in a bioreactor for water reprocessing, located at the NASA-Johnson Space Center. Results indicate a sensitivity enhancement of six times, in terms of improved minimum detectable absorption by the gas sensor.
In-situ estimation of MOCVD growth rate via a modified Kalman filter
Woo, W.W.; Svoronos, S.A.; Sankur, H.O.; Bajaj, J.; Irvine, S.J.C.
1996-05-01
In-situ laser reflectance monitoring of metal-organic chemical vapor deposition (MOCVD) is an effective way to monitor growth rate and epitaxial layer thickness of a variety of III-V and II-VI semiconductors. Materials with low optical extinction coefficients, such as ZnTe/GaAs and AlAs/GaAs for a 6,328 {angstrom} HeNe laser, are ideal for such an application. An extended Kalman filter modified to include a variable forgetting factor was applied to the MOCVD systems. The filter was able to accurately estimate thickness and growth rate while filtering out process noise and cope with sudden changes in growth rate, reflectance drift, and bias. Due to the forgetting factor, the Kalman filter was successful, even when based on very simple process models.
NASA Astrophysics Data System (ADS)
Fan, Y. R.; Huang, G. H.; Baetz, B. W.; Li, Y. P.; Huang, K.; Chen, X.; Gao, M.
2017-07-01
This study improved hydrologic data assimilation through integrating the capabilities of particle filter (PF) and ensemble Kalman filter (EnKF) methods, leading to two integrated data assimilation schemes: the coupled EnKF and PF (CEnPF) and parallelized EnKF and PF (PEnPF) approaches. The applicability and usefulness of CEnPF and PEnPF were demonstrated using a conceptual rainfall-runoff model. The performance of two new developed data assimilation methods and traditional EnKF and PF approaches was tested through a synthetic experiment and two real-world cases with one located in the Jing River basin and one located in the Yangtze River basin. The results show that both PEnPF and CEnPF approaches have more opportunities to provide better results for both deterministic and probabilistic predictions than traditional EnKF and PF approaches. Moreover, the computational time of the two integrated methods is manageable. But the proposed PEnPF may need much more time for some large-scale or time-consuming hydrologic models since it generally needs three times of model runs used by EnKF, PF and CEnPF.
Sabatini, Angelo Maria
2011-01-01
In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical. PMID:22163689
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 local ensemble transform Kalman filter data assimilation system for the NCEP global model
NASA Astrophysics Data System (ADS)
Szunyogh, Istvan; Kostelich, Eric J.; Gyarmati, Gyorgyi; Kalnay, Eugenia; Hunt, Brian R.; Ott, Edward; Satterfield, Elizabeth; Yorke, James A.
2008-01-01
The accuracy and computational efficiency of a parallel computer implementation of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme on the model component of the 2004 version of the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) is investigated. Numerical experiments are carried out at model resolution T62L28. All atmospheric observations that were operationally assimilated by NCEP in 2004, except for satellite radiances, are assimilated with the LETKF. The accuracy of the LETKF analyses is evaluated by comparing it to that of the Spectral Statistical Interpolation (SSI), which was the operational global data assimilation scheme of NCEP in 2004. For the selected set of observations, the LETKF analyses are more accurate than the SSI analyses in the Southern Hemisphere extratropics and are comparably accurate in the Northern Hemisphere extratropics and in the Tropics. The computational wall-clock times achieved on a Beowulf cluster of 3.6 GHz Xeon processors make our implementation of the LETKF on the NCEP GFS a widely applicable analysis-forecast system, especially for research purposes. For instance, the generation of four daily analyses at the resolution of the NCAR-NCEP reanalysis (T62L28) for a full season (90 d), using 40 processors, takes less than 4 d of wall-clock time.
An Extension to the Kalman Filter for an Improved Detection of Unknown Behavior
NASA Technical Reports Server (NTRS)
Benazera, Emmanuel; Narasimhan, Sriram
2005-01-01
The use of Kalman filter (KF) interferes with fault detection algorithms based on the residual between estimated and measured variables, since the measured values are used to update the estimates. This feedback results in the estimates being pulled closer to the measured values, influencing the residuals in the process. Here we present a fault detection scheme for systems that are being tracked by a KF. Our approach combines an open-loop prediction over an adaptive window and an information-based measure of the deviation of the Kalman estimate from the prediction to improve fault detection.
Real-Time Diagnosis of Faults Using a Bank of Kalman Filters
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
A new robust method of automated real-time diagnosis of faults in an aircraft engine or a similar complex system involves the use of a bank of Kalman filters. In order to be highly reliable, a diagnostic system must be designed to account for the numerous failure conditions that an aircraft engine may encounter in operation. The method achieves this objective though the utilization of multiple Kalman filters, each of which is uniquely designed based on a specific failure hypothesis. A fault-detection-and-isolation (FDI) system, developed based on this method, is able to isolate faults in sensors and actuators while detecting component faults (abrupt degradation in engine component performance). By affording a capability for real-time identification of minor faults before they grow into major ones, the method promises to enhance safety and reduce operating costs. The robustness of this method is further enhanced by incorporating information regarding the aging condition of an engine. In general, real-time fault diagnostic methods use the nominal performance of a "healthy" new engine as a reference condition in the diagnostic process. Such an approach does not account for gradual changes in performance associated with aging of an otherwise healthy engine. By incorporating information on gradual, aging-related changes, the new method makes it possible to retain at least some of the sensitivity and accuracy needed to detect incipient faults while preventing false alarms that could result from erroneous interpretation of symptoms of aging as symptoms of failures. The figure schematically depicts an FDI system according to the new method. The FDI system is integrated with an engine, from which it accepts two sets of input signals: sensor readings and actuator commands. Two main parts of the FDI system are a bank of Kalman filters and a subsystem that implements FDI decision rules. Each Kalman filter is designed to detect a specific sensor or actuator fault. When a sensor
Optical flow based Kalman filter for body joint prediction and tracking using HOG-LBP matching
NASA Astrophysics Data System (ADS)
Nair, Binu M.; Kendricks, Kimberley D.; Asari, Vijayan K.; Tuttle, Ronald F.
2014-03-01
We propose a real-time novel framework for tracking specific joints in the human body on low resolution imagery using optical flow based Kalman tracker without the need of a depth sensor. Body joint tracking is necessary for a variety of surveillance based applications such as recognizing gait signatures of individuals, identifying the motion patterns associated with a particular action and the corresponding interactions with objects in the scene to classify a certain activity. The proposed framework consists of two stages; the initialization stage and the tracking stage. In the initialization stage, the joints to be tracked are either manually marked or automatically obtained from other joint detection algorithms in the first few frames within a window of interest and appropriate image descriptions of each joint are computed. We employ the use of a well-known image coding scheme known as the Local Binary Patterns (LBP) to represent the joint local region where this image coding removes the variance to non-uniform lighting conditions as well as enhances the underlying edges and corner. The image descriptions of the joint region would then include a histogram computed from the LBP-coded ROI and a HOG (Histogram of Oriented Gradients) descriptor to represent the edge information. Next the tracking stage can be divided into two phases: Optical flow based detection of joints in corresponding frames of the sequence and prediction /correction phases of Kalman tracker with respect to the joint coordinates. Lucas Kanade optical flow is used to locate the individual joints in consecutive frames of the video based on their location in the previous frame. But more often, mismatches can occur due to the rotation of the joint region and the rotation variance of the optical flow matching technique. The mismatch is then determined by comparing the joint region descriptors using Chi-squared metric between a pair of frames and depending on this statistic, either the prediction
Menegaldo, Luciano L
2017-08-01
State-space control of myoelectric devices and real-time visualization of muscle forces in virtual rehabilitation require measuring or estimating muscle dynamic states: neuromuscular activation, tendon force and muscle length. This paper investigates whether regular (KF) and extended Kalman filters (eKF), derived directly from Hill-type muscle mechanics equations, can be used as real-time muscle state estimators for isometric contractions using raw electromyography signals (EMG) as the only available measurement. The estimators' amplitude error, computational cost, filtering lags and smoothness are compared with usual EMG-driven analysis, performed offline, by integrating the nonlinear Hill-type muscle model differential equations (offline simulations-OS). EMG activity of the three triceps surae components (soleus, gastrocnemius medialis and gastrocnemius lateralis), in three torque levels, was collected for ten subjects. The actualization interval (AI) between two updates of the KF and eKF was also varied. The results show that computational costs are significantly reduced (70x for KF and 17[Formula: see text] for eKF). The filtering lags presented sharp linear relationships with the AI (0-300 ms), depending on the state and activation level. Under maximum excitation, amplitude errors varied in the range 10-24% for activation, 5-8% for tendon force and 1.4-1.8% for muscle length, reducing linearly with the excitation level. Smoothness, measured by the ratio between the average standard variations of KF/eKF and OS estimations, was greatly reduced for activation but converged exponentially to 1 for the other states by increasing AI. Compared to regular KF, extended KF does not seem to improve estimation accuracy significantly. Depending on the particular application requirements, the most appropriate KF actualization interval can be selected.
Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang
2016-07-21
The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.
Li, Zenghui; Xu, Bin; Yang, Jian; Song, Jianshe
2015-01-01
This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy. PMID:25609038
Li, Zenghui; Xu, Bin; Yang, Jian; Song, Jianshe
2014-12-24
This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy.
Robust double gain unscented Kalman filter for small satellite attitude estimation
NASA Astrophysics Data System (ADS)
Cao, Lu; Yang, Weiwei; Li, Hengnian; Zhang, Zhidong; Shi, Jianjun
2017-08-01
Limited by the low precision of small satellite sensors, the estimation theories with high performance remains the most popular research topic for the attitude estimation. The Kalman filter (KF) and its extensions have been widely applied in the satellite attitude estimation and achieved plenty of achievements. However, most of the existing methods just take use of the current time-step's priori measurement residuals to complete the measurement update and state estimation, which always ignores the extraction and utilization of the previous time-step's posteriori measurement residuals. In addition, the uncertainty model errors always exist in the attitude dynamic system, which also put forward the higher performance requirements for the classical KF in attitude estimation problem. Therefore, the novel robust double gain unscented Kalman filter (RDG-UKF) is presented in this paper to satisfy the above requirements for the small satellite attitude estimation with the low precision sensors. It is assumed that the system state estimation errors can be exhibited in the measurement residual; therefore, the new method is to derive the second Kalman gain Kk2 for making full use of the previous time-step's measurement residual to improve the utilization efficiency of the measurement data. Moreover, the sequence orthogonal principle and unscented transform (UT) strategy are introduced to robust and enhance the performance of the novel Kalman Filter in order to reduce the influence of existing uncertainty model errors. Numerical simulations show that the proposed RDG-UKF is more effective and robustness in dealing with the model errors and low precision sensors for the attitude estimation of small satellite by comparing with the classical unscented Kalman Filter (UKF).
NASA Astrophysics Data System (ADS)
Hooshyar, M.; Hagen, S. C.; Wang, D.
2014-12-01
Hydrodynamic models are widely applied to coastal areas in order to predict water levels and flood inundation and typically involve solving a form of the Shallow Water Equations (SWE). The SWE are routinely discretized by applying numerical methods, such as the finite element method. Like other numerical models, hydrodynamic models include uncertainty. Uncertainties are generated due to errors in the discrete approximation of coastal geometry, bathymetry, bottom friction and forcing functions such as tides and wind fields. Methods to counteract these uncertainties should always begin with improvements to physical characterization of: the geometric description through increased resolution, parameters that describe land cover variations in the natural and urban environment, parameters that enhance transfer of surface forcings to the water surface, open boundary forcings, and the wetting/drying brought upon by flood and ebb cycles. When the best possible physical representation is achieved, we are left with calibration and data assimilation to reduce model uncertainty. Data assimilation has been applied to coastal hydrodynamic models to better estimate system states and/or system parameters by incorporating observed data into the model. Kalman Filter is one of the most studied data assimilation methods that minimizes the mean square errors between model state estimations and the observed data in linear systems (Kalman , 1960). For nonlinear systems, as with hydrodynamic models, a variation of Kalman filter called Ensemble Kalman Filter (EnKF), is applied to update the system state according to error statistics in the context of Monte Carlo simulations (Evensen , 2003) & (Hitoshi et. al, 2014). In this research, Kalman Filter is incorporated to simultaneously estimate an influential parameter used in the shallow water equations, bottom roughness, and to adjust the physical feature of bathymetry. Starting from an initial estimate of bottom roughness and bathymetry, and
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.
Application of a Bank of Kalman Filters for Aircraft Engine Fault Diagnostics
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2003-01-01
In this paper, a bank of Kalman filters is applied to aircraft gas turbine engine sensor and actuator fault detection and isolation (FDI) in conjunction with the detection of component faults. This approach uses multiple Kalman filters, each of which is designed for detecting a specific sensor or actuator fault. In the event that a fault does occur, all filters except the one using the correct hypothesis will produce large estimation errors, thereby isolating the specific fault. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The proposed FDI approach is applied to a nonlinear engine simulation at nominal and aged conditions, and the evaluation results for various engine faults at cruise operating conditions are given. The ability of the proposed approach to reliably detect and isolate sensor and actuator faults is demonstrated.
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Siano, Pierluigi
2013-10-01
Using differential flatness theory it is shown that the model of a quadropter can be transformed to linear canonical form. For the linearized equivalent of the quadropter it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system can not be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is is shown that one can estimate simultaneously external disturbances terms that affect the quadropter or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed control scheme is checked through simulation experiments.
Bds/gps Integrated Positioning Method Research Based on Nonlinear Kalman Filtering
NASA Astrophysics Data System (ADS)
Ma, Y.; Yuan, W.; Sun, H.
2017-09-01
In order to realize fast and accurate BDS/GPS integrated positioning, it is necessary to overcome the adverse effects of signal attenuation, multipath effect and echo interference to ensure the result of continuous and accurate navigation and positioning. In this paper, pseudo-range positioning is used as the mathematical model. In the stage of data preprocessing, using precise and smooth carrier phase measurement value to promote the rough pseudo-range measurement value without ambiguity. At last, the Extended Kalman Filter(EKF), the Unscented Kalman Filter(UKF) and the Particle Filter(PF) algorithm are applied in the integrated positioning method for higher positioning accuracy. The experimental results show that the positioning accuracy of PF is the highest, and UKF is better than EKF.
NASA Astrophysics Data System (ADS)
Rahimi, Afshin; Kumar, Krishna Dev; Alighanbari, Hekmat
2017-05-01
Reaction wheels, as one of the most commonly used actuators in satellite attitude control systems, are prone to malfunction which could lead to catastrophic failures. Such malfunctions can be detected and addressed in time if proper analytical redundancy algorithms such as parameter estimation and control reconfiguration are employed. Major challenges in parameter estimation include speed and accuracy of the employed algorithm. This paper presents a new approach for improving parameter estimation with adaptive unscented Kalman filter. The enhancement in tracking speed of unscented Kalman filter is achieved by systematically adapting the covariance matrix to the faulty estimates using innovation and residual sequences combined with an adaptive fault annunciation scheme. The proposed approach provides the filter with the advantage of tracking sudden changes in the system non-measurable parameters accurately. Results showed successful detection of reaction wheel malfunctions without requiring a priori knowledge about system performance in the presence of abrupt, transient, intermittent, and incipient faults. Furthermore, the proposed approach resulted in superior filter performance with less mean squared errors for residuals compared to generic and adaptive unscented Kalman filters, and thus, it can be a promising method for the development of fail-safe satellites.
A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan
2014-10-01
The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.
Adaptive Kalman filtering methods for tracking GPS signals in high noise/high dynamic environments
NASA Astrophysics Data System (ADS)
Zuo, Qiyao; Yuan, Hong; Lin, Baojun
2007-11-01
GPS C/A signal tracking algorithms have been developed based on adaptive Kalman filtering theory. In the research, an adaptive Kalman filter is used to substitute for standard tracking loop filters. The goal is to improve estimation accuracy and tracking stabilization in high noise and high dynamic environments. The linear dynamics model and the measurements model are designed to estimate code phase, carrier phase, Doppler shift, and rate of change of Doppler shift. Two adaptive algorithms are applied to improve robustness and adaptive faculty of the tracking, one is Sage adaptive filtering approach and the other is strong tracking method. Both the new algorithms and the conventional tracking loop have been tested by using simulation data. In the simulation experiment, the highest jerk of the receiver is set to 10G m/s 3 with the lowest C/No 30dBHz. The results indicate that the Kalman filtering algorithms are more robust than the standard tracking loop, and performance of tracking loop using the algorithms is satisfactory in such extremely adverse circumstances.
2004-08-01
fault detection and isolation (FDI) of aircraft engine sensors based on a bank of Kalman filters is developed. This approach utilizes multiple Kalman filters, each of which is designed based on a specific fault hypothesis. When the propulsion system experiences a fault, only one Kalman filter with the correct hypothesis is able to maintain the nominal estimation performance. Based on this knowledge, the isolation of faults is achieved. Since the propulsion system may experience component and actuator faults as well, a sensor FDI system must be robust
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
NASA Technical Reports Server (NTRS)
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2013-01-01
Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.
Dual Extended Kalman Filter for the Identification of Time-Varying Human Manual Control Behavior
NASA Technical Reports Server (NTRS)
Popovici, Alexandru; Zaal, Peter M. T.; Pool, Daan M.
2017-01-01
A Dual Extended Kalman Filter was implemented for the identification of time-varying human manual control behavior. Two filters that run concurrently were used, a state filter that estimates the equalization dynamics, and a parameter filter that estimates the neuromuscular parameters and time delay. Time-varying parameters were modeled as a random walk. The filter successfully estimated time-varying human control behavior in both simulated and experimental data. Simple guidelines are proposed for the tuning of the process and measurement covariance matrices and the initial parameter estimates. The tuning was performed on simulation data, and when applied on experimental data, only an increase in measurement process noise power was required in order for the filter to converge and estimate all parameters. A sensitivity analysis to initial parameter estimates showed that the filter is more sensitive to poor initial choices of neuromuscular parameters than equalization parameters, and bad choices for initial parameters can result in divergence, slow convergence, or parameter estimates that do not have a real physical interpretation. The promising results when applied to experimental data, together with its simple tuning and low dimension of the state-space, make the use of the Dual Extended Kalman Filter a viable option for identifying time-varying human control parameters in manual tracking tasks, which could be used in real-time human state monitoring and adaptive human-vehicle haptic interfaces.
Using a LRF sensor in the Kalman-filtering-based localization of a mobile robot.
Teslić, Luka; Skrjanc, Igor; Klancar, Gregor
2010-01-01
This paper deals with the problem of estimating the output-noise covariance matrix that is involved in the localization of a mobile robot. The extended Kalman filter (EKF) is used to localize the mobile robot with a laser range finder (LRF) sensor in an environment described with line segments. The covariances of the observed environment lines, which compose the output-noise covariance matrix in the correction step of the EKF, are the result of the noise arising from a range-sensor's (e.g., a LRF) distance and angle measurements. A method for estimating the covariances of the line parameters based on classic least squares (LSQ) is proposed. This method is compared with the method resulting from the orthogonal LSQ in terms of computational complexity. The results of a comparison show that the use of classic LSQ instead of orthogonal LSQ reduce the number of computations in a localization algorithm which is a part of a SLAM (simultaneous localization and mapping) algorithm. Statistical accuracy of both methods is also compared by simulating the LRF's measurements and the comparison proves the efficiency of the proposed approach.
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Auger, Ludovic
2003-01-01
A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.
NASA Astrophysics Data System (ADS)
Pan, M.-Ch.; Chu, W.-Ch.; Le, Duc-Do
2016-12-01
The paper presents an alternative Vold-Kalman filter order tracking (VKF_OT) method, i.e. adaptive angular-velocity VKF_OT technique, to extract and characterize order components in an adaptive manner for the condition monitoring and fault diagnosis of rotary machinery. The order/spectral waveforms to be tracked can be recursively solved by using Kalman filter based on the one-step state prediction. The paper comprises theoretical derivation of computation scheme, numerical implementation, and parameter investigation. Comparisons of the adaptive VKF_OT scheme with two other ones are performed through processing synthetic signals of designated order components. Processing parameters such as the weighting factor and the correlation matrix of process noise, and data conditions like the sampling frequency, which influence tracking behavior, are explored. The merits such as adaptive processing nature and computation efficiency brought by the proposed scheme are addressed although the computation was performed in off-line conditions. The proposed scheme can simultaneously extract multiple spectral components, and effectively decouple close and crossing orders associated with multi-axial reference rotating speeds.
Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications
2013-01-01
Background Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. Methods To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. Results The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Conclusions Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement. PMID:24274109
Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications.
Wang, Yubo; Veluvolu, Kalyana C; Lee, Minho
2013-11-25
Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement.
NASA Astrophysics Data System (ADS)
Chirico, G. B.; Medina, H.; Romano, N.
2014-07-01
This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.
A Novel Kalman Filter for Human Motion Tracking With an Inertial-Based Dynamic Inclinometer.
Ligorio, Gabriele; Sabatini, Angelo M
2015-08-01
Design and development of a linear Kalman filter to create an inertial-based inclinometer targeted to dynamic conditions of motion. The estimation of the body attitude (i.e., the inclination with respect to the vertical) was treated as a source separation problem to discriminate the gravity and the body acceleration from the specific force measured by a triaxial accelerometer. The sensor fusion between triaxial gyroscope and triaxial accelerometer data was performed using a linear Kalman filter. Wrist-worn inertial measurement unit data from ten participants were acquired while performing two dynamic tasks: 60-s sequence of seven manual activities and 90 s of walking at natural speed. Stereophotogrammetric data were used as a reference. A statistical analysis was performed to assess the significance of the accuracy improvement over state-of-the-art approaches. The proposed method achieved, on an average, a root mean square attitude error of 3.6° and 1.8° in manual activities and locomotion tasks (respectively). The statistical analysis showed that, when compared to few competing methods, the proposed method improved the attitude estimation accuracy. A novel Kalman filter for inertial-based attitude estimation was presented in this study. A significant accuracy improvement was achieved over state-of-the-art approaches, due to a filter design that better matched the basic optimality assumptions of Kalman filtering. Human motion tracking is the main application field of the proposed method. Accurately discriminating the two components present in the triaxial accelerometer signal is well suited for studying both the rotational and the linear body kinematics.
NASA Astrophysics Data System (ADS)
SchöNiger, A.; Nowak, W.; Hendricks Franssen, H.-J.
2012-04-01
Ensemble Kalman filters (EnKFs) are a successful tool for estimating state variables in atmospheric and oceanic sciences. Recent research has prepared the EnKF for parameter estimation in groundwater applications. EnKFs are optimal in the sense of Bayesian updating only if all involved variables are multivariate Gaussian. Subsurface flow and transport state variables, however, generally do not show Gaussian dependence on hydraulic log conductivity and among each other, even if log conductivity is multi-Gaussian. To improve EnKFs in this context, we apply nonlinear, monotonic transformations to the observed states, rendering them Gaussian (Gaussian anamorphosis, GA). Similar ideas have recently been presented by Béal et al. (2010) in the context of state estimation. Our work transfers and adapts this methodology to parameter estimation. Additionally, we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of GA beforehand. For illustration, we present a first-time application of an EnKF to parameter estimation from 3-D hydraulic tomography in multi-Gaussian log conductivity fields. Results show that (1) GA achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and (2) this makes both parameter identification and prediction of flow and transport more accurate. Combining EnKFs with GA yields a computationally efficient tool for nonlinear inversion of data with improved accuracy. This is an attractive benefit, given that linearization-free methods such as particle filters are computationally extremely demanding.
NASA Technical Reports Server (NTRS)
Herring, Thomas A.; Davis, James L.; Shapiro, Irwin I.
1990-01-01
The application of Kalman filtering techniques to the analysis of VLBI data is discussed. The VLBI observables are geometrically related to the geodetic and astrometric parameters which can be determined from them. However, contributions to the observables from the clocks at, and the atmospheres above, the VLBI sites must be accounted for if reliable estimates of geodetic and astrometric parameters are to be obtained. Here, an implementation of a Kalman filter to account for stochastic behavior on those parameters which vary during the course of a VLBI experiment is discussed. Both the nature of the stochastic processes which should be used in the model for the VLBI data and the implementation of the Kalman filter estimator are considered. It is concluded that the Kalman filter is appropriate for analyzing VLBI data.
Veen, E.H. van; de Loos-Vollebregt, T.C. de; Wassink, A.P.; Kalter, H.
1992-08-01
Trace impurities in uranium hexafluoride were analyzed by ICP-AES. The data were reduced using a Kalman filtering technique. Normally, multiple extraction steps are required for this analysis using conventional ICP-AES.
Deriche, Rachid; Calder, Jeff; Descoteaux, Maxime
2009-08-01
Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation. Since its inception, Diffusion MRI has expanded considerably to include a number of variations such as diffusion tensor imaging (DTI), diffusion spectrum imaging (DSI) and Q-ball imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real-time during the repetition time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard offline processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. This work enables a clinician to start an acquisition with just the minimum number of gradient directions and an initial estimate of the orientation distribution functions (ODF) and then the next gradient directions and ODF estimates can be recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal ODF estimates. This opens new and interesting opportunities for
Analysis of ICESat Data Using Kalman Filter and Kriging to Study Height Changes in East Antarctica
NASA Technical Reports Server (NTRS)
Herring, Thomas A.
2005-01-01
We analyze ICESat derived heights collected between Feb. 03-Nov. 04 using a kriging/Kalman filtering approach to investigate height changes in East Antarctica. The model's parameters are height change to an a priori static digital height model, seasonal signal expressed as an amplitude Beta and phase Theta, and height-change rate dh/dt for each (100 km)(exp 2) block. From the Kalman filter results, dh/dt has a mean of -0.06 m/yr in the flat interior of East Antarctica. Spatially correlated pointing errors in the current data releases give uncertainties in the range 0.06 m/yr, making height change detection unreliable at this time. Our test shows that when using all available data with pointing knowledge equivalent to that of Laser 2a, height change detection with an accuracy level 0.02 m/yr can be achieved over flat terrains in East Antarctica.
Analysis of ICESat Data Using Kalman Filter and Kriging to Study Height Changes in East Antarctica
NASA Technical Reports Server (NTRS)
Herring, Thomas A.
2005-01-01
We analyze ICESat derived heights collected between Feb. 03-Nov. 04 using a kriging/Kalman filtering approach to investigate height changes in East Antarctica. The model's parameters are height change to an a priori static digital height model, seasonal signal expressed as an amplitude Beta and phase Theta, and height-change rate dh/dt for each (100 km)(exp 2) block. From the Kalman filter results, dh/dt has a mean of -0.06 m/yr in the flat interior of East Antarctica. Spatially correlated pointing errors in the current data releases give uncertainties in the range 0.06 m/yr, making height change detection unreliable at this time. Our test shows that when using all available data with pointing knowledge equivalent to that of Laser 2a, height change detection with an accuracy level 0.02 m/yr can be achieved over flat terrains in East Antarctica.
Sensor fault diagnosis for fast steering mirror system based on Kalman filter
NASA Astrophysics Data System (ADS)
Wang, Hongju; Bao, Qiliang; Yang, Haifeng; Tao, Sunjie
2015-10-01
In this paper, to improve the reliability of a two-axis fast steering mirror system with minimum hardware consumption, a fault diagnosis method based on Kalman filter was developed. The dynamics model of the two-axis FSM was established firstly, and then the state-space form of the FSM was adopted. A bank of Kalman filters for fault detection was designed based on the state-space form. The effects of the sensor faults on the innovation sequence were investigated, and a decision approach called weighted sum-squared residual (WSSR) was adopted to isolate the sensor faults. Sensor faults could be detected and isolated when the decision statistics changed. Experimental studies on a prototype system show that the faulty sensor can be isolated timely and accurately. Meanwhile, the mathematical model of FSM system was used to design fault diagnosis scheme in the proposed method, thus the consumption of the hardware and space is decreased.
Parameter estimation and control for a neural mass model based on the unscented Kalman filter
NASA Astrophysics Data System (ADS)
Liu, Xian; Gao, Qing
2013-10-01
Recent progress in Kalman filters to estimate states and parameters in nonlinear systems has provided the possibility of applying such approaches to neural systems. We here apply the nonlinear method of unscented Kalman filters (UKFs) to observe states and estimate parameters in a neural mass model that can simulate distinct rhythms in electroencephalography (EEG) including dynamical evolution during epilepsy seizures. We demonstrate the efficiency of the UKF in estimating states and parameters. We also develop an UKF-based control strategy to modulate the dynamics of the neural mass model. In this strategy the UKF plays the role of observing states, and the control law is constructed via the estimated states. We demonstrate the feasibility of using such a strategy to suppress epileptiform spikes in the neural mass model.
Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude
NASA Technical Reports Server (NTRS)
Sedlak, J.
1994-01-01
Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.
Real time prediction of marine vessel motions using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Triantafyllou, M. S.; Bodson, M.
1982-01-01
The present investigation is concerned with the prediction of the future behavior of a vessel within some confidence bounds at a specific instant of time, taking into account an interval of a few seconds. The ability to predict accurately the motions of a vessel can reduce significantly the probability of failure of operations in rough seas. The investigation was started as part of an effort to ensure safe landing of aircraft on relatively small vessels. However, the basic principles involved in the study are the same for any offshore operation, such as carbo transfer in the open sea, structure installation, and floating crane operation. The Kalman filter is a powerful tool for achieving the goals of the prediction procedure. Attention is given to a linear optimal predictor, the equations of motion of the vessel, the wave spectrum, rational approximation, the use of Kalman filter and predictor in an application for a ship, and the motions of a semisubmersible.
Noise adaptive fading Kalman filter for free-space laser communication beacon tracking.
Li, Lixing; Huang, Yongmei; Wang, Qiang; Yang, Fasheng
2016-10-20
We proposed a prediction algorithm for laser communication pointing, acquisition, and tracking (PAT) subsystems in order to further improve PAT accuracy and reduce the effect of processing delay. In terms of this prediction algorithm, a fading Kalman filter is employed, with the observation noise obtained by the gray value distribution of the laser images. Moreover, to better fit the dynamics of a laser target, the two-stage dynamic model has been chosen as the state transition model for Kalman filtering. In addition, the two-stage dynamic model has been modified by accommodating its form to a change of time lag, thereby compensating the effect of time delay. A series of horizontal path (17 km) experiments under different atmospheric conditions were conducted in the fields. According to the experimental results, the algorithm we proposed could effectively reduce the tracking error and improve pointing accuracy.
Li, Jing; Song, Ningfang; Yang, Gongliu; Jiang, Rui
2016-07-01
In the initial alignment process of strapdown inertial navigation system (SINS), large misalignment angles always bring nonlinear problem, which can usually be processed using the scaled unscented Kalman filter (SUKF). In this paper, the problem of large misalignment angles in SINS alignment is further investigated, and the strong tracking scaled unscented Kalman filter (STSUKF) is proposed with fixed parameters to improve convergence speed, while these parameters are artificially constructed and uncertain in real application. To further improve the alignment stability and reduce the parameters selection, this paper proposes a fuzzy adaptive strategy combined with STSUKF (FUZZY-STSUKF). As a result, initial alignment scheme of large misalignment angles based on FUZZY-STSUKF is designed and verified by simulations and turntable experiment. The results show that the scheme improves the accuracy and convergence speed of SINS initial alignment compared with those based on SUKF and STSUKF.
Rapid Transfer Alignment of MEMS SINS Based on Adaptive Incremental Kalman Filter.
Chu, Hairong; Sun, Tingting; Zhang, Baiqiang; Zhang, Hongwei; Chen, Yang
2017-01-14
In airborne MEMS SINS transfer alignment, the error of MEMS IMU is highly environment-dependent and the parameters of the system model are also uncertain, which may lead to large error and bad convergence of the Kalman filter. In order to solve this problem, an improved adaptive incremental Kalman filter (AIKF) algorithm is proposed. First, the model of SINS transfer alignment is defined based on the "Velocity and Attitude" matching method. Then the detailed algorithm progress of AIKF and its recurrence formulas are presented. The performance and calculation amount of AKF and AIKF are also compared. Finally, a simulation test is designed to verify the accuracy and the rapidity of the AIKF algorithm by comparing it with KF and AKF. The results show that the AIKF algorithm has better estimation accuracy and shorter convergence time, especially for the bias of the gyroscope and the accelerometer, which can meet the accuracy and rapidity requirement of transfer alignment.
Rapid Transfer Alignment of MEMS SINS Based on Adaptive Incremental Kalman Filter
Chu, Hairong; Sun, Tingting; Zhang, Baiqiang; Zhang, Hongwei; Chen, Yang
2017-01-01
In airborne MEMS SINS transfer alignment, the error of MEMS IMU is highly environment-dependent and the parameters of the system model are also uncertain, which may lead to large error and bad convergence of the Kalman filter. In order to solve this problem, an improved adaptive incremental Kalman filter (AIKF) algorithm is proposed. First, the model of SINS transfer alignment is defined based on the “Velocity and Attitude” matching method. Then the detailed algorithm progress of AIKF and its recurrence formulas are presented. The performance and calculation amount of AKF and AIKF are also compared. Finally, a simulation test is designed to verify the accuracy and the rapidity of the AIKF algorithm by comparing it with KF and AKF. The results show that the AIKF algorithm has better estimation accuracy and shorter convergence time, especially for the bias of the gyroscope and the accelerometer, which can meet the accuracy and rapidity requirement of transfer alignment. PMID:28098829
State of Charge estimation of lithium ion battery based on extended Kalman filtering algorithm
NASA Astrophysics Data System (ADS)
Yang, Fan; Feng, Yiming; Pan, Binbiao; Wan, Renzhuo; Wang, Jun
2017-08-01
Accurate estimation of state-of-charge (SOC) for lithium ion battery is crucial for real-time diagnosis and prognosis in green energy vehicles. In this paper, a state space model of the battery based on Thevenin model is adopted. The strategy of estimating state of charge (SOC) based on extended Kalman fil-ter is presented, as well as to combine with ampere-hour counting (AH) and open circuit voltage (OCV) methods. The comparison between simulation and experiments indicates that the model’s performance matches well with that of lithium ion battery. The algorithm of extended Kalman filter keeps a good accura-cy precision and less dependent on its initial value in full range of SOC, which is proved to be suitable for online SOC estimation.
Huang, Lei
2015-09-30
To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required.
Frequency-scanning interferometry for dynamic absolute distance measurement using Kalman filter.
Tao, Long; Liu, Zhigang; Zhang, Weibo; Zhou, Yangli
2014-12-15
We propose a frequency-scanning interferometry using the Kalman filtering technique for dynamic absolute distance measurement. Frequency-scanning interferometry only uses a single tunable laser driven by a triangle waveform signal for forward and backward optical frequency scanning. The absolute distance and moving speed of a target can be estimated by the present input measurement of frequency-scanning interferometry and the previously calculated state based on the Kalman filter algorithm. This method not only compensates for movement errors in conventional frequency-scanning interferometry, but also achieves high-precision and low-complexity dynamic measurements. Experimental results of dynamic measurements under static state, vibration and one-dimensional movement are presented.
Unscented Kalman Filter-Trained Neural Networks for Slip Model Prediction.
Li, Zhencai; Wang, Yang; Liu, Zhen
2016-01-01
The purpose of this work is to investigate the accurate trajectory tracking control of a wheeled mobile robot (WMR) based on the slip model prediction. Generally, a nonholonomic WMR may increase the slippage risk, when traveling on outdoor unstructured terrain (such as longitudinal and lateral slippage of wheels). In order to control a WMR stably and accurately under the effect of slippage, an unscented Kalman filter and neural networks (NNs) are applied to estimate the slip model in real time. This method exploits the model approximating capabilities of nonlinear state-space NN, and the unscented Kalman filter is used to train NN's weights online. The slip parameters can be estimated and used to predict the time series of deviation velocity, which can be used to compensate control inputs of a WMR. The results of numerical simulation show that the desired trajectory tracking control can be performed by predicting the nonlinear slip model.
Wang, Hongxia; Li, Junfeng; Chen, Zhengxia; Liu, Mingyang; Wang, Hongyan
2005-09-01
A fast and highly efficient Kalman Filter analysis-flow injection chemiluminescence (FI-CL) method was developed to simultaneously determine trace amounts of niobium and tantalum in geological samples. The method, without the boring process of separation and dear instruments, is suitable for field scene analysis. The mixed chemiluminescence kinetic curve was analyzed by a Kalman Filter (KF) in this method to realize the simultaneous determination of niobium and tantalum. Possible interference elements in the determination were investigated. Under the selected conditions, the detection limits (3sigma, n = 11) of niobium(V) and tantalum(V) were 2.1 x 10(-3) microg g(-1) and 4.0 x 10(-3) microg g(-1), respectively, and the relative standard deviations were 4.9% and 3.3% (n = 9). The method was applied to the determination of niobium and tantalum in geological samples with satisfactory results.
Unscented Kalman Filter-Trained Neural Networks for Slip Model Prediction
Li, Zhencai; Wang, Yang; Liu, Zhen
2016-01-01
The purpose of this work is to investigate the accurate trajectory tracking control of a wheeled mobile robot (WMR) based on the slip model prediction. Generally, a nonholonomic WMR may increase the slippage risk, when traveling on outdoor unstructured terrain (such as longitudinal and lateral slippage of wheels). In order to control a WMR stably and accurately under the effect of slippage, an unscented Kalman filter and neural networks (NNs) are applied to estimate the slip model in real time. This method exploits the model approximating capabilities of nonlinear state–space NN, and the unscented Kalman filter is used to train NN’s weights online. The slip parameters can be estimated and used to predict the time series of deviation velocity, which can be used to compensate control inputs of a WMR. The results of numerical simulation show that the desired trajectory tracking control can be performed by predicting the nonlinear slip model. PMID:27467703
A Kalman-Filter-Based Approach to Combining Independent Earth-Orientation Series
NASA Technical Reports Server (NTRS)
Gross, Richard S.; Eubanks, T. M.; Steppe, J. A.; Freedman, A. P.; Dickey, J. O.; Runge, T. F.
1998-01-01
An approach. based upon the use of a Kalman filter. that is currently employed at the Jet Propulsion Laboratory (JPL) for combining independent measurements of the Earth's orientation, is presented. Since changes in the Earth's orientation can be described is a randomly excited stochastic process, the uncertainty in our knowledge of the Earth's orientation grows rapidly in the absence of measurements. The Kalman-filter methodology allows for an objective accounting of this uncertainty growth, thereby facilitating the intercomparison of measurements taken at different epochs (not necessarily uniformly spaced in time) and with different precision. As an example of this approach to combining Earth-orientation series, a description is given of a combination, SPACE95, that has been generated recently at JPL.
Lepine, Nicholas N; Tajima, Takuro; Ogasawara, Takayuki; Kasahara, Ryoichi; Koizumi, Hiroshi; Lepine, Nicholas N; Tajima, Takuro; Ogasawara, Takayuki; Kasahara, Ryoichi; Koizumi, Hiroshi; Koizumi, Hiroshi; Ogasawara, Takayuki; Tajima, Takuro; Kasahara, Ryoichi; Lepine, Nicholas N
2016-08-01
An adaptive Kalman filter-based fusion algorithm capable of estimating respiration rate for unobtrusive respiratory monitoring is proposed. Using both signal characteristics and a priori information, the Kalman filter is adaptively optimized to improve accuracy. Furthermore, the system is able to combine the respiration-related signals extracted from a textile ECG sensor and an accelerometer to create a single robust measurement. We measured derived respiratory rates and, when compared to a reference, found root-mean-square error of 2.11 breaths-per-minute (BrPM) while lying down, 2.30 BrPM while sitting, 5.97 BrPM while walking, and 5.98 BrPM while running. These results demonstrate that the proposed system is applicable to unobtrusive monitoring for various applications.
Fusion techniques using distributed Kalman filtering for detecting changes in systems
NASA Technical Reports Server (NTRS)
Belcastro, Celeste M.; Fischl, Robert; Kam, Moshe
1991-01-01
A comparison is made of the performances of two detection strategies that are based on different data fusion techniques. The strategies detect changes in a linear system. One detection strategy involves combining the estimates and error covariance matrices of distributed Kalman filters, generating a residual from the used estimates, comparing this residual to a threshold, and making a decision. The other detection strategy involves a distributed decision process in which estimates from distributed Kalman filters are used to generate distributed residuals which are compared locally to a threshold. Local decisions are made and these decisions are then fused into a global decision. The performances of each of these detection schemes are compared, and it is concluded that better performance is achieved when local decisions are made and then fused into a global decision.
Analysis of high-impedance fault generated signals using a Kalman filtering approach
Girgis, A.A.; Chang, W.; Makram, E.B. . Dept. of Electrical and Computer Engineering)
1990-10-01
High-impedance faults are accompanied by variations in the 60-Hz and harmonic components. However, these variations are not stationary, but time-varying in nature due to the dynamics of the fault arc. Therefore, an approach that accounts for the time-varying nature of the fundamental and harmonic components is developed. This approach is based on Kalman filtering theory to obtain the best estimation of the time variations of the fundamental and harmonic components. Four actual recorded data sets for staged arcing fault on different types of soil are investigated by the proposed Kalman filtering technique. The time variations of fundamental and low-order harmonic components significantly contribute to high-impedance fault detection using the features presented in this paper.
NASA Astrophysics Data System (ADS)
Li, Jing; Song, Ningfang; Yang, Gongliu; Jiang, Rui
2016-07-01
In the initial alignment process of strapdown inertial navigation system (SINS), large misalignment angles always bring nonlinear problem, which can usually be processed using the scaled unscented Kalman filter (SUKF). In this paper, the problem of large misalignment angles in SINS alignment is further investigated, and the strong tracking scaled unscented Kalman filter (STSUKF) is proposed with fixed parameters to improve convergence speed, while these parameters are artificially constructed and uncertain in real application. To further improve the alignment stability and reduce the parameters selection, this paper proposes a fuzzy adaptive strategy combined with STSUKF (FUZZY-STSUKF). As a result, initial alignment scheme of large misalignment angles based on FUZZY-STSUKF is designed and verified by simulations and turntable experiment. The results show that the scheme improves the accuracy and convergence speed of SINS initial alignment compared with those based on SUKF and STSUKF.