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.
Two-Dimensional Systolic Array For Kalman-Filter Computing
NASA Technical Reports Server (NTRS)
Chang, Jaw John; Yeh, Hen-Geul
1988-01-01
Two-dimensional, systolic-array, parallel data processor performs Kalman filtering in real time. Algorithm rearranged to be Faddeev algorithm for generalized signal processing. Algorithm mapped onto very-large-scale integrated-circuit (VLSI) chip in two-dimensional, regular, simple, expandable array of concurrent processing cells. Processor does matrix/vector-based algebraic computations. Applications include adaptive control of robots, remote manipulators and flexible structures and processing radar signals to track targets.
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.
A cognition-based method to ease the computational load for an extended Kalman filter.
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-01-01
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. PMID:25479332
A Cognition-Based Method to Ease the Computational Load for an Extended Kalman Filter
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-01-01
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. PMID:25479332
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.
Application of computed order tracking, Vold-Kalman filtering and EMD in rotating machine vibration
NASA Astrophysics Data System (ADS)
Wang, K. S.; Heyns, P. S.
2011-01-01
This paper presents a study on rotating machine vibration signals by using computed order tracking, Vold-Kalman filtering and intrinsic mode functions from the empirical mode decomposition method. Through the sequential use of intrinsic mode function and order tracking methods, both speed synchronous and non-synchronous vibrations that modulate orders in rotating machine vibrations are distinguished, which is difficult when using each of the techniques in isolation alone. Simulation and experimental studies demonstrate the ability of extracting vibrations that modulate order signals through combining the techniques.
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.
NASA Astrophysics Data System (ADS)
Colburn, Christopher; Bewley, Thomas
2010-11-01
The Kalman Filter (KF) is celebrated as the optimal estimator for systems with linear dynamics and gaussian uncertainty. Although most systems of interest do not have linear dynamics and are not forced by gaussian noise, the KF is used ubiquitously within industry. Thus, we present a novel estimation algorithm, the Game-theoretic Kalman Filter (GKF), which intelligently hedges between competing sequential filters and does not require the assumption of gaussian statistics to provide a "best" estimate.
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.
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1977-01-01
Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.
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. PMID:24807449
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.
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.
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.
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.
Fast SIMDized Kalman filter based track fit
NASA Astrophysics Data System (ADS)
Gorbunov, S.; Kebschull, U.; Kisel, I.; Lindenstruth, V.; Müller, W. F. J.
2008-03-01
Modern high energy physics experiments have to process terabytes of input data produced in particle collisions. The core of many data reconstruction algorithms in high energy physics is the Kalman filter. Therefore, the speed of Kalman filter based algorithms is of crucial importance in on-line data processing. This is especially true for the combinatorial track finding stage where the Kalman filter based track fit is used very intensively. Therefore, developing fast reconstruction algorithms, which use maximum available power of processors, is important, in particular for the initial selection of events which carry signals of interesting physics. One of such powerful feature supported by almost all up-to-date PC processors is a SIMD instruction set, which allows packing several data items in one register and to operate on all of them, thus achieving more operations per clock cycle. The novel Cell processor extends the parallelization further by combining a general-purpose PowerPC processor core with eight streamlined coprocessing elements which greatly accelerate vector processing applications. In the investigation described here, after a significant memory optimization and a comprehensive numerical analysis, the Kalman filter based track fitting algorithm of the CBM experiment has been vectorized using inline operator overloading. Thus the algorithm continues to be flexible with respect to any CPU family used for data reconstruction. Because of all these changes the SIMDized Kalman filter based track fitting algorithm takes 1 μs per track that is 10000 times faster than the initial version. Porting the algorithm to a Cell Blade computer gives another factor of 10 of the speedup. Finally, we compare performance of the tracking algorithm running on three different CPU architectures: Intel Xeon, AMD Opteron and Cell Broadband Engine.
Identifying Optimal Measurement Subspace for the Ensemble Kalman Filter
Zhou, Ning; Huang, Zhenyu; Welch, Greg; Zhang, J.
2012-05-24
To reduce the computational load of the ensemble Kalman filter while maintaining its efficacy, an optimization algorithm based on the generalized eigenvalue decomposition method is proposed for identifying the most informative measurement subspace. When the number of measurements is large, the proposed algorithm can be used to make an effective tradeoff between computational complexity and estimation accuracy. This algorithm also can be extended to other Kalman filters for measurement subspace selection.
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
Mandel, Jan; Beezley, Jonathan D; Cobb, Loren; Krishnamurthy, Ashok
2010-05-01
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.
The History Of The Kalman Filter
NASA Technical Reports Server (NTRS)
Mcgee, Leonard A.; Schmidt, Stanley F.
1991-01-01
Paper presents historical view of adaptation of Kalman filtering techniques to aerospace applications and eventually to fields as diverse as exploration for oil and control of powerplants. Describes scientific breakthroughs and reformulations that transformed Kalman filtering techniques into fundamental tool for analyzing and solving broad class of estimation problems.
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.
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Trigo, F. C.; Martins, F. P. R.; Fleury, A. T.; Silva, H. C.
2014-02-01
Aiming at overcoming the difficulties derived from the traditional camera calibration methods to record the underwater environment of a towing tank where experiments of scaled-model risers are carried on, a computer vision method, combining traditional image processing algorithms and a self-calibration technique was implemented. This method was used to identify the coordinates of control-points viewed on a scaled-model riser submitted to a periodic force applied to its fairlead attachment point. To study the observed motion, the riser was represented as a pseudo-rigid body model (PRBM) and the hypotheses of compliant mechanisms theory were assumed in order to cope with its elastic behavior. The derived Lagrangian equations of motion were linearized and expressed as a state-space model in which the state variables include the generalized coordinates and the unknown generalized forces. The state-vector thus assembled is estimated through a Kalman Filter. The estimation procedure allows the determination of both the generalized forces and the tension along the cable, with statistically proven convergence.
Is the hippocampus a Kalman filter?
Bousquet, O; Balakrishnan, K; Honavar, V
1998-01-01
Based on a large body of neurophysiological, neuroanatomical, and behavioral data, it has been suggested that the hippocampal formation serves as a spatial learning and localization system. This spatial representation is metric in nature and arises as a result of associations between sensory inputs and dead-reckoning information generated by the animal. However, despite the fact that these two information streams provide uncertain information (e.g., recognition errors, dead-reckoning drifts, etc.), the hippocampal computational models suggested to date have not explicitly addressed information fusion from erroneous sources. In this paper we develop a computational model of hippocampal spatial learning and relate its functioning to a probabilistic tool used for uncertain sensory fusion in robots: the Kalman filter. This parallel allows us to derive statistically optimal update expressions for the localization performed by our computational model. PMID:9697220
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.
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. PMID:22481785
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.
Ensemble Kalman Filtering without a Model
NASA Astrophysics Data System (ADS)
Hamilton, Franz; Berry, Tyrus; Sauer, Timothy
2016-01-01
Methods of data assimilation are established in physical sciences and engineering for the merging of observed data with dynamical models. When the model is nonlinear, methods such as the ensemble Kalman filter have been developed for this purpose. At the other end of the spectrum, when a model is not known, the delay coordinate method introduced by Takens has been used to reconstruct nonlinear dynamics. In this article, we merge these two important lines of research. A model-free filter is introduced based on the filtering equations of Kalman and the data-driven modeling of Takens. This procedure replaces the model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to reconcile new observations. We find that this combination of approaches results in comparable efficiency to parametric methods in identifying underlying dynamics, and may actually be superior in cases of model error.
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.
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
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.
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.
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.
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 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.
Ijaz, Umer Zeeshan; Khambampati, Anil Kumar; Lee, Jeong Seong; Kim, Sin; Kim, Kyung Youn
2008-07-20
In this paper, an effective nonstationary phase boundary estimation scheme in electrical impedance tomography is presented based on the unscented Kalman filter. The inverse problem is treated as a stochastic nonlinear state estimation problem with the nonstationary phase boundary (state) being estimated online with the aid of unscented Kalman filter. This research targets the industrial applications, such as imaging of stirrer vessel for detection of air distribution or detecting large air bubbles in pipelines. Within the domains, there exist 'voids' having zero conductivity. The design variables for phase boundary estimation are truncated Fourier coefficients. Computer simulations and experimental results are provided to evaluate the performance of unscented Kalman filter in comparison with extended Kalman filter to show a better performance of the unscented Kalman filter approach.
A Reduced Dimension Static, Linearized Kalman Filter and Smoother
NASA Technical Reports Server (NTRS)
Fukumori, I.
1995-01-01
An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.
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.
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
Spectral abundance fraction estimation of materials using Kalman filters
NASA Astrophysics Data System (ADS)
Wang, Su; Chang, Chein; Jensen, Janet L.; Jensen, James O.
2004-12-01
Kalman filter has been widely used in statistical signal processing for parameter estimation. Although a Kalman filter approach has been recently developed for spectral unmixing, referred to as Kalman filter-based linear unmixing (KFLU), its applicability to spectral characterization within a single pixel vector has not been explored. This paper presents a new application of Kalman filtering in spectral estimation and quantification. It develops a Kalman filter-based spectral signature esimator (KFSSE) which is different from the KFLU in the sense that the former performs a Kalman filter wavelength by wavelength across a spectral signature as opposed to the latter which implements a Kalman filter pixel vector by pixel vector in an image cube. The idea of the KFSSE is to implement the state equation to characterize the true spectral signature, while the measurement equation is being used to describe the spectral signature to be processed. Additionally, since a Kalman filter can accurately estimate spectral abundance fraction of a signature, our proposed KFSSE can further used for spectral quantification for subpixel targets and mixed pixel vectors, called Kalman filter-based spectral quantifier (KFSQ). Such spectral quantification is particularly important for chemical/biological defense which requires quantification of detected agents for damage control assessment. Several different types of hyperspectral data are used for experiments to demonstrate the ability of the KFSSE in estimation of spectral signature and the utility of the KFSQ in spectral quantification.
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).
Streamflow Data Assimilation in SWAT Model Using Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Sun, L.; Nistor, I.; Seidou, O.
2014-12-01
Although Extended Kalman Filter (EKF) is regarded as the de facto method for the application of Kalman Filter in non-linear system, it's application to complex distributed hydrological models faces a lot of challenges. Ensemble Kalman Filter (EnKF) is often preferred because it avoids the calculation of the linearization Jacobian Matrix and the propagation of estimation error covariance. EnKF is however difficult to apply to large models because of the huge computation demand needed for parallel propagation of ensemble members. This paper deals with the application of EKF in stream flow prediction using the SWAT model in the watershed of Senegal River, West Africa. In the Jacobian Matrix calculation, SWAT is regarded as a black box model and the derivatives are calculated in the form of differential equations. The state vector is the combination of runoff, soil, shallow aquifer and deep aquifer water contents. As an initial attempt, only stream flow observations are assimilated. Despite the fact that EKF is a sub-optimal filter, the coupling of EKF significantly improves the estimation of daily streamflow. The results of SWAT+EKF are also compared to those of a simpler quasi linear streamflow prediction model where both state and parameters are updated with the EKF.
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.
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
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. PMID:24883349
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.
Misguided resistance using extended Kalman filter for imaging seeker
NASA Astrophysics Data System (ADS)
Li, Fugui; Bu, Kuichen; Zhao, Hong
2015-10-01
Fake targets had essential effect on target trace and guidance information extraction. Measures based on extended Kalman filter were recommended in this paper. The model of an imaging seeker was established firstly. Then the interfered model that the imaging seeker was misguided by the fake targets was introduced. The process how the fake targets misguided the imaging seeker was analyzed. An extended Kalman filter was established in the sphere coordinates, which could help to enhance the estimate level. The measurement of the seeker was transformed to the suitable information to spur the extended Kalman filter. The strategies were composed of four stages. Before the fake targets appeared, the extended Kalman filter estimated the motion information and the trend of the target quickly. When the fake targets appeared, the motion of the seeker will be controlled with the information predicted by the extended Kalman filter. The measured information of the seeker will not be used as stimulus to the extended Kalman filter until the true target was identified. After the true target was chosen, the seeker averted to the real target, and the angular information of line of sight measured by the seeker would be used to ensure the stability of the extended Kalman filter. When the transit time of the seeker from the previous direction to the target was finished, the rate of line of sight will be used to make the extended Kalman filter converged quickly. Theoretical analysis and simulation results show that the method is reasonable and efficient.
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.
Distributed Dynamic State Estimation with Extended Kalman Filter
Du, Pengwei; Huang, Zhenyu; Sun, Yannan; Diao, Ruisheng; Kalsi, Karanjit; Anderson, Kevin K.; Li, Yulan; Lee, Barry
2011-08-04
Increasing complexity associated with large-scale renewable resources and novel smart-grid technologies necessitates real-time monitoring and control. Our previous work applied the extended Kalman filter (EKF) with the use of phasor measurement data (PMU) for dynamic state estimation. However, high computation complexity creates significant challenges for real-time applications. In this paper, the problem of distributed dynamic state estimation is investigated. One domain decomposition method is proposed to utilize decentralized computing resources. The performance of distributed dynamic state estimation is tested on a 16-machine, 68-bus test system.
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.
Fast Kalman Filter for Random Walk Forecast model
NASA Astrophysics Data System (ADS)
Saibaba, A.; Kitanidis, P. K.
2013-12-01
Kalman filtering is a fundamental tool in statistical time series analysis to understand the dynamics of large systems for which limited, noisy observations are available. However, standard implementations of the Kalman filter are prohibitive because they require O(N^2) in memory and O(N^3) in computational cost, where N is the dimension of the state variable. In this work, we focus our attention on the Random walk forecast model which assumes the state transition matrix to be the identity matrix. This model is frequently adopted when the data is acquired at a timescale that is faster than the dynamics of the state variables and there is considerable uncertainty as to the physics governing the state evolution. We derive an efficient representation for the a priori and a posteriori estimate covariance matrices as a weighted sum of two contributions - the process noise covariance matrix and a low rank term which contains eigenvectors from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the above terms and the computation of eigenmodes of the generalized eigenvalue problem (GEP). The resulting algorithm for the Kalman filter with Random walk forecast model scales as O(N) or O(N log N), both in memory and computational cost. This opens up the possibility of real-time adaptive experimental design and optimal control in systems of much larger dimension than was previously feasible. For a small number of measurements (~ 300 - 400), this procedure can be made numerically exact. However, as the number of measurements increase, for several choices of measurement operators and noise covariance matrices, the spectrum of the (GEP) decays rapidly and we are justified in only retaining the dominant eigenmodes. We discuss tradeoffs between accuracy and computational cost. The resulting algorithms are applied to an example application from ray-based travel time
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.
2014-01-01
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
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
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…
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 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.
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).
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.
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.
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.
A Physics-Based Kalman Filter for the Ionosphere
NASA Astrophysics Data System (ADS)
Scherliess, L.; Schunk, R.; Sojka, J.; Thompson, D.
A physics-based data assimilation model of the ionosphere is under development as the central part of a DoD MURI funded program called GAIM (Global Assimilation of Ionospheric Measurements). With the significant increase in the number of ionospheric observations that will become available over the next decade, this model will provide a powerful tool towards an improved specification and forecasting of the global ionosphere, with an unprecedented accuracy and reliability. The goal of this effort will be the development of an operational ionospheric assimilation model that will provide specifications and forecasts on spatial grids that can be global, regional, or local (50 km x 50 km). The specification/forecast will be in the form of 3-dimensional electron density distributions from 90 km to geosynchronous altitudes (35,000 km). In this paper we report on the development of a Kalman filter for GAIM using a new physics-based ionosphere/plasmasphere model (IPM). The model solves the continuity and momentum equations for 5 ion species (O+ , N+ , NO+ , O+ , and H+ ) and 2 2 covers the low and mid latitudes from 90 km to about 30,000 km altitude. The Kalman filter used in GAIM is based on approximations of the state error covariance matrix, employing a reduction of the model dimension and a linearization of the physical model for the propagation of the error covariance matrix. These approximations lead to a dramatic reduction in the computational requirements. In this paper, we will give an update on the status of the Kalman filter development and present initial results from a global assimilation run.
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.
Subsurface characterization with localized ensemble Kalman filter employing adaptive thresholding
NASA Astrophysics Data System (ADS)
Delijani, Ebrahim Biniaz; Pishvaie, Mahmoud Reza; Boozarjomehry, Ramin Bozorgmehry
2014-07-01
Ensemble Kalman filter, EnKF, as a Monte Carlo sequential data assimilation method has emerged promisingly for subsurface media characterization during past decade. Due to high computational cost of large ensemble size, EnKF is limited to small ensemble set in practice. This results in appearance of spurious correlation in covariance structure leading to incorrect or probable divergence of updated realizations. In this paper, a universal/adaptive thresholding method is presented to remove and/or mitigate spurious correlation problem in the forecast covariance matrix. This method is, then, extended to regularize Kalman gain directly. Four different thresholding functions have been considered to threshold forecast covariance and gain matrices. These include hard, soft, lasso and Smoothly Clipped Absolute Deviation (SCAD) functions. Three benchmarks are used to evaluate the performances of these methods. These benchmarks include a small 1D linear model and two 2D water flooding (in petroleum reservoirs) cases whose levels of heterogeneity/nonlinearity are different. It should be noted that beside the adaptive thresholding, the standard distance dependant localization and bootstrap Kalman gain are also implemented for comparison purposes. We assessed each setup with different ensemble sets to investigate the sensitivity of each method on ensemble size. The results indicate that thresholding of forecast covariance yields more reliable performance than Kalman gain. Among thresholding function, SCAD is more robust for both covariance and gain estimation. Our analyses emphasize that not all assimilation cycles do require thresholding and it should be performed wisely during the early assimilation cycles. The proposed scheme of adaptive thresholding outperforms other methods for subsurface characterization of underlying benchmarks.
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).
Tractography from HARDI using an Intrinsic Unscented Kalman Filter
Cheng, Guang; Salehian, Hesamoddin; Forder, John R.; Vemuri, Baba C.
2014-01-01
A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor 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 multi-tensor 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 multi-tensors 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. PMID:25203986
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. PMID:25203986
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.
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.
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-01-01
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. PMID:27171081
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-01-01
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. PMID:27171081
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.
NASA Astrophysics Data System (ADS)
Culp, Robert D.; Mackison, Don; Fu, Ho-Ling
This paper deals with an advanced Kalman filter application to orbit determination from satellite tracking data. Modern control theory is used to set up an optimal Kalman gain for the estimation problem and to estimate its errors out of the system outputs. The classical orbit determination techniques have been used over the years for the evaluation of data analysis. A recent study was conducted to find the initial state values by modern orbit determination with Kalman gain. An original algorithm introduced by Born et al. (1986) has been applied to the spacecraft and earth satellite orbit determination for several years. The determination of the desired process and special Kalman gain for the best estimator include three kinds of computational algorithms: Batch, Sequential, and Extended Sequential processors. The model is based on a minimum variance using estimation and prediction techniques. Moreover, the estimation and computational algorithms have been modified in the UNIX system simulating to the TOPEX satellite orbit data process.
Deconvolution Kalman filtering for force measurements of revolving wings
NASA Astrophysics Data System (ADS)
Vester, R.; Percin, M.; van Oudheusden, B.
2016-09-01
The applicability of a deconvolution Kalman filtering approach is assessed for the force measurements on a flat plate undergoing a revolving motion, as an alternative procedure to correct for test setup vibrations. The system identification process required for the correct implementation of the deconvolution Kalman filter is explained in detail. It is found that in the presence of a relatively complex forcing history, the DK filter is better suited to filter out structural test rig vibrations than conventional filtering techniques that are based on, for example, low-pass or moving-average filtering. The improvement is especially found in the characterization of the generated force peaks. Consequently, more reliable force data is obtained, which is vital to validate semi-empirical estimation models, but is also relevant to correlate identified flow phenomena to the force production.
Kriged Kalman filtering for predicting the wildfire temperature evolution
NASA Astrophysics Data System (ADS)
Phan, Connie N. K. K.
Existing wildfire evolution models have been mostly developed in a deterministic modelling framework. As a complementary alternative, this thesis presents a stochastic framework based on the Kriged Kalman filter to obtain global temperature predictions given local temperature measurements. By solving the heat transfer partial differential equation driving the wildfire evolution, it is shown that the spatio-temporal mean temperature process associated with a wildfire evolving in a finite spatial domain under certain prescribed conditions can be approximated by a Fourier series. The potential of the proposed Kriged Kalman filtering framework in predicting the wildfire temperature evolution is demonstrated in simulations on temperature data generated by a simplified physical wildfire propagation model. The performance of the Kriged Kalman filter in predicting the wildfire temperature evolution is compared to that of standard Gaussian process regression.
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.
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. PMID:27557170
On the equivalence of Kalman filtering and least-squares estimation
NASA Astrophysics Data System (ADS)
Mysen, E.
2016-07-01
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.
Extended Kalman filter sensor failure detection method for pressurizer monitoring
Filho, E.O.A.; Nakata, H. )
1992-01-01
This work presents the development of the sensor failure detection and isolation system (FDIS) methodology, which is suitable for implementation in nuclear plant control systems. The methodology is based on the extended Kalman filter applied to a pressurized water reactor pressurizer. The utilization of the Kalman filter follows the standard procedure: First, an estimate of the state variables and the corresponding covariances are obtained; then, based on the state equations, the estimated state variables are propagated until the next measurements for the new estimate.
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.
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
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. PMID:27420508
Performance enhancement for GPS positioning using constrained Kalman filtering
NASA Astrophysics Data System (ADS)
Guo, Fei; Zhang, Xiaohong; Wang, Fuhong
2015-08-01
Over the past decades Kalman filtering (KF) algorithms have been extensively investigated and applied in the area of kinematic positioning. In the application of KF in kinematic precise point positioning (PPP), it is often the case where some known functional or theoretical relations exist among the unknown state parameters, which can be and should be made use of to enhance the performance of kinematic PPP, especially in an urban and forest environment. The central task of this paper is to effectively blend the commonly used GNSS data and internal/external additional constrained information to generate an optimal PPP solution. This paper first investigates the basic algorithm of constrained Kalman filtering. Then two types of PPP model with speed constraints and trajectory constraints, respectively, are proposed. Further validation tests based on a variety of situations show that the positioning performances (positioning accuracy, reliability and continuity) from the constrained Kalman filter are significantly superior to those from the conventional Kalman filter, particularly under extremely poor observation conditions.
Combining Earth Orientation Measurements Using a Kalman Filter
NASA Technical Reports Server (NTRS)
Gross, R.
2000-01-01
A Kalman filter has many properties that make it an attractive choice as a technique for combining Earth orientation measurements. It allows the full accuracy of the measurements to be used, whether the measurements are degenerate or are of full rank, are irregularly or regularly spaced in time, or are corrupted by systematic or other errors that can be described by stochastic models.
Application of Kalman filtering in VLBI data analysis
NASA Astrophysics Data System (ADS)
Nilsson, Tobias; Soja, Benedikt; Karbon, Maria; Heinkelmann, Robert; Schuh, Harald
2015-08-01
In this paper, we demonstrate the advantage of applying a Kalman filter for the parameter estimation in very-long-baseline interferometry (VLBI) data analysis. We present the implementation of a Kalman filter in the VLBI software VieVS@GFZ. The performance is then investigated by looking at the accuracy obtained for various parameters, like baseline lengths, Earth Orientation Parameters, radio source coordinates, and tropospheric delays. The results are compared to those obtained when the classical least squares method (LSM) is applied for the parameter estimation, where clocks and zenith wet delays are estimated with 30-min intervals and gradients with 120-min intervals. We show that the accuracy generally is better for the Kalman filter solution, for example, the baseline length repeatabilities are on average about 10 % better compared to the LSM solution. We also discuss the possibilities to use the Kalman filter to estimate sub-diurnal station position variations and show that the variations caused by solid Earth tides can be retrieved with an accuracy of about 2 cm.
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.
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. PMID:26831389
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.
Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation
NASA Technical Reports Server (NTRS)
Chang, Lang-Ping; Lyster, Peter M.; Menard, R.; Cohn, S. E.
1998-01-01
A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.
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. PMID:21509065
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.
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.
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.
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).
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.
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. PMID:23972569
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.
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.
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.
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.
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 comparison of EAKF and particle filter: towards a ensemble adjustment Kalman particle filter
NASA Astrophysics Data System (ADS)
Zhang, Xiangming; Shen, Zheqi; Tang, Youmin
2016-04-01
Bayesian estimation theory provides a general approach for the state estimate. In this study, we first explore two Bayesian-based methods: ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF can be regarded as a deterministic scheme of the ensemble Kalman filter (EnKF), which performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is very large that can avoid the filter degeneracy, and vice versa. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.
Traditional Tracking with Kalman Filter on Parallel Architectures
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Lantz, Steven; MacNeill, Ian; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-05-01
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 most common track finding techniques in use today are however those based on the Kalman Filter. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. We report the results of our investigations into the potential and limitations of these algorithms on the new parallel hardware.
An ensemble adjustment Kalman filter study for Argo data
NASA Astrophysics Data System (ADS)
Yin, Xunqiang; Qiao, Fangli; Yang, Yongzeng; Xia, Changshui
2010-05-01
An ensemble adjustment Kalman filter system is developed to assimilate Argo profiles into the Northwest Pacific MASNUM wave-circulation coupled model, which is based on the Princeton Ocean Model (POM). This model was recoded in FORTRAN-90 style, and some new data types were defined to improve the efficiency of system design and execution. This system is arranged for parallel computing by using UNIX shell scripts: it is easier with single models running separately with the required information exchanged through input/output files. Tests are carried out to check the performance of the system: one for checking the ensemble spread and another for the performance of assimilation of the Argo data in 2005. The first experiment shows that the assimilation system performs well. The comparison with the Satellite derived sea surface temperature (SST) shows that modeled SST errors are reduced after assimilation; at the same time, the spatial correlation between the simulated SST anomalies and the satellite data is improved because of Argo assimilation. Furthermore, the temporal evolution/trend of SST becomes much better than those results without data assimilation. The comparison against GTSPP profiles shows that the improvement is not only in the upper layers of ocean, but also in the deeper layers. All these results suggest that this system is potentially capable of reconstructing oceanic data sets that are of high quality and are temporally and spatially continuous.
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.
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.
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
Temperature profile retrievals with extended Kalman-Bucy filters
NASA Technical Reports Server (NTRS)
Ledsham, W. H.; Staelin, D. H.
1979-01-01
The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.
Multi-channel Kalman filters for active noise control.
van Ophem, S; Berkhoff, A P
2013-04-01
By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm. PMID:23556580
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.
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.
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
Probability fields revisited in the context of ensemble Kalman filtering
NASA Astrophysics Data System (ADS)
Xu, Teng; Gómez-Hernández, J. Jaime
2015-12-01
Hu et al. (2013) proposed an approach to update complex geological facies models generated by multiple-point geostatistical simulation while keeping geological and statistical consistency. Their approach is based on mapping the facies realization onto the spatially uncorrelated uniform random numbers used by the sequential multiple-point simulation to generate the facies realization itself. The ensemble Kalman filter was then used to update the uniform random number realizations, which were then used to generate a new facies realization by multiple-point simulation. This approach has not a good performance that we attribute to the fact that, being the probabilities random and spatially uncorrelated, their correlation with the state variable (piezometric heads) is very weak, and the Kalman gain is always small. The approach is reminiscent of the probability field simulation, which also maps the conductivity realizations onto a field of uniform random numbers; although the mapping now is done using the local conditional distribution functions built based on a prior statistical model and the conditioning data. Contrary to Hu et al. (2013) approach, this field of uniform random numbers, termed a probability field, displays spatial patterns related to the conductivity spatial patterns, and, therefore, the correlation between probabilities and state variable is as strong as the correlation between conductivities and state variable could be. Similarly to Hu et al. (2013), we propose to use the ensemble Kalman filter to update the probability fields, and show that the existence of this correlation between probability values and state variables provides better results.
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.
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.
NASA Astrophysics Data System (ADS)
Ghorbanidehno, H.; Kokkinaki, A.; Darve, E. F.; Kitanidis, P. K.
2014-12-01
The Kalman Filter has been widely used for dynamic monitoring in reservoir engineering, and has recently gained popularity in hydrogeologic applications. A common characteristic of such applications is that the physical processes of interest are greatly affected by preferential flow (e.g., contaminant spreading, CO2 leakage), which can only be delineated if the problem is finely discretized into a large number of unknowns. However, for problems with large numbers of unknowns (e.g., larger than 10,000), the Kalman Filter has prohibitively expensive computation and storage costs. The EnKF, which is typically used to reduce the cost of computing the covariance in such cases converges slowly to the best estimate, and for a reasonable number of realizations, the estimate may not be accurate, especially for strongly heterogeneous systems. We present the Spectral Kalman Filter, a new Kalman Filter implementation that has a dramatically reduced computational cost compared to the full Kalman Filter, with comparable or higher accuracy than the EnKF for the same computational cost. Our algorithm's computational efficiency is achieved by a recurrence that updates small cross-covariance matrices instead of large covariance matrices, in combination with a low-rank approximation of the noise covariance matrix. In addition, instead of computing the expensive Jacobian matrix, a matrix-free method is used to obtain sensitivities. Finally, the error of our method can be explicitly controlled by reducing the time between matrix updates. The frequency of these updates is controlled independently from the data assimilation steps. We demonstrate the performance of the Spectral Kalman Filter for the joint estimation of domain properties and state evolution by assimilation of quasi-continuous data during a hypothetical CO2 injection in a heterogeneous domain.
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.
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. PMID:26835722
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Li Jia; Xiu Dongbin
2009-08-20
As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter.
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.
Nonlinear Kalman filters for calibration in radio interferometry
NASA Astrophysics Data System (ADS)
Tasse, C.
2014-06-01
The data produced by the new generation of interferometers are affected by a wide variety of partially unknown complex effects such as pointing errors, phased array beams, ionosphere, troposphere, Faraday rotation, or clock drifts. Most algorithms addressing direction-dependent calibration solve for the effective Jones matrices, and cannot constrain the underlying physical quantities of the radio interferometry measurement equation (RIME). A related difficulty is that they lack robustness in the presence of low signal-to-noise ratios, and when solving for moderate to large numbers of parameters they can be subject to ill-conditioning. These effects can have dramatic consequences in the image plane such as source or even thermal noise suppression. The advantage of solvers directly estimating the physical terms appearing in the RIME is that they can potentially reduce the number of free parameters by orders of magnitudes while dramatically increasing the size of usable data, thereby improving conditioning. We present here a new calibration scheme based on a nonlinear version of the Kalman filter that aims at estimating the physical terms appearing in the RIME. We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. Using simulations we show that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly computationally cheap algorithm that we believe to be robust, especially in low signal-to-noise regimes. Potentially, the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that
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
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 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.
Robust Kalman filter design for active flutter suppression systems
NASA Technical Reports Server (NTRS)
Garrard, W. L.; Mahesh, J. K.; Stone, C. R.; Dunn, H. J.
1982-01-01
Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.
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.
Analysis of dynamic deformation processes with adaptive KALMAN-filtering
NASA Astrophysics Data System (ADS)
Eichhorn, Andreas
2007-05-01
In this paper the approach of a full system analysis is shown quantifying a dynamic structural ("white-box"-) model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivated from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simulation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests thermal load steps are applied to an aluminum column. Independent control measurements show that the identified model can be used to predict the columns bend with a mean deviation (
NASA Astrophysics Data System (ADS)
Wetterer, C.; Hunt, B.; Kervin, P.; Jah, M.
2014-09-01
Forward modeling will never be perfect. The shape model will never be able to account for every wrinkle in the MLI coating, and similarly, the surface model as represented by the bidirectional reflectance distribution function (BRDF) will never be identical to that found on actual space objects due to space weathering and inherent differences in the same material from lot to lot. The key to making estimation filters work is thus to continually improve the shape and surface models of the space object, and to intelligently and completely account for all remaining error sources in the models and how these manifest in the observations. This paper uses a multiple hypothesis filtering scheme to determine the attitude of a model geosynchronous satellite with possible surface modeling errors to compare the estimates made when each hypothesis is either propagated by an unscented Kalman filter (UKF) or an unscented Schmidt Kalman filter (USKF). It is shown that the USKF, which incorporates the influence of the known modeling errors in so-called consider terms, provides a better estimate and a more realistic uncertainty on the final attitude estimate.
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
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.
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.
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.
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. PMID:26168453
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.
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.
Several recursive techniques for observer/Kalman filter system identification from data
NASA Technical Reports Server (NTRS)
Chen, Chung-Wen; Lee, Gordon; Juang, Jer-Nan
1992-01-01
This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.
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
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.
Ensemble Kalman filter data assimilation for the MPAS system
NASA Astrophysics Data System (ADS)
Ha, Soyoung; Snyder, Chris
2015-04-01
The Model for Prediction Across Scales (MPAS; http://mpas-dev.github.io/) is a global non-hydrostatic numerical atmospheric model based on unstructured centroidal Voronoi meshes that allow both uniform and variable resolutions. The variable resolution allows locally high-resolution meshes that transition smoothly to coarser resolution over the rest of the globe, avoiding the need to drive a limited-area model with lateral boundary conditions from a separate global model. The nonhydrostatic MPAS solver (for both atmospheric and oceanic components) is now coupled to the Data Assimilation Research Testbed (DART; http://www.image.ucar.edu/ DAReS/DART) system with a full capability of ensemble Kalman filter data assimilation. The analysis/forecast cycling experiments using MPAS/DART is successfully tested with real observations for different retrospective cases. Assimilated observations are all conventional data as well as satellite winds and GPS radio occultation refractivity data. Testing on different grid mesh, we examine issues specific to the MPAS grid, such as smoothing in the interpolation and the update of horizontal wind fields, and show their impact on the Ensemble Kalman Filter (EnKF) analysis and the following short-range forecast. Up to 5-day forecasts for a month-long cycle period are verified against observations and compared to the NCEP GFS (Global Forecast System) forecasts.
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.
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)
Shen, Zheqi; Tang, Youmin
2016-04-01
The ensemble Kalman particle filter (EnKPF) is a combination of two Bayesian-based algorithms, namely, the ensemble Kalman filter (EnKF) and the sequential importance resampling particle filter(SIR-PF). It was recently introduced to address non-Gaussian features in data assimilation for highly nonlinear systems, by providing a continuous interpolation between the EnKF and SIR-PF analysis schemes. In this paper, we first extend the EnKPF algorithm by modifying the formula for the computation of the covariancematrix, making it suitable for nonlinear measurement functions (we will call this extended algorithm nEnKPF). Further, a general form of the Kalman gain is introduced to the EnKPF to improve the performance of the nEnKPF when the measurement function is highly nonlinear (this improved algorithm is called mEnKPF). The Lorenz '63 model and Lorenz '96 model are used to test the two modified EnKPF algorithms. The experiments show that the mEnKPF and nEnKPF, given an affordable ensemble size, can perform better than the EnKF for the nonlinear systems with nonlinear observations. These results suggest a promising opportunity to develop a non-Gaussian scheme for realistic numerical models.
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. PMID:25913233
Kalman filter based range estimation for autonomous navigation using imaging sensors
NASA Technical Reports Server (NTRS)
Sridhar, Banavar
1990-01-01
Rotorcraft operating in high-threat environments fly close to the surface of the earth to utilize surrounding terrain, vegetation, or man-made objects to minimize the risk of being detected by the enemy. Two basic requirements for obstacle avoidance are detection and range estimation of the object from the current rotorcraft position. There are many approaches to the estimation of range using a sequence of images. The approach used in this analysis differes from previous methods in two significant ways: an attempt is not made to estimate the rotorcraft's motion from the images; and the interest lies in recursive algorithms. The rotorcraft parameters are assumed to be computed using an onboard inertial navigation system. Given a sequence of images, using image-object differential equations, a Kalman filter (Sridhar and Phatak, 1988) can be used to estimate both the relative coordinates and the earth coordinates of the objects on the ground. The Kalman filter can also be used in a predictive mode to track features in the images, leading to a significant reduction of search effort in the feature extraction step of the algorithm. The purpose is to summarize early results obtained in extending the Kalman filter for use with actual image sequences. The experience gained from the application of this algorithm to real images is very valuable and is a necessary step before proceeding to the estimation of range during low-altitude curvilinear flight. A simple recursive method is presented to estimate range to objects using a sequence of images. The method produces good range estimates using real images in a laboratory set up and needs to be evaluated further using several different image sequences to test its robustness. The feature generation part of the algorithm requires further refinement on the strategies to limit the number of features (Sridhar and Phatak, 1989). The extension of the work reported here to curvilinear flight may require the use of the extended Kalman
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. PMID:22346641
Some interesting observations regarding the initialization of unscented and extended Kalman filters
NASA Astrophysics Data System (ADS)
Noushin, A. J.; Daum, F. E.
2008-04-01
Contrary to assertions in the literature, we show that the Extended Kalman Filter (EKF) is superior to the Unscented Kalman Filter (UKF) for certain nonlinear estimation problems. In particular, for nonlinearities that are odd functions of the state vector (e.g., x 3) the Unscented Kalman Filter usually performs well, whereas for even nonlinearities (e.g., x2), the Extended Kalman Filter is sometimes much better than the Unscented Kalman Filter. This is contrary to the usual engineering folklore, and therefore we have checked our results very thoroughly. In particular, the Unscented Kalman Filter correctly approximates the conditional mean using a 4th order Gauss-Hermite quadrature, in contrast to the Extended Kalman Filter which uses a simple 0th order approximation, but the conditional mean is not the desired estimate in practical applications for strongly bimodal conditional probability densities, which are induced by even nonlinearities, owing to a sign ambiguity. On the other hand, even nonlinearities do not always induce multimodal densities that persist for a significant amount of time, and thus the Unscented Kalman Filter sometimes performs well for such problems. We study the effects of initial uncertainty of the state vector and nonlinearity in measurements.
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
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.
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.
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.
[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. PMID:12914186
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.
VLBI real-time analysis by Kalman Filtering
NASA Astrophysics Data System (ADS)
Karbon, M.; Nilsson, T.; Soja, B.; Heinkelmann, R.; Raposo-Pulido, V.; Schuh, H.
2013-12-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques providing the full set of Earth Orientation Parameter (EOP) and is unique for observing long term Universal Time (UT1) and precession/nutation. Accurate and continuous EOP obtained in near real-time are essential for satellite based navigation and positioning and for enabling the precise tracking of interplanetary spacecrafts. To meet this necessity the International VLBI Service for Geodesy and Astrometry (IVS) increased its efforts to reduce the time span between the VLBI observations and the availability of the final results. Currently the timeliness is about two weeks, but the goal is to reduce it to less than one day with the future VGOS (VLBI2010 Global Observing System) network. The FWF project VLBI-ART contributes to this new generation VLBI system by considerably accelerating the VLBI analysis procedure through the implementation of an elaborate Kalman filter. This true real-time Kalman filter will be embedded in the Vienna VLBI Software (VieVS) as a completely automated tool with no need of human interaction. This filter also allows the prediction and combination of EOP from various space geodetic techniques by implementing stochastic models to statistically account for unpredictable changes in EOP. Additionally, atmospheric angular momenta calculated from numerical weather prediction models are introduced to support the short-term EOP prediction. To optimize the performance of the new software various investigations with real as well as simulated data are foreseen. The results are compared to the ones obtained by conventional VLBI parameter estimation methods (e.g. least squares method) and to corresponding parameter series from other techniques, such as from the Global Navigation Satellite Systems (GNSS).
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). PMID:24592186
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
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.
Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki
2014-10-01
A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.
Effects of measurement unobservability on neural extended Kalman filter tracking
NASA Astrophysics Data System (ADS)
Stubberud, Stephen C.; Kramer, Kathleen A.
2009-05-01
An important component of tracking fusion systems is the ability to fuse various sensors into a coherent picture of the scene. When multiple sensor systems are being used in an operational setting, the types of data vary. A significant but often overlooked concern of multiple sensors is the incorporation of measurements that are unobservable. An unobservable measurement is one that may provide information about the state, but cannot recreate a full target state. A line of bearing measurement, for example, cannot provide complete position information. Often, such measurements come from passive sensors such as a passive sonar array or an electronic surveillance measure (ESM) system. Unobservable measurements will, over time, result in the measurement uncertainty to grow without bound. While some tracking implementations have triggers to protect against the detrimental effects, many maneuver tracking algorithms avoid discussing this implementation issue. One maneuver tracking technique is the neural extended Kalman filter (NEKF). The NEKF is an adaptive estimation algorithm that estimates the target track as it trains a neural network on line to reduce the error between the a priori target motion model and the actual target dynamics. The weights of neural network are trained in a similar method to the state estimation/parameter estimation Kalman filter techniques. The NEKF has been shown to improve target tracking accuracy through maneuvers and has been use to predict target behavior using the new model that consists of the a priori model and the neural network. The key to the on-line adaptation of the NEKF is the fact that the neural network is trained using the same residuals as the Kalman filter for the tracker. The neural network weights are treated as augmented states to the target track. Through the state-coupling function, the weights are coupled to the target states. Thus, if the measurements cause the states of the target track to be unobservable, then the
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
4D-Var or Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Kalnay, E.; Li, H.; Yang, S.; Miyoshi, T.; Ballabrera, J.
2007-05-01
We consider the relative advantages of two advanced data assimilation systems, 4D-Var and ensemble Kalman filter (EnKF), currently in use or considered for operational implementation. We explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4D-Var, the variance inflation in EnKF, and the effect of model errors and reduced observation coverage in both systems. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4D-Var, and for infrequent observations, when ensemble perturbations grow nonlinearly and become non-Gaussian, 4D-Var attains lower errors than EnKF. Results obtained with variations of EnKF using operational models and both simulated and real observations are reviewed. A table summarizes the pros and cons of the two methods.
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.
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.
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.
Model Calibration of Exciter and PSS Using Extended Kalman Filter
Kalsi, Karanjit; Du, Pengwei; Huang, Zhenyu
2012-07-26
Power system modeling and controls continue to become more complex with the advent of smart grid technologies and large-scale deployment of renewable energy resources. As demonstrated in recent studies, inaccurate system models could lead to large-scale blackouts, thereby motivating the need for model calibration. Current methods of model calibration rely on manual tuning based on engineering experience, are time consuming and could yield inaccurate parameter estimates. In this paper, the Extended Kalman Filter (EKF) is used as a tool to calibrate exciter and Power System Stabilizer (PSS) models of a particular type of machine in the Western Electricity Coordinating Council (WECC). The EKF-based parameter estimation is a recursive prediction-correction process which uses the mismatch between simulation and measurement to adjust the model parameters at every time step. Numerical simulations using actual field test data demonstrate the effectiveness of the proposed approach in calibrating the parameters.
NASA Astrophysics Data System (ADS)
Kokkinaki, A.; Li, J. Y.; Zhou, Q.; Birkholzer, J. T.; Kitanidis, P. K.
2014-12-01
Carbon dioxide (CO2) storage in deep geologic formations is gaining ground as a potential measure for climate change mitigation. Such storage projects typically operate at large scales (~km), but their performance is often governed by smaller-scale (~m) heterogeneities. The large domain sizes prohibit detailed site characterization and dense monitoring networks, leading to predictions of CO2 migration and trapping based on rough geologic models that cannot capture preferential flow. Kalman Filtering can be used to improve these prior models by assimilating available monitoring data, thereby tracking system performance and reducing prediction uncertainty. However, for large systems with fine discretization, the number of unknowns is in the order of tens of thousands or more, in which case the textbook version of the Kalman Filter has prohibitively expensive computation and storage costs. We present the Compressed State Kalman Filter (CSKF) that can be effectively used for systems with a large number of unknowns to estimate the underlying heterogeneity and to predict the state of interest (e.g., pressure and CO2 saturation). The algorithm's computational efficiency is achieved by using a low-rank approximation of the covariance matrix, as well as a Jacobian-free approach. We demonstrate the estimation and computational performance of our method in a typical CO2 storage scenario with a spatially sparse monitoring network, but with multiple datasets obtained before and during CO2 injection. Our data assimilation framework provides an efficient and practical way to characterize geological formations intended for CO2 injection and storage using monitoring data commonly collected in field applications, as well as to quantify the reduction in uncertainty brought by different types of monitoring data.
NASA Astrophysics Data System (ADS)
Wu, Xiaoping; Abbondanza, Claudio; Altamimi, Zuheir; Chin, T. Mike; Collilieux, Xavier; Gross, Richard S.; Heflin, Michael B.; Jiang, Yan; Parker, Jay W.
2015-05-01
The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.
NASA Astrophysics Data System (ADS)
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.
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. PMID:26565359
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.
Convergence of discrete-time Kalman filter estimate to continuous time estimate
NASA Astrophysics Data System (ADS)
Aalto, Atte
2016-04-01
This article is concerned with the convergence of the state estimate obtained from the discrete-time Kalman filter to the continuous time estimate as the temporal discretisation is refined. The convergence follows from Martingale convergence theorem as demonstrated below; however, surprisingly, no results exist on the rate of convergence. We derive convergence rate estimates for the discrete-time Kalman filter estimate for finite and infinite dimensional systems. The proofs are based on applying the discrete-time Kalman filter on a dense numerable subset of a certain time interval [0, T].
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.
An effective automatic tracking algorithm based on Camshift and Kalman filter
NASA Astrophysics Data System (ADS)
Liang, Juan; Hou, Jianhua; Xiang, Jun; Da, Bangyou; Chen, Shaobo
2011-11-01
An automatic tracking algorithm based on Camshift and Kalman filter is proposed in this paper to deal with the problems in traditional Camshift algorithm, such as artificial orientation and increasing possibility of tracking failure under occlusion. The inter-frame difference and canny edge detection are combined to segment perfect moving object region accurately, and the center point of the region is obtained as the initial position of the object. With regard to tracking under occlusion, Kalman filter is used to predict the position and velocity of the target. Specifically, the initial iterative position of Camshift algorithm is obtained by Kalman filter in every frame, and then Camshift algorithm is utilized to track the target position. Finally, the parameters of adaptive Kalman filter are updated by the optimal position. However, when severe occlusion appears, the optimal position calculated by Camshift algorithm is inaccurate, and the Kalman filter fails to estimate the coming state effectively. In this situation, the Kalman filter is updated by the Kalman predictive value instead of the value calculated by the Camshift algorithm. The experiment results demonstrate that the proposed algorithm can detect and track the target object accurately and has better robustness to occlusion.
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-01-01
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). PMID:27258285
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-01-01
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). PMID:27258285
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. PMID:24342270
Adaptive Kalman filter implementation by a neural network scheme for tracking maneuvering targets
NASA Astrophysics Data System (ADS)
Amoozegar, Farid; Sundareshan, Malur K.
1995-07-01
Conventional target tracking algorithms based on linear estimation techniques perform quite efficiently when the target motion does not involve maneuvers. Target maneuvers involving short term accelerations, however, cause a bias (e.g. jump) in the measurement sequence, which unless compensated, results in divergence of the Kalman filter that provides estimates of target position and velocity, in turn leading to a loss of track. Accurate compensation for the bias requires processing more samples of the input signals which adds to the computational complexity. The waiting time for more samples can also result in a total loss of track since the target can begin a new maneuver and if the target begins a new maneuver before the first one is compensated for, the filter would never converge. Most of the proposed algorithms in the current literature hence have the disadvantage of losing the target in short term accelerations, i.e., when the duration of acceleration is comparable to the time period between the measurements. The time lag for maneuver modelings, which have been based on Bayesian probability calculations and linear estimation shall propose a neural network scheme for the modeling of target maneuvers. The primary motivation for employing compensation. The parallel processing capability of a properly trained neural network can permit fast processing of features to yield correct acceleration estimates and hence can take the burden off the primary Kalman filter which still provides the target position and velocity estimates.
Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering
Wu, Pei-Hsun; Agarwal, Ashutosh; Hess, Henry; Khargonekar, Pramod P.; Tseng, Yiider
2010-01-01
Abstract 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. PMID:20550894
NASA Astrophysics Data System (ADS)
Borodachev, S. M.
2016-06-01
The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.
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. PMID:26736727
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.
Real-time data assimilation for large-scale systems: The spectral Kalman filter
NASA Astrophysics Data System (ADS)
Ghorbanidehno, Hojat; Kokkinaki, Amalia; Li, Judith Yue; Darve, Eric; Kitanidis, Peter K.
2015-12-01
The Kalman Filter (KF) is a data assimilation method that has been widely used for estimating spatially varying unknown states evolving in time. Recently, KF methods have shown potential for tracking CO2 plumes injected in deep geologic formations. Such real-time estimation would serve as an early warning system for leakage incidents. However, for the large number of unknowns of such large systems, KF methods are impractical, because updating the huge state covariance matrix is computationally expensive. Low rank approximation methods have been devised to overcome this problem; these methods assume a low rank of the covariance matrix, which they approximate by smaller matrices. The approximation error is small for smooth functions, but may be larger for more complex physical problems, potentially leading to filter divergence and inaccurate state estimates. We present the Spectral Kalman Filter (SpecKF), a new algorithm that utilizes the exact covariance matrix. Thus it avoids the approximation error and does so in a computationally efficient way, which is specially important for systems with large numbers of unknowns. The computational speed-up of the SpecKF is achieved by updating cross-covariance matrices instead of the larger covariance matrices. The benefit can be considerable, especially in large systems, because the computational complexity of the SpecKF scales with the number of measurements, as opposed to the effective rank of the covariance matrix in low-rank KFs or the number of ensemble members in ensemble methods. We investigate the accuracy and performance of the SpecKF for a diffusion problem with random perturbations, and for a more complex case of CO2 injection in a homogeneous two-dimensional domain. Our results show that the SpecKF reduces greatly the computational cost compared to the original KF algorithm, and that it can provide higher accuracy than the Ensemble Kalman Filter (EnKF) with the same or even smaller computational cost. Finally, we
A Physics-Based Kalman Filter for the Ionosphere in GAIM
NASA Astrophysics Data System (ADS)
Scherliess, L.; Schunk, R. W.; Sojka, J. J.; Thompson, D. C.
2002-12-01
A physics-based data assimilation model of the ionosphere is under development as the central part of a DoD MURI funded program called GAIM (Global Assimilation of Ionospheric Measurements). With the significant increase in the number of ionospheric observations that will become available over the next decade, this model will provide a powerful tool towards an improved specification and forecasting of the global ionosphere, with an unprecedented accuracy and reliability. The goal of this effort will be the development of an operational ionospheric assimilation model that will provide specifications and forecasts on spatial grids that can be global, regional, or local (50 km x 50 km). The specification/forecast will be in the form of 3-dimensional electron density distributions from 90 km to geosynchronous altitudes (35,000 km). In GAIM, the data assimilation is performed by a Kalman filter using a new physics-based ionosphere/plasmasphere model (IPM). This model includes 6 ion species (O2+, N2+, NO+, O+, H+, and He+) and currently covers the low and mid-latitudes from 90 km to about 20,000 km altitude. As a practical implementation the Kalman filter in GAIM is based on approximations of the state error covariance matrix, employing a reduction of the model dimension and a linearization of the physical model for the propagation of the error covariance matrix. These approximations lead to a dramatic reduction in the computational requirements. In this paper, we will give an update on the status of the Kalman filter development and present results from a global assimilation run. In this test three different data types were considered, including bottomside electron density profiles obtained from several digisondes, slant TEC from a network of ground-based GPS receivers, and in situ electron density measurements from DMSP satellites.
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. PMID:26396646
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.
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.
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.
4-D-Var or ensemble Kalman filter?
NASA Astrophysics Data System (ADS)
Kalnay, Eugenia; Li, Hong; Miyoshi, Takemasa; Yang, Shu-Chih; Ballabrera-Poy, Joaquim
2007-10-01
We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4-D-Var. For infrequent observations, when ensemble perturbations grow non-linearly and become non-Gaussian, 4-D-Var attains lower errors than EnKF. If the model is imperfect, the 4-D-Var with long windows requires weak constraint. Similar results are obtained with a quasi-geostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3-D-Var and guidance on model error and `observation localization'. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4-D-Var, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.
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.
A multimodel data assimilation framework via the ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Xue, Liang; Zhang, Dongxiao
2014-05-01
The ensemble Kalman filter (EnKF) is a widely used data assimilation method that has the capacity to sequentially update system parameters and states as new observations become available. One noticeable feature of the EnKF is that it not only can provide real-time updates of model parameters and state variables, but also can give the uncertainty associated with them in each assimilation step. The natural system is open and complex, rendering it prone to multiple interpretations and mathematical descriptions. In this paper, a multimodel data assimilation method is proposed by embedding the EnKF into the Bayesian model averaging framework to account for the uncertainty stemming from the model itself. An illustrative example, considering both hydrogeological and groundwater flow uncertainties, is employed to demonstrate the proposed multimodel data assimilation approach via the EnKF. Results show that statistical bias and uncertainty underestimation can occur when the data assimilation process relies on a single postulated model. The posterior model weight can adjust itself dynamically in time according to its consistency with observations. The performances of log conductivity estimation and head prediction are compared to the standard EnKF method based on the postulated single model and the proposed multimodel EnKF method. Comparisons show that the multimodel EnKF performs better in terms of statistical measures, such as log score and coverage, when sufficient observations have been assimilated in this case.
Updating multipoint simulations using the ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Hu, L. Y.; Zhao, Y.; Liu, Y.; Scheepens, C.; Bouchard, A.
2013-02-01
In the last two decades, the multipoint simulation (MPS) method has been developed and increasingly used for building complex geological facies models that are conditioned to geological and geophysical data. In the meantime, the ensemble Kalman filter (EnKF) approach has been developed and recognized as a promising way for assimilating dynamic production data into reservoir models. So far, the EnKF approach is proven efficient for updating continuous model parameters that have a linear statistical relation with the flow responses. It remains challenging to extend the EnKF approach to updating complex geological facies models generated by MPS, while preserving their geological and statistical consistency. In this paper, we introduce a new method for parameterizing geostatistical reservoir models generated by MPS. It is mathematically proven that updating these parameters during a history matching process does not compromise the hard data conditioning and the geological and statistical consistency of the reservoir model defined by the training image and other information including global facies proportions, trend maps etc. This method is an alternative to the gradual deformation method but has an enlarged search space for covering possible solutions. Based on the above parameterization, we present two algorithms of using EnKF approach to update multipoint simulations to dynamic data. We also present results of using the above methodology to condition a sector model of a fluvial reservoir to dynamic data.
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.
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.
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.
Ensemble Kalman Filter Data Assimilation for the Martian Atmosphere
NASA Astrophysics Data System (ADS)
Hoffman, Matthew J.; Greybush, S.; Wilson, R. J.; Gyarmati, G.; Ide, K.; Miyoshi, T.; Szunyogh, I.; Kalnay, E.
2009-09-01
A data assimilation system provides a means of optimally combining information from sparse observations and an atmospheric model to provide an accurate depiction of the state of a planetary atmosphere. Here a Mars General Circulation Model (MGCM) is coupled with the local ensemble transform Kalman filter (LETKF) as the basis of an advanced data assimilation system for Mars. Identical twin experiments, in which observations are generated synthetically from a nature run of the MGCM to approximate the spatial distribution of PDS TES profiles, explore the potential of ensemble data assimilation for the Martian atmosphere. The experiments find that the LETKF is able to correct errors in the Martian atmospheric model and improve the state estimates of the temperature and wind fields, even in the absence of wind observations. The error in the state estimate quickly reduces to below the observation error, and both the forecast and subsequent analysis errors remain low for the duration of a 60 day simulation. Large-scale baroclinic waves along the Northern (winter) Hemisphere temperature front and instabilities in the upper atmosphere zonal wind jet are two predominant sources of error in the MGCM-LETKF system. This study forms the first step toward creating the MGCM-LETKF Martian Atmosphere Reanalysis, which will be incorporating real observations obtained from the MGS TES instrument.
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.
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.
Ensemble Kalman filter implementations based on shrinkage covariance matrix estimation
NASA Astrophysics Data System (ADS)
Nino-Ruiz, Elias D.; Sandu, Adrian
2015-11-01
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the Rao-Blackwell Ledoit and Wolf estimator, which has been specifically developed to approximate high-dimensional covariance matrices using a small number of samples. Two implementations are considered: in the EnKF full-space (EnKF-FS) approach, the assimilation process is performed in the model space, while the EnKF reduce-space (EnKF-RS) formulation performs the analysis in the subspace spanned by the ensemble members. In the context of EnKF-RS, additional samples are taken from the normal distribution described by the background ensemble mean and the estimated background covariance matrix, in order to increase the size of the ensemble and reduce the sampling error of the filter. This increase in the size of the ensemble is obtained without running the forward model. After the assimilation step, the additional samples are discarded and only the model-based ensemble members are propagated further. Methodologies to reduce the impact of spurious correlations and under-estimation of sample variances in the context of the EnKF-FS and EnKF-RS implementations are discussed. An adjoint-free four-dimensional extension of EnKF-RS is also discussed. Numerical experiments carried out with the Lorenz-96 model and a quasi-geostrophic model show that the use of shrinkage covariance matrix estimation can mitigate the impact of spurious correlations during the assimilation process.
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. PMID:21045884
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.
NASA Astrophysics Data System (ADS)
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bertino, Laurent; Bocquet, Marc; Fusco, Thierry
2013-12-01
We propose a new algorithm for an AO control law which allows to reduce the computation burden in the case of an Extremely Large Telescope and to deal with a non stationary behavior of the atmospheric turbulence. This approach uses Ensemble Transform Kalman Filter (ETKF) and localizations by domains decomposition: the assimilation is split into local domains on the pupil of the telescope and each of the update data assimilation for each domain is performed independently. This kind of assimilation enables parallel computation of much less data during the update stage. This is a Kalman Filter adaptation for large scale systems with a non stationary turbulence when the explicit storage and manipulation of extremely large covariance matrices are impossible. This distributed parallel environment implementation is highlighted and studied in the context of an ELT application. First simulation results are proposed to assess our theoretical analysis and to demonstrate the potentiality of this new approach for an AO control law on ELTs.
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
Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea
NASA Astrophysics Data System (ADS)
Ponsar, Stéphanie; Luyten, Patrick; Dulière, Valérie
2016-07-01
Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters' values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.
Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea
NASA Astrophysics Data System (ADS)
Ponsar, Stéphanie; Luyten, Patrick; Dulière, Valérie
2016-08-01
Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters' values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.
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
Design of Jitter Compensation Algorithm for Robot Vision Based on Optical Flow and Kalman Filter
Wang, B. R.; Jin, Y. L.; Shao, D. L.; Xu, Y.
2014-01-01
Image jitters occur in the video of the autonomous robot moving on bricks road, which will reduce robot operation precision based on vision. In order to compensate the image jitters, the affine transformation kinematics were established for obtaining the six image motion parameters. The feature point pair detecting method was designed based on Eigen-value of the feature windows gradient matrix, and the motion parameters equation was solved using the least square method and the matching point pairs got based on the optical flow. The condition number of coefficient matrix was proposed to quantificationally analyse the effect of matching errors on parameters solving errors. Kalman filter was adopted to smooth image motion parameters. Computing cases show that more point pairs are beneficial for getting more precise motion parameters. The integrated jitters compensation software was developed with feature points detecting in subwindow. And practical experiments were conducted on two mobile robots. Results show that the compensation costing time is less than frame sample time and Kalman filter is valid for robot vision jitters compensation. PMID:24600320
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.
Design of jitter compensation algorithm for robot vision based on optical flow and Kalman filter.
Wang, B R; Jin, Y L; Shao, D L; Xu, Y
2014-01-01
Image jitters occur in the video of the autonomous robot moving on bricks road, which will reduce robot operation precision based on vision. In order to compensate the image jitters, the affine transformation kinematics were established for obtaining the six image motion parameters. The feature point pair detecting method was designed based on Eigen-value of the feature windows gradient matrix, and the motion parameters equation was solved using the least square method and the matching point pairs got based on the optical flow. The condition number of coefficient matrix was proposed to quantificationally analyse the effect of matching errors on parameters solving errors. Kalman filter was adopted to smooth image motion parameters. Computing cases show that more point pairs are beneficial for getting more precise motion parameters. The integrated jitters compensation software was developed with feature points detecting in subwindow. And practical experiments were conducted on two mobile robots. Results show that the compensation costing time is less than frame sample time and Kalman filter is valid for robot vision jitters compensation. PMID:24600320
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.
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.
Off-line removal of TMS-induced artifacts on human electroencephalography by Kalman filter.
Morbidi, Fabio; Garulli, Andrea; Prattichizzo, Domenico; Rizzo, Cristiano; Manganotti, Paolo; Rossi, Simone
2007-05-15
In this paper we present an off-line Kalman filter approach to remove transcranial magnetic stimulation (TMS)-induced artifacts from electroencephalographic (EEG) recordings. Two dynamic models describing EEG and TMS signals generation are identified from data and the Kalman filter is applied to the linear system arising from their combination. The keystone of the approach is the use of time-varying covariance matrices suitably tuned on the physical parameters of the problem that allow to model the nonstationary components of the EEG-TMS signal. This guarantees an efficient deletion of TMS-induced artifacts while preserving the integrity of EEG signals around TMS impulses. Experimental results show that the Kalman filter is more effective than stationary filters (Wiener filter) for the problem under investigation. PMID:17399798
NASA Astrophysics Data System (ADS)
Keppenne, Christian L.; Rienecker, Michele M.
2003-04-01
Temperature data from the Tropical Atmosphere and Ocean (TAO) array are assimilated into the Pacific basin configuration of the Poseidon quasi-isopycnal ocean general circulation model (OGCM) using a multivariate ensemble Kalman filter (EnKF) implemented on a massively parallel computer architecture. An assimilation algorithm whereby each processing element (PE) solves a localized analysis problem is used. The algorithm relies on a locally supported error-covariance model to avoid the introduction of spurious long-range covariances associated with small ensemble sizes and to facilitate its efficient parallel implementation on a computing platform with distributed memory. Each time data are assimilated, multivariate background-error statistics estimated from the phase-space distribution of an ensemble of model states are used to calculate the Kalman gain matrix and the analysis increments. The resulting cross-field covariances are used to compute temperature, salinity and current increments. The layer thicknesses are left unchanged by the analysis. Instead, they are dynamically adjusted by the model between successive analyses. Independent acoustic Doppler current profiler data are used to assess the performance of the temperature data assimilation. The temperature analyses are also compared to analyses obtained with a univariate optimal interpolation (UOI) algorithm and to a control run without temperature assimilation. The results demonstrate that the multivariate EnKF is both practical and effective for assimilating in situ and remotely sensed observations into a high resolution ocean model in a quasi-operational framework.
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.
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. PMID:25451818
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
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.
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.
Approach to in-process tool wear monitoring in drilling: Application of Kalman filter theory
NASA Astrophysics Data System (ADS)
He, Ning; Zhang, Youzhen; Pan, Liangxian
1993-05-01
The two parameters often used in adaptive control, tool wear and wear rate, are the important factors affecting machinability. In this paper, it is attempted to use the modern cybernetics to solve the in-process tool wear monitoring problem by applying the Kalman filter theory to monitor drill wear quantitatively. Based on the experimental results, a dynamic model, a measuring model and a measurement conversion model suitable for Kalman filter are established. It is proved that the monitoring system possesses complete observability but does not possess complete controllability. A discriminant for selecting the characteristic parameters is put forward. The thrust force Fz is selected as the characteristic parameter in monitoring the tool wear by this discriminant. The in-process Kalman filter drill wear monitoring system composed of force sensor microphotography and microcomputer is well established. The results obtained by the Kalman filter, the common indirect measuring method and the real drill wear measured by the aid of microphotography are compared. The result shows that the Kalman filter has high precision of measurement and the real time requirement can be satisfied.
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.
NASA Astrophysics Data System (ADS)
Kiani, Maryam; Pourtakdoust, Seid H.
2014-12-01
A novel algorithm is presented in this study for estimation of spacecraft's attitudes and angular rates from vector observations. In this regard, a new cubature-quadrature particle filter (CQPF) is initially developed that uses the Square-Root Cubature-Quadrature Kalman Filter (SR-CQKF) to generate the importance proposal distribution. The developed CQPF scheme avoids the basic limitation of particle filter (PF) with regards to counting the new measurements. Subsequently, CQPF is enhanced to adjust the sample size at every time step utilizing the idea of confidence intervals, thus improving the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). In addition, application of the q-method for filter initialization has intensified the computation burden as well. The current study also applies ACQPF to the problem of attitude estimation of a low Earth orbit (LEO) satellite. For this purpose, the undertaken satellite is equipped with a three-axis magnetometer (TAM) as well as a sun sensor pack that provide noisy geomagnetic field data and Sun direction measurements, respectively. The results and performance of the proposed filter are investigated and compared with those of the extended Kalman filter (EKF) and the standard particle filter (PF) utilizing a Monte Carlo simulation. The comparison demonstrates the viability and the accuracy of the proposed nonlinear estimator.
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.
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.
Kalman filtering for GPS/magnetometer integrated navigation system
NASA Astrophysics Data System (ADS)
Guo, Hang; Yu, Min; Zou, Chengwu; Huang, Wenwen
2010-06-01
This paper investigated the data processing method for a GPS/IMU/magnetometer integrated system with Kalman filtering (KF). As a result of GPS/IMU/magnetometer land vehicle system, dead-reckoning of magnetometer and accelerometer integrated subsystem bridged very well the GPS signal outage due to the trees on the two sides of the road. Both differential GPS data processing method and the carrier-phase method with magnetometers' outputs for predicting the car position, velocity, and acceleration (PVA) are presented. The results from DGPS with Kinematical Positioning (KINPOS) software shown that the averages of the north, east, and down direction standard deviation (short for "std") are 0.014, 0.010, and 0.018 m, respectively. The std of velocities and accelerations derived by the position and velocity differentiation are 10, 7, 13 mm/s, 7, 5, 9 mm/s 2, respectively. This method for getting velocities and accelerations requires higher accurate position coordinates. But the position accuracy has frequently been degraded in this case when the car drove under the trees or other similar kinematical environments. That caused the larger velocity and acceleration errors. While the results from the carrier-phase method are std of the velocities = 2.1 mm/s, 1.3 mm/s, 3.7 mm/s in north, east, down, and std of the accelerations = 1.5 mm/s 2, 0.9 mm/s 2, 2.3 mm/s 2 for the static test period; as compared with KINPOS software results, std of the velocity difference between the carrier-phase method and the DGPS method = 7 mm/s, 6.9 mm/s, 9.7 mm/s in north, east, down direction, and std of acceleration difference = 5.0 mm/s 2, 4.5 mm/s 2, 7.5 mm/s 2 in north, east, down direction for the kinematical test period. Obviously, errors come from both the carrier-phase method and DGPS velocity and acceleration results derived directly by the position differentiation. In addition, better accuracy of positions than that before KF has been got by means of velocities and accelerations derived
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
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.
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.
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
2016-01-01
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
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. PMID:26725505
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.
Feasibility Studies of Applying Kalman Filter Techniques to Power System Dynamic State Estimation
Huang, Zhenyu; Schneider, Kevin P.; Nieplocha, Jarek
2007-08-01
Abstract—Lack of dynamic information in power system operations mainly attributes to the static modeling of traditional state estimation, as state estimation is the basis driving many other operations functions. This paper investigates the feasibility of applying Kalman filter techniques to enable the inclusion of dynamic modeling in the state estimation process and the estimation of power system dynamic states. The proposed Kalman-filter-based dynamic state estimation is tested on a multi-machine system with both large and small disturbances. Sensitivity studies of the dynamic state estimation performance with respect to measurement characteristics – sampling rate and noise level – are presented as well. The study results show that there is a promising path forward to implementation the Kalman-filter-based dynamic state estimation with the emerging phasor measurement technologies.
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.
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.
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.
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.
PID Control Simulation and Kalman Filter State Estimation of HIT-SI Injector Flux Circuit
NASA Astrophysics Data System (ADS)
Kraske, Matthew
In order to implement an optimal modern control system on the HIT-SI injector voltage and flux circuits, it is first necessary to apply state estimation techniques, allowing the physical system to be observed by the controller. To test these estimation methods prior to implementation on the experiment, a simulation must be developed which accurately represents the dynamics and behavior of the experiment. Kalman filter state estimation is implemented using a circuit dynamics model which yields observable state tracking with very low error. Extended Kalman filter estimation is implemented for circuit parameter estimation and for sine wave fitting but requires additional development.
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.
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.
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.
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.
Extended Kalman filtering for the detection of damage in linear mechanical structures
NASA Astrophysics Data System (ADS)
Liu, X.; Escamilla-Ambrosio, P. J.; Lieven, N. A. J.
2009-09-01
This paper addresses the problem of assessing the location and extent of damage in a vibrating structure by means of vibration measurements. Frequency domain identification methods (e.g. finite element model updating) have been widely used in this area while time domain methods such as the extended Kalman filter (EKF) method, are more sparsely represented. The difficulty of applying EKF in mechanical system damage identification and localisation lies in: the high computational cost, the dependence of estimation results on the initial estimation error covariance matrix P(0), the initial value of parameters to be estimated, and on the statistics of measurement noise R and process noise Q. To resolve these problems in the EKF, a multiple model adaptive estimator consisting of a bank of EKF in modal domain was designed, each filter in the bank is based on different P(0). The algorithm was iterated by using the weighted global iteration method. A fuzzy logic model was incorporated in each filter to estimate the variance of the measurement noise R. The application of the method is illustrated by simulated and real examples.
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.
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.
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.
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. PMID:26011898
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. PMID:23719169
Technology Transfer Automated Retrieval System (TEKTRAN)
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 ...
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
Assimilating Remotely Sensed Surface Soil Moisture into SWAT using Ensemble Kalman Filter
Technology Transfer Automated Retrieval System (TEKTRAN)
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 ...
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:…
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...
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.
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). PMID:26280184
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.
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
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.
Application of extended Kalman particle filter for dynamic interference fringe processing
NASA Astrophysics Data System (ADS)
Ermolaev, Petr A.; Volynsky, Maxim A.
2016-04-01
The application of extended Kalman particle filter for dynamic estimation of interferometric signal parameters is considered. A detail description of the algorithm is given. Proposed algorithm allows obtaining satisfactory estimates of model interferometric signals even in the presence of erroneous information on model signal parameters. It provides twice as high calculation speed in comparison with conventional particle filter by reducing the number of vectors approximating probability density function of signal parameters distribution
Sabatini, Angelo M
2006-07-01
In this paper, a quaternion based extended Kalman filter (EKF) is developed for determining the orientation of a rigid body from the outputs of a sensor which is configured as the integration of a tri-axis gyro and an aiding system mechanized using a tri-axis accelerometer and a tri-axis magnetometer. The suggested applications are for studies in the field of human movement. In the proposed EKF, the quaternion associated with the body rotation is included in the state vector together with the bias of the aiding system sensors. Moreover, in addition to the in-line procedure of sensor bias compensation, the measurement noise covariance matrix is adapted, to guard against the effects which body motion and temporary magnetic disturbance may have on the reliability of measurements of gravity and earth's magnetic field, respectively. By computer simulations and experimental validation with human hand orientation motion signals, improvements in the accuracy of orientation estimates are demonstrated for the proposed EKF, as compared with filter implementations where either the in-line calibration procedure, the adaptive mechanism for weighting the measurements of the aiding system sensors, or both are not implemented. PMID:16830938
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
NASA Astrophysics Data System (ADS)
Ait-El-Fquih, Boujemaa; El Gharamti, Mohamad; Hoteit, Ibrahim
2016-08-01
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKFOSA. Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.
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
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
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 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.
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Gonçalves, L. D.; Rocco, E. M.; de Moraes, R. V.; Kuga, H. K.
2015-10-01
This paper aims to simulate part of the orbital trajectory of Lunar Prospector mission to analyze the relevance of using a Kalman filter to estimate the trajectory. For this study it is considered the disturbance due to the lunar gravitational potential using one of the most recent models, the LP100K model, which is based on spherical harmonics, and considers the maximum degree and order up to the value 100. In order to simplify the expression of the gravitational potential and, consequently, to reduce the computational effort required in the simulation, in some cases, lower values for degree and order are used. Following this aim, it is made an analysis of the inserted error in the simulations when using such values of degree and order to propagate the spacecraft trajectory and control. This analysis was done using the standard deviation that characterizes the uncertainty for each one of the values of the degree and order used in LP100K model for the satellite orbit. With knowledge of the uncertainty of the gravity model adopted, lunar orbital trajectory simulations may be accomplished considering these values of uncertainty. Furthermore, it was also used a Kalman filter, where is considered the sensor's uncertainty that defines the satellite position at each step of the simulation and the uncertainty of the model, by means of the characteristic variance of the truncated gravity model. Thus, this procedure represents an effort to approximate the results obtained using lower values for the degree and order of the spherical harmonics, to the results that would be attained if the maximum accuracy of the model LP100K were adopted. Also a comparison is made between the error in the satellite position in the situation in which the Kalman filter is used and the situation in which the filter is not used. The data for the comparison were obtained from the standard deviation in the velocity increment of the space vehicle.
NASA Astrophysics Data System (ADS)
Torabi, H.; Pariz, N.; Karimpour, A.
2016-02-01
This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.
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.
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
NASA Astrophysics Data System (ADS)
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2014-05-01
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 algorithm 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.
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 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.
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.
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
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.
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. PMID:27475606
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.
On convergence of the unscented Kalman-Bucy filter using contraction theory
NASA Astrophysics Data System (ADS)
Maree, J. P.; Imsland, L.; Jouffroy, J.
2016-06-01
Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman-Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual-actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman-Bucy filter. The theoretical concepts are illustrated in two case studies.
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.
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.
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.
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. PMID:25503050
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.
Huang, Lei
2015-01-01
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. PMID:26437409
NASA Astrophysics Data System (ADS)
Xin, Tiantian; Zhao, Hongying; Liu, Sijie; Wang, Lu
2015-03-01
Videos from a small Unmanned Aerial Vehicle (UAV) are always unstable because of the wobble of the vehicle and the impact of surroundings, especially when the motion has a large drifting. Electronic image stabilization aims at removing the unwanted wobble and obtaining the stable video. Then estimation of intended motion, which represents the tendency of global motion, becomes the key to image stabilization. It is usually impossible for general methods of intended motion estimation to obtain stable intended motion remaining as much information of video images and getting a path as much close to the real flying path at the same time. This paper proposed a fuzzy Kalman filtering method to estimate the intended motion to solve these problems. Comparing with traditional methods, the fuzzy Kalman filtering method can achieve better effect to estimate the intended motion.
Prediction of L70 lumen maintenance and chromaticity for LEDs using extended Kalman filter models
NASA Astrophysics Data System (ADS)
Lall, Pradeep; Wei, Junchao; Davis, Lynn
2013-09-01
Solid-state lighting (SSL) luminaires containing light emitting diodes (LEDs) have the potential of seeing excessive temperatures during operation or during transportation and storage. Presently, the TM-21 test standard is used to predict the L70 life of SSL Luminaires from LM-80 test data. The underlying TM-21 Arrhenius Model is based on population averages, may not capture the failure physics in presence of multiple failure mechanisms, and does not predict the chromaticity shift. In this paper, Kalman Filter (KF) and Extended Kalman Filters (EKF) have been used to develop models for 70-percent Lumen Maintenance Life Prediction and chromaticity shift for a LEDs used in SSL luminaires. Ten-thousand hour LM-80 test data for various LEDs have been used for model development.
Huang, Lei
2015-01-01
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. PMID:26437409
Dynamic interaction of separate INS/GPS Kalman filters (Filter-driving - Filter dynamics)
NASA Astrophysics Data System (ADS)
Cunningham, Joseph R.; Lewantowicz, Zdzislaw H.
This paper examines the basic behavior of the inertial navigation system (INS) errors under high-dynamic conditions, such as combat maneuvering of a fighter aircraft. Examination of the INS linearized error dynamics eigenvalue migrations during various dynamic maneuvers reveals significantly stronger instability than the classical vertical channel instability. The Global Positioning System (GPS) offers high accuracy navigation performance benefits with global coverage, but is has limitations during the dynamic maneuvering of fighter aircraft. The optimal integration of the GPS with an INS promises synergistic system performance benefits not realizable with either system individually. A candidate maneuver is selected for which a covariance analysis is performed to demonstrate the performance characteristics of an optimally integrated INS/GPS system. Significant insight into the potential instability of a particular INS/GPS integration scheme is presented. The characteristic and unstable behavior of the INS error dynamics eigenfunctions provides the basis for the 'filter-driving-filter' performance analysis. Several phenomena were observed which should aid future efforts attempting to characterize the performance of various INS/GPS integration methods.
Sun, Yongliang; Xu, Yubin; Li, Cheng; Ma, Lin
2013-01-01
A Kalman/map filtering (KMF)-aided fast normalized cross correlation (FNCC)-based Wi-Fi fingerprinting location sensing system is proposed in this paper. Compared with conventional neighbor selection algorithms that calculate localization results with received signal strength (RSS) mean samples, the proposed FNCC algorithm makes use of all the on-line RSS samples and reference point RSS variations to achieve higher fingerprinting accuracy. The FNCC computes efficiently while maintaining the same accuracy as the basic normalized cross correlation. Additionally, a KMF is also proposed to process fingerprinting localization results. It employs a new map matching algorithm to nonlinearize the linear location prediction process of Kalman filtering (KF) that takes advantage of spatial proximities of consecutive localization results. With a calibration model integrated into an indoor map, the map matching algorithm corrects unreasonable prediction locations of the KF according to the building interior structure. Thus, more accurate prediction locations are obtained. Using these locations, the KMF considerably improves fingerprinting algorithm performance. Experimental results demonstrate that the FNCC algorithm with reduced computational complexity outperforms other neighbor selection algorithms and the KMF effectively improves location sensing accuracy by using indoor map information and spatial proximities of consecutive localization results. PMID:24233027
Kalman Filter Chemical Data Assimilation: A Case Study in January 1992
NASA Technical Reports Server (NTRS)
Lary, D. J.; Khattatov, B.; Atlas, Robert; Mussa, H.
2002-01-01
This paper describes a Kalman filter chemical data assimilation system and its use for analysing a vertical atmospheric profile during January 1992. The vertical profile was at an equivalent PV latitude (phi(sub e)) of 55 deg S and consisted of 21 potential temperature (theta) levels spaced equally in log(theta) between 400 K and 2000 K. This equivalent latitude was chosen as it was well observed during January 1992 by instruments on board the Upper Atmosphere Research Satellite (UARS).
NASA Technical Reports Server (NTRS)
Bar-Itzhack, I. Y.; Deutschmann, J.; Markley, F. L.
1991-01-01
This work introduces, examines and compares several quaternion normalization algorithms, which are shown to be an effective stage in the application of the additive extended Kalman filter to spacecraft attitude determination, which is based on vector measurements. Three new normalization schemes are introduced. They are compared with one another and with the known brute force normalization scheme, and their efficiency is examined. Simulated satellite data are used to demonstate the performance of all four schemes.
En route position and time control of aircraft using Kalman filtering of radio aid data
NASA Technical Reports Server (NTRS)
Mcgee, L. A.; Christensen, J. V.
1973-01-01
Fixed-time-of-arrival (FTA) guidance and navigation is investigated as a possible technique capable of operation within much more stringent en route separation standards and offering significant advantages in safety, higher traffic densities, and improved scheduling reliability, both en route and in the terminal areas. This study investigated the application of FTA guidance previously used in spacecraft guidance. These FTA guidance techniques have been modified and are employed to compute the velocity corrections necessary to return an aircraft to a specified great-circle reference path in order to exercise en route time and position control throughout the entire flight. The necessary position and velocity estimates to accomplish this task are provided by Kalman filtering of data from Loran-C, VORTAC/TACAN, Doppler radar, radio or barometric altitude,and altitude rate. The guidance and navigation system was evaluated using a digital simulation of the cruise phase of supersonic and subsonic flights between San Francisco and New York City, and between New York City and London.
Capellari, Giovanni; Eftekhar Azam, Saeed; Mariani, Stefano
2015-01-01
Health monitoring of lightweight structures, like thin flexible plates, is of interest in several engineering fields. In this paper, a recursive Bayesian procedure is proposed to monitor the health of such structures through data collected by a network of optimally placed inertial sensors. As a main drawback of standard monitoring procedures is linked to the computational costs, two remedies are jointly considered: first, an order-reduction of the numerical model used to track the structural dynamics, enforced with proper orthogonal decomposition; and, second, an improved particle filter, which features an extended Kalman updating of each evolving particle before the resampling stage. The former remedy can reduce the number of effective degrees-of-freedom of the structural model to a few only (depending on the excitation), whereas the latter one allows to track the evolution of damage and to locate it thanks to an intricate formulation. To assess the effectiveness of the proposed procedure, the case of a plate subject to bending is investigated; it is shown that, when the procedure is appropriately fed by measurements, damage is efficiently and accurately estimated. PMID:26703615
Dogra, Debi Prosad; Badri, Vishal; Majumdar, Arun Kumar; Sural, Shamik; Mukherjee, Jayanta; Mukherjee, Suchandra; Singh, Arun
2014-09-01
Video object tracking plays an important role in many computer vision-aided applications. This paper presents a novel multi-path analysis-based video object tracking algorithm. Trajectory of the moving object is refined using a Kalman filter-based prediction method. The proposed algorithm has been used successfully to analyze one of the complex infant neurological examinations often referred to as Hammersmith lateral tilting test. This is an important test of the infant neurological assessment process, and this test is difficult to grade by visual observation. It has been shown in this paper that the proposed video object tracking algorithm can be used to analyze the videos of fast moving objects by incorporating application-specific information. For example, the proposed tracking algorithm can be used to assess lateral tilting test of the Hammersmith infant neurological examinations. The algorithm has been tested with several video recordings of this test which were captured at the neurodevelopment clinic of the SSKM Hospital, Kolkata, India during the period of the study. It is found that the proposed algorithm is capable of estimating the score for the test with high values of sensitivity and specificity. PMID:25096789
Bersvendsen, Jorn; Orderud, Fredrik; Massey, Richard John; Fosså, Kristian; Gerard, Olivier; Urheim, Stig; Samset, Eigil
2016-01-01
As the right ventricle's (RV) role in cardiovascular diseases is being more widely recognized, interest in RV imaging, function and quantification is growing. However, there are currently few RV quantification methods for 3D echocardiography presented in the literature or commercially available. In this paper we propose an automated RV segmentation method for 3D echocardiographic images. We represent the RV geometry by a Doo-Sabin subdivision surface with deformation modes derived from a training set of manual segmentations. The segmentation is then represented as a state estimation problem and solved with an extended Kalman filter by combining the RV geometry with a motion model and edge detection. Validation was performed by comparing surface-surface distances, volumes and ejection fractions in 17 patients with aortic insufficiency between the proposed method, magnetic resonance imaging (MRI), and a manual echocardiographic reference. The algorithm was efficient with a mean computation time of 2.0 s. The mean absolute distances between the proposed and manual segmentations were 3.6 ± 0.7 mm. Good agreements of end diastolic volume, end systolic volume and ejection fraction with respect to MRI ( -26±24 mL , -16±26 mL and 0 ± 10%, respectively) and a manual echocardiographic reference (7 ± 30 mL, 13 ± 17 mL and -5±7% , respectively) were observed. PMID:26168434
Simple hydraulic conductivity estimation by the Kalman filtered double constraint method.
El-Rawy, M A; Batelaan, O; Zijl, W
2015-01-01
This paper presents the Kalman Filtered Double Constraint Method (DCM-KF) as a technique to estimate the hydraulic conductivities in the grid blocks of a groundwater flow model. The DCM is based on two forward runs with the same initial grid block conductivities, but with alternating flux-head conditions specified on parts of the boundary and the wells. These two runs are defined as: (1) the flux run, with specified fluxes (recharge and well abstractions), and (2) the head run, with specified heads (measured in piezometers). Conductivities are then estimated as the initial conductivities multiplied by the fluxes obtained from the flux run and divided by the fluxes obtained from the head run. The DCM is easy to implement in combination with existing models (e.g., MODFLOW). Sufficiently accurate conductivities are obtained after a few iterations. Because of errors in the specified head-flux couples, repeated estimation under varying hydrological conditions results in different conductivities. A time-independent estimate of the conductivities and their inaccuracy can be obtained by a simple linear KF with modest computational requirements. For the Kleine Nete catchment, Belgium, the DCM-KF yields sufficiently accurate calibrated conductivities. The method also results in distinguishing regions where the head-flux observations influence the calibration from areas where it is not able to influence the hydraulic conductivity. PMID:24854328
Cursor control by Kalman filter with a non-invasive body–machine interface
Seáñez-González, Ismael; Mussa-Ivaldi, Ferdinando A
2015-01-01
Objective We describe a novel human–machine interface for the control of a two-dimensional (2D) computer cursor using four inertial measurement units (IMUs) placed on the user’s upper-body. Approach A calibration paradigm where human subjects follow a cursor with their body as if they were controlling it with their shoulders generates a map between shoulder motions and cursor kinematics. This map is used in a Kalman filter to estimate the desired cursor coordinates from upper-body motions. We compared cursor control performance in a centre-out reaching task performed by subjects using different amounts of information from the IMUs to control the 2D cursor. Main results Our results indicate that taking advantage of the redundancy of the signals from the IMUs improved overall performance. Our work also demonstrates the potential of non-invasive IMU-based body–machine interface systems as an alternative or complement to brain–machine interfaces for accomplishing cursor control in 2D space. Significance The present study may serve as a platform for people with high-tetraplegia to control assistive devices such as powered wheelchairs using a joystick. PMID:25242561
Incremental multi-class semi-supervised clustering regularized by Kalman filtering.
Mehrkanoon, Siamak; Agudelo, Oscar Mauricio; Suykens, Johan A K
2015-11-01
This paper introduces an on-line semi-supervised learning algorithm formulated as a regularized kernel spectral clustering (KSC) approach. We consider the case where new data arrive sequentially but only a small fraction of it is labeled. The available labeled data act as prototypes and help to improve the performance of the algorithm to estimate the labels of the unlabeled data points. We adopt a recently proposed multi-class semi-supervised KSC based algorithm (MSS-KSC) and make it applicable for on-line data clustering. Given a few user-labeled data points the initial model is learned and then the class membership of the remaining data points in the current and subsequent time instants are estimated and propagated in an on-line fashion. The update of the memberships is carried out mainly using the out-of-sample extension property of the model. Initially the algorithm is tested on computer-generated data sets, then we show that video segmentation can be cast as a semi-supervised learning problem. Furthermore we show how the tracking capabilities of the Kalman filter can be used to provide the labels of objects in motion and thus regularizing the solution obtained by the MSS-KSC algorithm. In the experiments, we demonstrate the performance of the proposed method on synthetic data sets and real-life videos where the clusters evolve in a smooth fashion over time. PMID:26319050
Capellari, Giovanni; Azam, Saeed Eftekhar; Mariani, Stefano
2015-01-01
Health monitoring of lightweight structures, like thin flexible plates, is of interest in several engineering fields. In this paper, a recursive Bayesian procedure is proposed to monitor the health of such structures through data collected by a network of optimally placed inertial sensors. As a main drawback of standard monitoring procedures is linked to the computational costs, two remedies are jointly considered: first, an order-reduction of the numerical model used to track the structural dynamics, enforced with proper orthogonal decomposition; and, second, an improved particle filter, which features an extended Kalman updating of each evolving particle before the resampling stage. The former remedy can reduce the number of effective degrees-of-freedom of the structural model to a few only (depending on the excitation), whereas the latter one allows to track the evolution of damage and to locate it thanks to an intricate formulation. To assess the effectiveness of the proposed procedure, the case of a plate subject to bending is investigated; it is shown that, when the procedure is appropriately fed by measurements, damage is efficiently and accurately estimated. PMID:26703615
Non-intrusive Ensemble Kalman filtering for large scale geophysical models
NASA Astrophysics Data System (ADS)
Amour, Idrissa; Kauranne, Tuomo
2016-04-01
Advanced data assimilation techniques, such as variational assimilation methods, present often challenging implementation issues for large-scale models, both because of computational complexity and because of complexity of implementation. We present a non-intrusive wrapper library that addresses this problem by isolating the direct model and the linear algebra employed in data assimilation from each other completely. In this approach we have adopted a hybrid Variational Ensemble Kalman filter that combines Ensemble propagation with a 3DVAR analysis stage. The inverse problem of state and covariance propagation from prior to posterior estimates is thereby turned into a time-independent problem. This feature allows the linear algebra and minimization steps required in the variational step to be conducted outside the direct model and no tangent linear or adjoint codes are required. Communication between the model and the assimilation module is conducted exclusively via standard input and output files of the model. This non-intrusive approach is tested with the comprehensive 3D lake and shallow sea model COHERENS that is used to forecast and assimilate turbidity in lake Säkylän Pyhäjärvi in Finland, using both sparse satellite images and continuous real-time point measurements as observations.
Baker, Syed Murtuza; Poskar, C Hart; Junker, Björn H
2011-01-01
In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison. PMID:21989173
Cursor control by Kalman filter with a non-invasive body-machine interface
NASA Astrophysics Data System (ADS)
Seáñez-González, Ismael; Mussa-Ivaldi, Ferdinando A.
2014-10-01
Objective. We describe a novel human-machine interface for the control of a two-dimensional (2D) computer cursor using four inertial measurement units (IMUs) placed on the user’s upper-body. Approach. A calibration paradigm where human subjects follow a cursor with their body as if they were controlling it with their shoulders generates a map between shoulder motions and cursor kinematics. This map is used in a Kalman filter to estimate the desired cursor coordinates from upper-body motions. We compared cursor control performance in a centre-out reaching task performed by subjects using different amounts of information from the IMUs to control the 2D cursor. Main results. Our results indicate that taking advantage of the redundancy of the signals from the IMUs improved overall performance. Our work also demonstrates the potential of non-invasive IMU-based body-machine interface systems as an alternative or complement to brain-machine interfaces for accomplishing cursor control in 2D space. Significance. The present study may serve as a platform for people with high-tetraplegia to control assistive devices such as powered wheelchairs using a joystick.
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Balidakis, Kyriakos; Glaser, Susanne; Heinkelmann, Robert; Schuh, Harald
2016-06-01
Terrestrial reference frames (TRF), such as the ITRF2008, are primary products of geodesy. In this paper, we present TRF solutions based on Kalman filtering of very long baseline interferometry (VLBI) data, for which we estimate steady station coordinates over more than 30 years that are updated for every single VLBI session. By applying different levels of process noise, non-linear signals, such as seasonal and seismic effects, are taken into account. The corresponding stochastic model is derived site-dependent from geophysical loading deformation time series and is adapted during periods of post-seismic deformations. Our results demonstrate that the choice of stochastic process has a much smaller impact on the coordinate time series and velocities than the overall noise level. If process noise is applied, tests with and without additionally estimating seasonal signals indicate no difference between the resulting coordinate time series for periods when observational data are available. In a comparison with epoch reference frames, the Kalman filter solutions provide better short-term stability. Furthermore, we find out that the Kalman filter solutions are of similar quality when compared to a consistent least-squares solution, however, with the enhanced attribute of being easier to update as, for instance, in a post-earthquake period.
Optimal Tuner Selection for Kalman Filter-Based Aircraft Engine Performance Estimation
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Garg, Sanjay
2010-01-01
A linear point design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. This paper derives theoretical Kalman filter estimation error bias and variance values at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the conventional approach of tuner selection. Experimental simulation results are found to be in agreement with theoretical predictions. The new methodology is shown to yield a significant improvement in on-line engine performance estimation accuracy
Chen, Xiyuan; Wang, Xiying; Xu, Yuan
2014-01-01
This paper deals with the problem of state estimation for the vector-tracking loop of a software-defined Global Positioning System (GPS) receiver. For a nonlinear system that has the model error and white Gaussian noise, a noise statistics estimator is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) named adaptive iterated Kalman filter (AIEKF) is proposed. A vector-tracking GPS receiver utilizing AIEKF is implemented to evaluate the performance of the proposed method. Through road tests, it is shown that the proposed method has an obvious accuracy advantage over the IEKF and Adaptive Extended Kalman filter (AEKF) in position determination. The results show that the proposed method is effective to reduce the root-mean-square error (RMSE) of position (including longitude, latitude and altitude). Comparing with EKF, the position RMSE values of AIEKF are reduced by about 45.1%, 40.9% and 54.6% in the east, north and up directions, respectively. Comparing with IEKF, the position RMSE values of AIEKF are reduced by about 25.7%, 19.3% and 35.7% in the east, north and up directions, respectively. Compared with AEKF, the position RMSE values of AIEKF are reduced by about 21.6%, 15.5% and 30.7% in the east, north and up directions, respectively. PMID:25502124
Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks.
Puskorius, G V; Feldkamp, L A
1994-01-01
Although the potential of the powerful mapping and representational capabilities of recurrent network architectures is generally recognized by the neural network research community, recurrent neural networks have not been widely used for the control of nonlinear dynamical systems, possibly due to the relative ineffectiveness of simple gradient descent training algorithms. Developments in the use of parameter-based extended Kalman filter algorithms for training recurrent networks may provide a mechanism by which these architectures will prove to be of practical value. This paper presents a decoupled extended Kalman filter (DEKF) algorithm for training of recurrent networks with special emphasis on application to control problems. We demonstrate in simulation the application of the DEKF algorithm to a series of example control problems ranging from the well-known cart-pole and bioreactor benchmark problems to an automotive subsystem, engine idle speed control. These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise. PMID:18267797
A robust and self-tuning Kalman filter for autonomous spacecraft navigation
NASA Astrophysics Data System (ADS)
Truong, Son Hong
Most navigation systems currently operated by the National Aeronautics and Space Administration (NASA) and other major space agencies (e.g., European Space Agency (ESA)) are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and the Global Positioning System (GPS) or GPS-like data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing navigation autonomy without compromising accuracy and performance. The re-tuning process is more complex when dealing with geosynchronous and high-eccentricity orbits. This dissertation presents an approach to produce a high accuracy onboard navigation system that can recover from estimation errors in real time. It proposes a sophisticated application of neuro-fuzzy techniques to perform the self-tuning capability. It also demonstrates the feasibility and efficiency of a self-tuning component built from this concept to augment to a Kalman filter, which performs the state estimation. The core requirement is a method of state estimation that handles uncertainties robustly, is capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight software. The scope of the dissertation research has both theoretical and experimental dimensions. In the direction of theory, performance limits of Kalman filter and related major adaptive techniques, and new technologies popular in the areas of system identification and automatic controls are studied, with special emphasis on mathematical issues leading to the optimization of spacecraft navigation autonomy. In the experimental direction, a prototype self-tuning system is designed, developed, and tested. Filtered data from
Extended Kalman Filter for attitude estimation of the Earth Radiation Budget Satellite
NASA Technical Reports Server (NTRS)
Deutschmann, Julie; Bar-Itzhack, I. Y.
1990-01-01
The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.
Extended Kalman filter for attitude estimation of the earth radiation budget satellite
NASA Technical Reports Server (NTRS)
Deutschmann, Julie; Bar-Itzhack, Itzhack Y.
1989-01-01
The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.
NASA Astrophysics Data System (ADS)
Huang, Wei; Xie, Hongsheng; Shen, Chen; Li, Jinpeng
2016-04-01
This paper considers a robust strong tracking nonlinear filtering problem in the case there are model uncertainties including the model mismatch, unknown disturbance and status mutation in the spacecraft attitude estimation system with quaternion constraint. Two multiple fading factor matrices are employed to regulate the prediction error covariance matrix, which guarantees its symmetry. The spherical-radial cubature rule is developed to deal with the multi-dimensional integrals. The quaternion constraint is maintained by utilizing the gain correction method. Therefore a robust strong tracking cubature Kalman filter (RSTCKF) is formed for the spacecraft attitude estimation with quaternion constraint. Unlike adopting a single fading factor in the traditional strong tracking filter, the presented filter uses two multiple fading factor matrices to make different channels have respective filter adjustment capability, which improves the tracking performance of this algorithm. Simulation results show the effectiveness of the proposed RSTCKF.
NASA Astrophysics Data System (ADS)
Djalalova, Irina; Delle Monache, Luca; Wilczak, James
2015-05-01
A new post-processing method for surface particulate matter (PM2.5) predictions from the National Oceanic and Atmospheric Administration (NOAA) developmental air quality forecasting system using the Community Multiscale Air Quality (CMAQ) model is described. It includes three main components: • A real-time quality control procedure for surface PM2.5 observations; • Model post-processing at each observational site using historical forecast analogs and Kalman filtering; • Spreading the forecast corrections from the observation locations to the entire gridded domain. The methodology is tested using 12 months of CMAQ forecasts of hourly PM2.5, from December 01, 2009 through November 30, 2010. The model domain covers the contiguous USA, and model data are verified against U.S. Environmental Prediction Agency AIRNow PM2.5 observations measured at 716 stations over the CMAQ domain. The model bias is found to have a strong seasonal dependency, with a large positive bias in winter and a small bias in the summer months, and also to have a strong diurnal cycle. Five different post-processing techniques are compared, including a seven-day running mean subtraction, Kalman-filtering, analogs, and combinations of analogs and Kalman filtering. The most accurate PM2.5 forecasts have been found to be produced when using historical analogs of the hourly Kalman-filtered forecasts, referred to as KFAN. The choice of meteorological variables used in the hourly analog search is also found to have a significant effect. A monthly error analysis is computed, in each case using the remaining 11 months of the data set for the analog searches. The improvement of KFAN errors over the raw CMAQ model errors ranges from 50 to 75% for MAE and from 40 to 60% for the correlation coefficient. Since the post-processing analysis is only done at the locations where observations are available, the spreading of post-processing correction information over nearby model grid points is necessary to make
NASA Astrophysics Data System (ADS)
Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.
2014-04-01
Traditional Ensemble Kalman Filter (EnKF) data assimilation requires computationally intensive Monte Carlo (MC) sampling, which suffers from filter inbreeding unless the number of simulations is large. Recently we proposed an alternative EnKF groundwater-data assimilation method that obviates the need for sampling and is free of inbreeding issues. In our new approach, theoretical ensemble moments are approximated directly by solving a system of corresponding stochastic groundwater flow equations. Like MC-based EnKF, our moment equations (ME) approach allows Bayesian updating of system states and parameters in real-time as new data become available. Here we compare the performances and accuracies of the two approaches on two-dimensional transient groundwater flow toward a well pumping water in a synthetic, randomly heterogeneous confined aquifer subject to prescribed head and flux boundary conditions.
Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, Guillermo
1987-01-01
The recursive difference equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing, arising in the state estimation theory for linear state space systems, are used here to solve problems of serial manipulator inverse and forward dynamics. The configuration analyzed is that of a joint connected N-link serial manipulator attached to an immobile base. The equivalence between the filtering and smoothing techniques from state estimation theory and recursive robot dynamics methods is demonstrated. Several areas for future research are suggested.
A Kalman filter and 3dVAR inter-comparison with NCEP's new operational forecasting system
NASA Astrophysics Data System (ADS)
Fukumori, I.; Behringer, D.; Wang, O.; Wang, J.
2008-12-01
The ECCO Kalman filter is adapted to the Modular Ocean Model (MOM4) employed in the latest operational ocean analyses of the National Centers for Environmental Prediction (NCEP), National Oceanic and Atmospheric Administration. The ocean state estimates of the Kalman filter are compared with those of NCEP's 3dVAR method to assess the relative impact of the different approaches on analyzing and forecasting seasonal-to-interannual climate variability. The ECCO filter employs partitioned, reduced-state, and time-asymptotic approximations of the model state error covariance matrix associated with inaccuracies in atmospheric wind forcing. The filter assimilates temporal anomalies of satellite sea level and in situ temperature profile measurements over the world's oceans. New advancements are devised in filter implementation including use of adjoint codes and improvements in spatial interpolation around land masses and in estimating effects of vertical heaving motion. The next operational model of NCEP is based on MOM4 and employs a tripolar grid that spans the entire globe including the Arctic Ocean with a nominal 0.5-degree grid with 40 vertical levels. A 3dVAR method is employed to assimilate temperature and synthetic salinity profiles. The salinity profiles are constructed from the temperature profiles and a local TS relationship. The model error variances are assumed to be proportional to the local temperature and salinity gradients and are computed from the most recent 5-day model average. Utilizing identical models, the inter-comparison provides a unique assessment of the two assimilation methods independent of potential differences in models that are used. The two ocean state estimates will be compared with respect to various observations. Circulation indexes will be analyzed such as strengths of subtropical cells, meridional overturning circulation, and integrated upper ocean heat content changes. The assimilations' impact on subsequent variability of the ocean
Quantifying performance limitations of Kalman filters in state vector estimation problems
NASA Astrophysics Data System (ADS)
Bageshwar, Vibhor Lal
In certain applications, the performance objectives of a Kalman filter (KF) are to compute unbiased, minimum variance estimates of a state mean vector governed by a stochastic system. The KF can be considered as a model based algorithm used to recursively estimate the state mean vector and state covariance matrix. The general objective of this thesis is to investigate the performance limitations of the KF in three state vector estimation applications. Stochastic observability is a property of a system and refers to the existence of a filter for which the errors of the estimated state mean vector have bounded variance. In the first application, we derive a test to assess the stochastic observability of a KF implemented for discrete linear time-varying systems consisting of known, deterministic parameters. This class of system includes discrete nonlinear systems linearized about the true state vector trajectory. We demonstrate the utility of the stochastic observability test using an aided INS problem. Attitude determination systems consist of a sensor set, a stochastic system, and a filter to estimate attitude. In the second application, we design an inertially aided (IA) vector matching algorithm (VMA) architecture for estimating a spacecraft's attitude. The sensor set includes rate gyros and a three-axis magnetometer (TAM). The VMA is a filtering algorithm that solves Wahba's problem. The VMA is then extended by incorporating dynamic and sensor models to formulate the IA VMA architecture. We evaluate the performance of the IA VMA architectures by using an extended KF to blend post-processed spaceflight data. Model predictive control (MPC) algorithms achieve offset-free control by augmenting the nominal system model with a disturbance model. In the third application, we consider an offset-free MPC framework that includes an output integrator disturbance model and a KF to estimate the state and disturbance vectors. Using root locus techniques, we identify sufficient
NASA Technical Reports Server (NTRS)
Canfield, Stephen
1999-01-01
This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.
NASA Technical Reports Server (NTRS)
Keppenne, Christian L.
2013-01-01
A two-step ensemble recentering Kalman filter (ERKF) analysis scheme is introduced. The algorithm consists of a recentering step followed by an ensemble Kalman filter (EnKF) analysis step. The recentering step is formulated such as to adjust the prior distribution of an ensemble of model states so that the deviations of individual samples from the sample mean are unchanged but the original sample mean is shifted to the prior position of the most likely particle, where the likelihood of each particle is measured in terms of closeness to a chosen subset of the observations. The computational cost of the ERKF is essentially the same as that of a same size EnKF. The ERKF is applied to the assimilation of Argo temperature profiles into the OGCM component of an ensemble of NASA GEOS-5 coupled models. Unassimilated Argo salt data are used for validation. A surprisingly small number (16) of model trajectories is sufficient to significantly improve model estimates of salinity over estimates from an ensemble run without assimilation. The two-step algorithm also performs better than the EnKF although its performance is degraded in poorly observed regions.
NASA Astrophysics Data System (ADS)
Chaganti, Shikha; Nelson, Katrina; Mundy, Kevin; Luo, Yifu; Harrigan, Robert L.; Damon, Steve; Fabbri, Daniel; Mawn, Louise; Landman, Bennett
2016-03-01
Pathologies of the optic nerve and orbit impact millions of Americans and quantitative assessment of the orbital structures on 3-D imaging would provide objective markers to enhance diagnostic accuracy, improve timely intervention, and eventually preserve visual function. Recent studies have shown that the multi-atlas methodology is suitable for identifying orbital structures, but challenges arise in the identification of the individual extraocular rectus muscles that control eye movement. This is increasingly problematic in diseased eyes, where these muscles often appear to fuse at the back of the orbit (at the resolution of clinical computed tomography imaging) due to inflammation or crowding. We propose the use of Kalman filters to track the muscles in three-dimensions to refine multi-atlas segmentation and resolve ambiguity due to imaging resolution, noise, and artifacts. The purpose of our study is to investigate a method of automatically generating orbital metrics from CT imaging and demonstrate the utility of the approach by correlating structural metrics of the eye orbit with clinical data and visual function measures in subjects with thyroid eye disease. The pilot study demonstrates that automatically calculated orbital metrics are strongly correlated with several clinical characteristics. Moreover, it is shown that the superior, inferior, medial and lateral rectus muscles obtained using Kalman filters are each correlated with different categories of functional deficit. These findings serve as foundation for further investigation in the use of CT imaging in the study, analysis and diagnosis of ocular diseases, specifically thyroid eye disease.
Chaganti, Shikha; Nelson, Katrina; Mundy, Kevin; Luo, Yifu; Harrigan, Robert L; Damon, Steve; Fabbri, Daniel; Mawn, Louise; Landman, Bennett
2016-01-01
Pathologies of the optic nerve and orbit impact millions of Americans and quantitative assessment of the orbital structures on 3-D imaging would provide objective markers to enhance diagnostic accuracy, improve timely intervention and eventually preserve visual function. Recent studies have shown that the multi-atlas methodology is suitable for identifying orbital structures, but challenges arise in the identification of the individual extraocular rectus muscles that control eye movement. This is increasingly problematic in diseased eyes, where these muscles often appear to fuse at the back of the orbit (at the resolution of clinical computed tomography imaging) due to inflammation or crowding. We propose the use of Kalman filters to track the muscles in three-dimensions to refine multi-atlas segmentation and resolve ambiguity due to imaging resolution, noise, and artifacts. The purpose of our study is to investigate a method of automatically generating orbital metrics from CT imaging and demonstrate the utility of the approach by correlating structural metrics of the eye orbit with clinical data and visual function measures in subjects with thyroid eye disease. The pilot study demonstrates that automatically calculated orbital metrics are strongly correlated with several clinical characteristics. Moreover, the superior, inferior, medial and lateral rectus muscles obtained using Kalman filters are each correlated with different categories of functional deficit. These findings serve as foundation for further investigation in the use of CT imaging in the study, analysis and diagnosis of ocular diseases, specifically thyroid eye disease. PMID:27127330
NASA Astrophysics Data System (ADS)
Miyazawa, Y.; Miyama, T.; Varlamov, S. M.; Guo, X.; Waseda, T.
2010-12-01
Yasumasa Miyazawa1, Toru Miyama1, Sergey M. Varlamov1, Xinyu Guo1,2, and Takuji Waseda1,3 1Research Institute for Global Change, JAMSTEC, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan. E-mail: miyazawa@jamstec.go.jp 2Center for Marine Environmental Studies, Ehimeniversity, Matsuyama, Ehime, 790-8577, Japan. 3Graduate School of Frontier Science, University of Tokyo, Kashiwa, 277-8563, Japan We are developing the Ensemble Kalman Filter (EnKF) to allow assimilation of various types of the observational data including not only the traditional temperature and salinity data but also new types of data such as High Frequency radar ocean currents. EnKF is also useful for the detection of the highly variable phenomena associated with the western boundary currents because it represents the flow-dependent dynamic correlations among the model variables. Focusing on the Kuroshio variations south of Japan, we have developed an ocean model with horizontal resolution of 1/36 degree (3km) nested in the Northwestern Pacific OGCM with a coarser horizontal resolution of 1/12 degree. Based on 20 ensemble member models running on the parallel computers, we implemented the Local Ensemble Transformation Kalman Filter (LETKF) algorithm. Identical twin experiments using LETKF demonstrated good representation of the flow dependent correlations and effective assimilation of the ocean current observations. We further discuss results of sensitivity experiments to investigate the potential of LETKF.
Kalman filters for a missile with radar and/or imaging sensor
NASA Astrophysics Data System (ADS)
Uhrmeister, Bernd
1994-11-01
The scenario covers a missile in a head-on attack against a combat aircraft, performing evasive maneuver in a vertical plane. The improvement of the estimation of guidance signals is investigated when the radar as prime source for target is supported and finally replaced by an imaging sensor. Kalman filters estimate the guidance signals for an augmented proportional navigation, the line-of-sight (LOS) rate, and the target's normal acceleration. A second filter estimates the LOS rate from the radar measurement. Coupling of the filters by feeding the estimated target acceleration of the optical system into the radar's LOS rate filter improves its signal. A significant increase of performance is achieved when the imaging sensor replaces the radar also as a source for LOS information.
A Kalman filter for a two-dimensional shallow-water model
NASA Technical Reports Server (NTRS)
Parrish, D. F.; Cohn, S. E.
1985-01-01
A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.
Stable force identification in structural dynamics using Kalman filtering and dummy-measurements
NASA Astrophysics Data System (ADS)
Naets, F.; Cuadrado, J.; Desmet, W.
2015-01-01
Many engineering applications require the knowledge of input forces to mechanical systems. However, in practice, it is quite difficult to measure these forces directly. In order to obtain an estimate of the input forces to structural systems, Kalman filtering based techniques have recently been introduced. These state-estimation techniques allow estimating the forces concurrent with the states of a system, based on a limited number of measurements. In practice, acceleration measurements are most convenient to use in structural dynamics applications. This paper proposes an analytical analysis of the stability of the Kalman based force estimation techniques and shows that only using acceleration measurements inherently leads to unreliable results. In order to circumvent this issue, the addition of dummy-measurements on a position level is proposed. These fictitious measurements dictate the estimator to return to an undeformed state and lead to a stable estimation approach. The proposed method is validated through both a numerical and a practical experiment. Both experiments show the inadequacy of the augmented Kalman filter based on only acceleration measurements to provide stable results. The estimator with dummy measurements on the other hand provides good results in the case of an unbiased external load.
Digital filter synthesis computer program
NASA Technical Reports Server (NTRS)
Moyer, R. A.; Munoz, R. M.
1968-01-01
Digital filter synthesis computer program expresses any continuous function of a complex variable in approximate form as a computational algorithm or difference equation. Once the difference equation has been developed, digital filtering can be performed by the program on any input data list.
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-08-25
We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs). PMID:25321291
A Network of Kalman Filters for MAI and ISI Compensation in a Non-Gaussian Environment
NASA Astrophysics Data System (ADS)
Sayadi, Bessem; Marcos, Sylvie
2005-12-01
This paper develops a new multiuser detector based on a network of kalman filters (NKF) dealing with multiple access-interference (MAI), intersymbol Interference (ISI), and an impulsive observation noise. The two proposed schemes are based on the modeling of the DS-CDMA system by a discrete-time linear system that has non-Gaussian state and measurement noises. By approximating the non-Gaussian densities of the noises by a weighted sum of Gaussian terms and under the common MMSE estimation criterion, we first derive an NKF detector. This version is further optimized by introducing a feedback exploiting the ISI interference structure. The resulting scheme is an NKF detector based on a likelihood ratio test (LRT). Monte-Carlo simulations have shown that the NKF and the NKF based on LRT detectors significantly improve the efficiency and the performance of the classical Kalman algorithm.
Estimation of FBMC/OQAM fading channels using dual Kalman filters.
Aldababseh, Mahmoud; Jamoos, Ali
2014-01-01
We address the problem of estimating time-varying fading channels in filter bank multicarrier (FBMC/OQAM) wireless systems based on pilot symbols. The standard solution to this problem is the least square (LS) estimator or the minimum mean square error (MMSE) estimator with possible adaptive implementation using recursive least square (RLS) algorithm or least mean square (LMS) algorithm. However, these adaptive filters cannot well-exploit fading channel statistics. To take advantage of fading channel statistics, the time evolution of the fading channel is modeled by an autoregressive process and tracked by Kalman filter. Nevertheless, this requires the autoregressive parameters which are usually unknown. Thus, we propose to jointly estimate the FBMC/OQAM fading channels and their autoregressive parameters based on dual optimal Kalman filters. Once the fading channel coefficients at pilot symbol positions are estimated by the proposed method, the fading channel coefficients at data symbol positions are then estimated by using some interpolation methods such as linear, spline, or low-pass interpolation. The comparative simulation study we carried out with existing techniques confirms the effectiveness of the proposed method. PMID:24701181
Estimation of FBMC/OQAM Fading Channels Using Dual Kalman Filters
Aldababseh, Mahmoud
2014-01-01
We address the problem of estimating time-varying fading channels in filter bank multicarrier (FBMC/OQAM) wireless systems based on pilot symbols. The standard solution to this problem is the least square (LS) estimator or the minimum mean square error (MMSE) estimator with possible adaptive implementation using recursive least square (RLS) algorithm or least mean square (LMS) algorithm. However, these adaptive filters cannot well-exploit fading channel statistics. To take advantage of fading channel statistics, the time evolution of the fading channel is modeled by an autoregressive process and tracked by Kalman filter. Nevertheless, this requires the autoregressive parameters which are usually unknown. Thus, we propose to jointly estimate the FBMC/OQAM fading channels and their autoregressive parameters based on dual optimal Kalman filters. Once the fading channel coefficients at pilot symbol positions are estimated by the proposed method, the fading channel coefficients at data symbol positions are then estimated by using some interpolation methods such as linear, spline, or low-pass interpolation. The comparative simulation study we carried out with existing techniques confirms the effectiveness of the proposed method. PMID:24701181
The Kalman filter approach to inductively coupled plasma atomic emission spectrometry
NASA Astrophysics Data System (ADS)
Van Veen, E. H.; Bosch, S.; De Loos-Vollebregt, M. T. C.
1994-07-01
This article is an electronic publication in Spectrochimica Acta Electronica (SAE), the electronic section of Spectrochimica Acta Part B (SAB). The hardcopy text, comprising the main article and two appendices, is accompanied by a disk containing the compiled program, a reference manual and data files. The work deals with data handling in inductively coupled plasma atomic emission spectrometry (ICP-AES). With this technique, the analyte signal is superimposed on a background signal. When separating the signals by manual or automated three-point background correction, there are many instances in which the data reduction fails. Based on scans recorded in a fast-scanning mode and on a library of pure-component scans, the Kaiman filter approach models the emission in the spectral window (about 100 pm) of the analyte and mathematically solves the problem of background correction. By using a criterion-based algorithm to correct for optical instability, the uncertainty in the determination of the interferent line signal is eliminated. Therefore, the present filter implementation yields more accurate and precise results, especially in the case of line overlap. The Kalman filter Approach to Atomic Spectrometry (KAAS) software automatically processes Perkin-Elmer Plasma 1000/2000 text files, but can also handle ASCII data files. Practical and comprehensive examples are given to evoke the "Kalman filter feeling" in the crucial step of creating the emission model.
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2004-01-01
In this paper, an approach for in-flight 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 in terms of avoiding misclassifications of any anomalies. The proposed approach utilizes a bank of (m+1) Kalman filters where m is the number of sensors being monitored. One Kalman filter is used for the detection of component and actuator faults while each of the other m filters detects a fault in a specific sensor. With this setup, the overall robustness of the sensor FDI system to anomalies is enhanced. Moreover, numerous component fault events can be accounted for by the FDI system. The sensor FDI system is applied to a commercial aircraft engine simulation, and its performance is evaluated at multiple power settings at a cruise operating point using various fault scenarios.
Kalman filter estimation of attitude and gyro bias with the QUEST observation model
NASA Technical Reports Server (NTRS)
Sedlak, J.; Chu, D.
1993-01-01
The loss function for the Wahba attitude estimation problem employs unit vector observations with scalar weights. It is usually associated with the QUEST observation model, where the actual sensor noise is assumed the same for all components of the observed vector, regardless of the position in the field of view. The QUEST model has the great advantage of being sensor-independent except for the scalar parameter that characterizes the sensor errors. Although efficient algorithms for solving the Wahba problem exist, extending these algorithms to estimate gyro biases or sensor alignments has had mixed success. However, it is straightforward to estimate bias and alignment parameters with a Kalman filter. This paper investigates the use of an extended Kalman filter for the attitude and gyro bias that incorporates the QUEST observation model, to be referred to as the Unit Vector Filter (UVF). The UVF results are compared with those from a more conventional filter, the Real-Time Sequential Filter (RTSF), for which the residual is the two-dimensional projection of the unit vector onto the plane perpendicular to the sensor boresight. The RTSF is similar in design to that used by Multimission Modular Spacecraft for onboard attitude determination. An apparent obstacle to the use of unit vectors as measurements is their singular noise covariance matrix. Shuster has shown that this problem should not affect filter performance. The UVF and RTSF are tested using actual flight data from the Extreme Ultraviolet Explorer (EUVE). It is found that these filters generate nearly identical attitude and gyro bias estimates, thus validating the use of unit vectors and the QUEST noise model.
LIDAR-Aided Inertial Navigation with Extended Kalman Filtering for Pinpoint Landing
NASA Technical Reports Server (NTRS)
Busnardo, David M.; Aitken, Matthew L.; Tolson, Robert H.; Pierrottet, Diego; Amzajerdian, Farzin
2011-01-01
In support of NASA s Autonomous Landing and Hazard Avoidance Technology (ALHAT) project, an extended Kalman filter routine has been developed for estimating the position, velocity, and attitude of a spacecraft during the landing phase of a planetary mission. The proposed filter combines measurements of acceleration and angular velocity from an inertial measurement unit (IMU) with range and Doppler velocity observations from an onboard light detection and ranging (LIDAR) system. These high-precision LIDAR measurements of distance to the ground and approach velocity will enable both robotic and manned vehicles to land safely and precisely at scientifically interesting sites. The filter has been extensively tested using a lunar landing simulation and shown to improve navigation over flat surfaces or rough terrain. Experimental results from a helicopter flight test performed at NASA Dryden in August 2008 demonstrate that LIDAR can be employed to significantly improve navigation based exclusively on IMU integration.
NASA Astrophysics Data System (ADS)
Zhang, Q.; Meng, X.; Zhang, S.; Wang, Y.
2014-03-01
A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated GPS/SINS navigation system. The influence of different design parameters for H∞ cubature Kalman filter is analysed. It is found that when the design parameter is smaller, the robustness of the filter is stronger. However, the design parameter is easily out of step with the Riccati equation and the filter is easy to diverge. In this respect, the singular value decomposition algorithm is employed to replace Cholesky decomposition in the robust cubature Kalman filter. On the wider conditions for design parameter, the new filter is more robust. The testing results demonstrate that the proposed filter algorithm is more reliable and effective in dealing the data sets produced by the integrated GPS/SINS system.
Kalman Filter Based Feature Analysis for Tracking People from Airborne Images
NASA Astrophysics Data System (ADS)
Sirmacek, B.; Reinartz, P.
2011-09-01
Recently, analysis of man events in real-time using computer vision techniques became a very important research field. Especially, understanding motion of people can be helpful to prevent unpleasant conditions. Understanding behavioral dynamics of people can also help to estimate future states of underground passages, shopping center like public entrances, or streets. In order to bring an automated solution to this problem, we propose a novel approach using airborne image sequences. Although airborne image resolutions are not enough to see each person in detail, we can still notice a change of color components in the place where a person exists. Therefore, we propose a color feature detection based probabilistic framework in order to detect people automatically. Extracted local features behave as observations of the probability density function (pdf) of the people locations to be estimated. Using an adaptive kernel density estimation method, we estimate the corresponding pdf. First, we use estimated pdf to detect boundaries of dense crowds. After that, using background information of dense crowds and previously extracted local features, we detect other people in non-crowd regions automatically for each image in the sequence. We benefit from Kalman filtering to track motion of detected people. To test our algorithm, we use a stadium entrance image data set taken from airborne camera system. Our experimental results indicate possible usage of the algorithm in real-life man events. We believe that the proposed approach can also provide crucial information to police departments and crisis management teams to achieve more detailed observations of people in large open area events to prevent possible accidents or unpleasant conditions.
Data Assimilation for Vadose Zone Flow Modeling Using the Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Zhang, Y.; Schaap, M. G.; Zha, Y.; Xue, L.
2015-12-01
The natural system is open and complex and the hydraulic parameters needed for describing flow and transport in the vadose zone are often poorly known, making it prone to multiple interpretations, mathematical descriptions and uncertainty. Quite often a reasonable "handle" on a sites flow characteristics can be gained only through direct observation of the flow processes itself, determination of the spatial- and probability distributions of material properties combined with computationally expensive inversions of the Richards equation. In groundwater systems, the ensemble Kalman filter (EnKF) has proven to be an effective alternative to model inversions by assimilating observations directly into an ensemble of groundwater models from which time and/or space-variable variable probabilistic quantities of the flow process can be derived. Application of EnKF to Richards equation-type unsaturated flow problems, however, is more challenging than in groundwater systems because the relation of state and model parameters is strongly nonlinear. In addition, the type of functional dependence of moisture content and hydraulic conductivity on matric potential leads to high-dimensional (in the parameter space) problems even under conditions where closed-form expressions of these models such as van Genuchten-Mualem formulations are used. In this study, we updated soil water retention parameters and hydraulic conductivity together and used Restart EnKF, which rerun the nonlinear model from the initial time to obtain the updated state variables, in synthetic cases to explore the factors that may influence estimation results, including the initial estimate, the ensemble size, the observation error, and the assimilation interval. We embedded the EnKF into the Bayesian model averaging framework to enhance the model reliability and reduce predictive uncertainties. This approach is evaluated from a 15 m deep semi-arid highly heterogeneous and anisotropic vadose zone site at the
Data assimilation in terrestrial magnetism: An ensemble Kalman filter approach (Invited)
NASA Astrophysics Data System (ADS)
Fournier, A.; Aubert, J.; Nerger, L.; Sanchez, S. M.
2013-12-01
The convective flow of liquid metal inside the Earth's outer core sustains the Earth's magnetic field against Ohmic decay. The resulting nonlinear process, termed the geodynamo, operates on a wide range of time and length scales. Direct and indirect observations of the geomagnetic field at the Earth's surface document the variability of the geodynamo over the archeological, historical and modern periods, with increasing accuracy. These observations are slaved to changes in the magnetic field at the core-mantle boundary (CMB), that is the top of the region in which the geodynamo operates. The motivation behind considering the application of data assimilation techniques in geomagnetism is at least twofold: first, to combine data and physics to better constrain the state of Earth's core (at the CMB and below), and second, to forecast the evolution of the geomagnetic field. After a general introduction to the problem at hand, we will report on the application of the ensemble Kalman filter to a numerical dynamo model, whose state vector comprises 106 variables. Our strategy rests on a modified version of the parallel data assimilation framework of Nerger & Hiller (Comp. Geosci., 2013). Our synthetic tests demonstrate the efficacy and adaptivity of the method, provided the ensemble comprises O(500) members, in which case the typical spin-up time of the system is O(1000) years. We will show that the model we used for these proof-of-concept experiments is not so well-suited for the assimilation of real datasets, and we will conclude this presentation by discussing how it should be improved, and what this improvement implies in terms of computational and storage requirements.
A fuzzy-augmented Kalman filter for IMU/GPS integration
NASA Astrophysics Data System (ADS)
El-Sheimy, N.; Abdel-Hamid, W.
2007-09-01
Most of the present techniques for integrating Inertial Measurement Units (IMU) and Global Positioning Systems (GPS) utilize Kalman filtering (KF) as the integration estimation technique. KF is a recursive algorithm designed to compute corrections to a system based on external measurements. In inertial navigation, this can be accomplished by using an external navigation reference such as GPS. As long as GPS measurements are available, the KF solution of IMU/GPS integration works efficiently and provides accurate estimate of the navigation states. Nevertheless, during GPS signal outages, the functionality of KF update engine is disrupted due to the lack of GPS update measurements and therefore KF works only in prediction mode. Moreover, IMUs, particularly those integrating low-cost sensors, suffer from one serious limitation: drift rate errors rapidly accumulate with the passage of time. As a result, the corresponding state estimate will also quickly drift over time causing a dramatic degradation in the overall accuracy of the integrated system. Performance improvements of integrated IMUs, utilizing low-cost sensors, and GPS are presented in this paper. This achieved through the implantation of a new technique which augment KF and Fuzzy logic principles. In the innovation in the new technique is in its ability to generate the update measurements (positions and velocity error measurements) to the KF update engine even during GPS signal outages. This proposed technique has been tested on real MEMS inertial and GPS data collected in a land vehicle navigation test. The test results indicate that the proposed Fuzzy model can efficiently compensate for GPS updates during short GPS signal outages.
NASA Astrophysics Data System (ADS)
He, Chengfei; Zhi, Xiefei; You, Qinglong; Song, Bin; Fraedrich, Klaus
2015-08-01
This study conducted 24- to 72-h multi-model ensemble forecasts to explore the tracks and intensities (central mean sea level pressure) of tropical cyclones (TCs). Forecast data for the northwestern Pacific basin in 2010 and 2011 were selected from the China Meteorological Administration, European Centre for Medium-Range Weather Forecasts (ECMWF), Japan Meteorological Agency, and National Centers for Environmental Prediction datasets of the Observing System Research and Predictability Experiment Interactive Grand Global Ensemble project. The Kalman Filter was employed to conduct the TC forecasts, along with the ensemble mean and super-ensemble for comparison. The following results were obtained: (1) The statistical-dynamic Kalman Filter, in which recent observations are given more importance and model weighting coefficients are adjusted over time, produced quite different results from that of the super-ensemble. (2) The Kalman Filter reduced the TC mean absolute track forecast error by approximately 50, 80 and 100 km in the 24-, 48- and 72-h forecasts, respectively, compared with the best individual model (ECMWF). Also, the intensity forecasts were improved by the Kalman Filter to some extent in terms of average intensity deviation (AID) and correlation coefficients with reanalysis intensity data. Overall, the Kalman Filter technique performed better compared to multi-models, the ensemble mean, and the super-ensemble in 3-day forecasts. The implication of this study is that this technique appears to be a very promising statistical-dynamic method for multi-model ensemble forecasts of TCs.
NASA Astrophysics Data System (ADS)
Lorenz, Christof; Tourian, Mohammad J.; Devaraju, Balaji; Sneeuw, Nico; Kunstmann, Harald
2015-10-01
In order to cope with the steady decline of the number of in situ gauges worldwide, there is a growing need for alternative methods to estimate runoff. We present an Ensemble Kalman Filter based approach that allows us to conclude on runoff for poorly or irregularly gauged basins. The approach focuses on the application of publicly available global hydrometeorological data sets for precipitation (GPCC, GPCP, CRU, UDEL), evapotranspiration (MODIS, FLUXNET, GLEAM, ERA interim, GLDAS), and water storage changes (GRACE, WGHM, GLDAS, MERRA LAND). Furthermore, runoff data from the GRDC and satellite altimetry derived estimates are used. We follow a least squares prediction that exploits the joint temporal and spatial auto- and cross-covariance structures of precipitation, evapotranspiration, water storage changes and runoff. We further consider time-dependent uncertainty estimates derived from all data sets. Our in-depth analysis comprises of 29 large river basins of different climate regions, with which runoff is predicted for a subset of 16 basins. Six configurations are analyzed: the Ensemble Kalman Filter (Smoother) and the hard (soft) Constrained Ensemble Kalman Filter (Smoother). Comparing the predictions to observed monthly runoff shows correlations larger than 0.5, percentage biases lower than ± 20%, and NSE-values larger than 0.5. A modified NSE-metric, stressing the difference to the mean annual cycle, shows an improvement of runoff predictions for 14 of the 16 basins. The proposed method is able to provide runoff estimates for nearly 100 poorly gauged basins covering an area of more than 11,500,000 km2 with a freshwater discharge, in volume, of more than 125,000 m3/s.
Application of unscented Kalman filter for robust pose estimation in image-guided surgery
NASA Astrophysics Data System (ADS)
Vaccarella, Alberto; De Momi, Elena; Valenti, Marta; Ferrigno, Giancarlo; Enquobahrie, Andinet
2012-02-01
Image-guided surgery (IGS) allows clinicians to view current, intra-operative scenes superimposed on preoperative images (typically MRI or CT scans). IGS systems use localization systems to track and visualize surgical tools overlaid on top of preoperative images of the patient during surgery. The most commonly used localization systems in the Operating Rooms (OR) are optical tracking systems (OTS) due to their ease of use and cost effectiveness. However, OTS' suffer from the major drawback of line-of-sight requirements. State space approaches based on different implementations of the Kalman filter have recently been investigated in order to compensate for short line-of-sight occlusion. However, the proposed parameterizations for the rigid body orientation suffer from singularities at certain values of rotation angles. The purpose of this work is to develop a quaternion-based Unscented Kalman Filter (UKF) for robust optical tracking of both position and orientation of surgical tools in order to compensate marker occlusion issues. This paper presents preliminary results towards a Kalman-based Sensor Management Engine (SME). The engine will filter and fuse multimodal tracking streams of data. This work was motivated by our experience working in robot-based applications for keyhole neurosurgery (ROBOCAST project). The algorithm was evaluated using real data from NDI Polaris tracker. The results show that our estimation technique is able to compensate for marker occlusion with a maximum error of 2.5° for orientation and 2.36 mm for position. The proposed approach will be useful in over-crowded state-of-the-art ORs where achieving continuous visibility of all tracked objects will be difficult.
Dual extended Kalman filter for combined estimation of vehicle state and road friction
NASA Astrophysics Data System (ADS)
Zong, Changfu; Hu, Dan; Zheng, Hongyu
2013-03-01
Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute(HSRI) tire model; the dual extended Kalman filter (DEKF) technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions(high-friction, low-friction, and joint-friction). On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.
Adaptive Kalman filtering for real-time mapping of the visual field
Ward, B. Douglas; Janik, John; Mazaheri, Yousef; Ma, Yan; DeYoe, Edgar A.
2013-01-01
This paper demonstrates the feasibility of real-time mapping of the visual field for clinical applications. Specifically, three aspects of this problem were considered: (1) experimental design, (2) statistical analysis, and (3) display of results. Proper experimental design is essential to achieving a successful outcome, particularly for real-time applications. A random-block experimental design was shown to have less sensitivity to measurement noise, as well as greater robustness to error in modeling of the hemodynamic impulse response function (IRF) and greater flexibility than common alternatives. In addition, random encoding of the visual field allows for the detection of voxels that are responsive to multiple, not necessarily contiguous, regions of the visual field. Due to its recursive nature, the Kalman filter is ideally suited for real-time statistical analysis of visual field mapping data. An important feature of the Kalman filter is that it can be used for nonstationary time series analysis. The capability of the Kalman filter to adapt, in real time, to abrupt changes in the baseline arising from subject motion inside the scanner and other external system disturbances is important for the success of clinical applications. The clinician needs real-time information to evaluate the success or failure of the imaging run and to decide whether to extend, modify, or terminate the run. Accordingly, the analytical software provides real-time displays of (1) brain activation maps for each stimulus segment, (2) voxel-wise spatial tuning profiles, (3) time plots of the variability of response parameters, and (4) time plots of activated volume. PMID:22100663
On the convergence of (ensemble) Kalman filters and smoothers onto the unstable subspace
NASA Astrophysics Data System (ADS)
Bocquet, Marc
2016-04-01
The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters and smoothers. In particular, as emphasised in the seminal work of Anna Trevisan and co-authors, the error covariance matrix is asymptotically supported by the unstable and neutral subspace only, i.e. it is span by the backward Lyapunov vectors with non-negative exponents. This behaviour is at the heart of algorithms known as Assimilation in the Unstable Subspace, although its formal proof was still missing. This convergence property, its analytic proof, meaning and implications for the design of efficient reduced-order data assimilation algorithms are the topics of this talk. The structure of the talk is as follows. Firstly, we provide the analytic proof of the convergence on the unstable and neutral subspace in the linear dynamics and linear observation operator case, along with rigorous results giving the rate of such convergence. The derivation is based on an expression that relates explicitly the covariance matrix at an arbitrary time with the initial error covariance. Numerical results are also shown to illustrate and support the mathematical claims. Secondly, we discuss how this neat picture is modified when the dynamics become nonlinear and chaotic and when it is not possible to derive analytic formulas. In this case an ensemble Kalman filter (EnKF) is used and the connection between the convergence properties on the unstable-neutral subspace and the EnKF covariance inflation is discussed. We also explain why, in the perfect model setting, the iterative ensemble Kalman smoother (IEnKS), as an efficient filtering and smoothing technique, has an error covariance matrix whose projection is more focused on the unstable-neutral subspace than that of the EnKF. This contribution results from collaborations with A. Carrassi, K. S. Gurumoorthy, A. Apte, C. Grudzien, and C. K. R. T. Jones.
Wavefront correction with Kalman filtering for the WFIRST-AFTA coronagraph instrument
NASA Astrophysics Data System (ADS)
Riggs, A. J. Eldorado; Kasdin, N. Jeremy; Groff, Tyler D.
2015-09-01
The only way to characterize most exoplanets spectrally is via direct imaging. For example, the Coronagraph Instrument (CGI) on the proposed Wide-Field Infrared Survey Telescope-Astrophysics Focused Telescope Assets (WFIRST-AFTA) mission plans to image and characterize several cool gas giants around nearby stars. The integration time on these faint exoplanets will be many hours to days. A crucial assumption for mission planning is that the time required to dig a dark hole (a region of high star-to-planet contrast) with deformable mirrors is small compared to science integration time. The science camera must be used as the wavefront sensor to avoid non-common path aberrations, but this approach can be quite time intensive. Several estimation images are required to build an estimate of the starlight electric field before it can be partially corrected, and this process is repeated iteratively until high contrast is reached. Here we present simulated results of batch process and recursive wavefront estimation schemes. In particular, we test a Kalman filter and an iterative extended Kalman filter (IEKF) to reduce the total exposure time and improve the robustness of wavefront correction for the WFIRST-AFTA CGI. An IEKF or other nonlinear filter also allows recursive, real-time estimation of sources incoherent with the star, such as exoplanets and disks, and may therefore reduce detection uncertainty.
A simulation study of turbofan engine deterioration estimation using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Lambert, Heather H.
1991-01-01
Deterioration of engine components may cause off-normal engine operation. The result is an unecessary loss of performance, because the fixed schedules are designed to accommodate a wide range of engine health. These fixed control schedules may not be optimal for a deteriorated engine. This problem may be solved by including a measure of deterioration in determining the control variables. These engine deterioration parameters usually cannot be measured directly but can be estimated. A Kalman filter design is presented for estimating two performance parameters that account for engine deterioration: high and low pressure turbine delta efficiencies. The delta efficiency parameters model variations of the high and low pressure turbine efficiencies from nominal values. The filter has a design condition of Mach 0.90, 30,000 ft altitude, and 47 deg power level angle (PLA). It was evaluated using a nonlinear simulation of the F100 engine model derivative (EMD) engine, at the design Mach number and altitude over a PLA range of 43 to 55 deg. It was found that known high pressure turbine delta efficiencies of -2.5 percent and low pressure turbine delta efficiencies of -1.0 percent can be estimated with an accuracy of + or - 0.25 percent efficiency with a Kalman filter. If both the high and low pressure turbine are deteriorated, the delta efficiencies of -2.5 percent to both turbines can be estimated with the same accuracy.
Aircraft Engine Sensor/Actuator/Component Fault Diagnosis Using a Bank of Kalman Filters
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L. (Technical Monitor)
2003-01-01
In this report, a fault detection and isolation (FDI) system which utilizes a bank of Kalman filters is developed for aircraft engine sensor and actuator FDI in conjunction with the detection of component faults. This FDI approach uses multiple Kalman filters, each of which is designed based on a specific hypothesis 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, from which a specific fault is isolated. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The performance of the FDI system is evaluated against a nonlinear engine simulation for various engine faults at cruise operating conditions. In order to mimic the real engine environment, the nonlinear simulation is executed not only at the nominal, or healthy, condition but also at aged conditions. When the FDI system designed at the healthy condition is applied to an aged engine, the effectiveness of the FDI system is impacted by the mismatch in the engine health condition. Depending on its severity, this mismatch can cause the FDI system to generate incorrect diagnostic results, such as false alarms and missed detections. To partially recover the nominal performance, two approaches, which incorporate information regarding the engine s aging condition in the FDI system, will be discussed and evaluated. The results indicate that the proposed FDI system is promising for reliable diagnostics of aircraft engines.
Tracking and Data Relay Satellite (TDRS) Orbit Estimation Using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Ward, Douglas T.; Dang, Ket D.; Slojkowski, Steve; Blizzard, Mike; Jenkins, Greg
2007-01-01
Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.
NASA Astrophysics Data System (ADS)
Gao, Min; Zhang, Heng; Zhou, Yulong; Zhang, Baoquan
2016-03-01
In an effort to improve the tracking accuracy of the ground maneuvering target in infrared images, a method is proposed based on the strong tracking filter (STF) and the cubature Kalman filter (CKF) algorithms. In this method, the fading factor is introduced from the STF algorithm and is calculated by transforming the nonlinear measurement variance matrix to be linear approximately, and then the fading factor is used to correct the prediction error covariance matrix (PECM) of CKF, so that the gain matrix can be adjusted at real time and hence the tracking ability of the maneuvering target could be improved. After the digital simulation experiment, it is shown that, comparing with CKF and the unscented Kalman filter algorithms, the average tracking accuracy of the location is increased by more than 20% with the target velocity under 20 m/s and acceleration under 5 m/s2, and it can even be increased by 50% when the target step maneuver occurs. With the tracking experiment on the real infrared tank images, it can be concluded that the target could be tracked stably by the proposed method, and the maximum tracking error is not more than 8 pixels even though the 180 deg turning takes place.
NASA Technical Reports Server (NTRS)
Galvan, Jose Ramon; Saxena, Abhinav; Goebel, Kai Frank
2012-01-01
This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process, and how it relates to uncertainty representation, management and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for two while considering prognostics in making critical decisions.
Liu, Zhe; Liu, Zhigang; Deng, Zhongwen; Tao, Long
2016-04-10
Optical frequency scanning nonlinearity seriously affects interference signal phase extraction accuracy in frequency-scanning interferometry systems using external cavity diode lasers. In this paper, an interference signal frequency tracking method using an extended Kalman filter is proposed. The interferometric phase is obtained by integrating the estimated instantaneous frequency over time. The method is independent of the laser's optical frequency scanning nonlinearity. The method is validated through simulations and experiments. The experimental results demonstrate that the relative phase extraction error in the fractional part is <1.5% with the proposed method and the standard deviation of absolute distance measurement is <2.4 μm. PMID:27139864
Inertial Head-Tracker Sensor Fusion by a Complementary Separate-Bias Kalman Filter
NASA Technical Reports Server (NTRS)
Foxlin, Eric
1996-01-01
Current virtual environment and teleoperator applications are hampered by the need for an accurate, quick-responding head-tracking system with a large working volume. Gyroscopic orientation sensors can overcome problems with jitter, latency, interference, line-of-sight obscurations, and limited range, but suffer from slow drift. Gravimetric inclinometers can detect attitude without drifting, but are slow and sensitive to transverse accelerations. This paper describes the design of a Kalman filter to integrate the data from these two types of sensors in order to achieve the excellent dynamic response of an inertial system without drift, and without the acceleration sensitivity of inclinometers.
Czaplewski, Raymond L.
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 study variables and auxiliary sensor variables. A National Forest Inventory (NFI) illustrates application within an official statistics program. Practical recommendations regarding remote sensing and statistical issues are offered. This algorithm has the potential to increase the value of synoptic sensor data for statistical monitoring of large geographic areas. PMID:26393588
On-board identification of tyre cornering stiffness using dual Kalman filter and GPS
NASA Astrophysics Data System (ADS)
Lee, Seungyong; Nakano, Kimihiko; Ohori, Masanori
2015-04-01
Cornering stiffness is one of the important vehicle parameters for steering control of a vehicle. Accurate vehicle parameters are essential for a high performance of vehicle control because vehicle control is significantly affected by variations in vehicle parameters. In this study, a novel identification method is proposed using a dual Kalman filter algorithm and a GPS (global positioning system) measurement system to estimate the cornering stiffness for on-board identification. Performance of the identification method is examined with experiments, and the estimation results show that this identification method is effective on both a flat road and a banked curve road.
Czaplewski, Raymond L
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 study variables and auxiliary sensor variables. A National Forest Inventory (NFI) illustrates application within an official statistics program. Practical recommendations regarding remote sensing and statistical issues are offered. This algorithm has the potential to increase the value of synoptic sensor data for statistical monitoring of large geographic areas. PMID:26393588
Application of Ensemble Kalman Filter in Power System State Tracking and Sensitivity
Li, Yulan; Huang, Zhenyu; Zhou, Ning; Lee, Barry; Diao, Ruisheng; Du, Pengwei
2012-05-01
Ensemble Kalman Filter (EnKF) is proposed to track dynamic states of generators. The algorithm of EnKF and its application to generator state tracking are presented in detail. The accuracy and sensitivity of the method are analyzed with respect to initial state errors, measurement noise, unknown fault locations, time steps and parameter errors. It is demonstrated through simulation studies that even with some errors in the parameters, the developed EnKF can effectively track generator dynamic states using disturbance data.
Application of Extended Kalman Filter Techniques for Dynamic Model Parameter Calibration
Huang, Zhenyu; Du, Pengwei; Kosterev, Dmitry; Yang, Bo
2009-07-26
Abstract -Phasor measurement has previously been used for sub-system model validation, which enables rigorous comparison of model simulation and recorded dynamics and facilitates identification of problematic model components. Recent work extends the sub-system model validation approach with a focus on how model parameters may be calibrated to match recorded dynamics. In this paper, a calibration method using Extended Kalman Filter (EKF) technique is proposed. This paper presents the formulation as well as case studies to show the validity of the EKF-based parameter calibration method. The proposed calibration method is expected to be a cost-effective means complementary to traditional equipment testing for improving dynamic model quality.
Inertial head-tracker sensor fusion by a complementary separate-bias Kalman filter
NASA Technical Reports Server (NTRS)
Foxlin, Eric
1996-01-01
Current virtual environment and teleoperator applications are hampered by the need for an accurate, quick responding head-tracking system with a large working volume. Gyroscopic orientation sensors can overcome problems with jitter, latency, interference, line-of-sight obscurations, and limited range, but suffer from slow drift. Gravimetric inclinometers can detect attitude without drifting, but are slow and sensitive to transverse accelerations. This paper describes the design of a Kalman filter to integrate the data from these two types of sensors in order to achieve the excellent dynamic response of an inertial system without drift, and without the acceleration sensitivity of inclinometers.
Fast Ensemble Kalman Filter for Model Calibration with Streamline-Assisted Pseudo Forecasts
NASA Astrophysics Data System (ADS)
King, M. J.; Khodabakhshi, M.; Jafarpour, B.
2011-12-01
Characterization and modeling of subsurface flow and transport properties is critical for modeling, performance prediction and design of a number of important environmental and energy applications, including groundwater flow and contaminant transport, energy recovery from geothermal and hydrocarbon reservoirs, and geologic storage of CO2. Inverse modeling is typically applied to infer hydraulic rock properties from available static and dynamic measurements. Data sparsity and nonlinearity with respect to model parameters often result in significant uncertainty and solution non-uniqueness in solving the resulting inverse problems. Stochastic methods have become increasingly popular for dealing with inverse modeling solution non-uniqueness and uncertainty quantification. In particular, the ensemble Kalman filter (EnKF) has been widely applied for stochastic characterization of aquifer hydraulic properties from dynamic field measurements. For practical applications, where large-scale models are used, the computational cost of the forward simulation severely constrains the number of model realizations that can be included in ensemble predictions. Consequently, the statistics computed from a limited-size ensemble becomes spurious, making the resulting EnKF model updates unreliable. Localization and local analysis methods have been introduced to mitigate the effect of spurious correlations by reducing or removing the unphysical numerical correlations between model parameters (and/or states) and observations at distant locations. While these methods have proven useful, they require prior tuning of localization parameters and do not address the impact of small ensemble size approximation on the existing physical correlations between parameters and close-by observations. An alternative approach to localization is to approximate the correct statistics from computationally efficient surrogate models. Here, we present an efficient streamline-based pseudo forecast method for
NASA Astrophysics Data System (ADS)
Wang, Xudong; Syrmos, Vassilis L.
2004-07-01
In this paper, an adaptive reconfigurable control system based on extended Kalman filter approach and eigenstructure assignments is proposed. System identification is carried out using an extended Kalman filter (EKF) approach. An eigenstructure assignment (EA) technique is applied for reconfigurable feedback control law design to recover the system dynamic performance. The reconfigurable feedforward controllers are designed to achieve the steady-state tracking using input weighting approach. The proposed scheme can identify not only actuator and sensor variations, but also changes in the system structures using the extended Kalman filtering method. The overall design is robust with respect to uncertainties in the state-space matrices of the reconfigured system. To illustrate the effectiveness of the proposed reconfigurable control system design technique, an aircraft longitudinal vertical takeoff and landing (VTOL) control system is used to demonstrate the reconfiguration procedure.
NASA Astrophysics Data System (ADS)
Zaugg, David A.; Samuel, Alphonso A.; Waagen, Donald E.; Schmitt, Harry A.
2004-07-01
Bearings-only tracking is widely used in the defense arena. Its value can be exploited in systems using optical sensors and sonar, among others. Non-linearity and non-Gaussian prior statistics are among the complications of bearings-only tracking. Several filters have been used to overcome these obstacles, including particle filters and multiple hypothesis extended Kalman filters (MHEKF). Particle filters can accommodate a wide range of distributions and do not need to be linearized. Because of this they seem ideally suited for this problem. A MHEKF can only approximate the prior distribution of a bearings-only tracking scenario and needs to be linearized. However, the likelihood distribution maintained for each MHEKF hypothesis demonstrates significant memory and lends stability to the algorithm, potentially enhancing tracking convergence. Also, the MHEKF is insensitive to outliers. For the scenarios under investigation, the sensor platform is tracking a moving and a stationary target. The sensor is allowed to maneuver in an attempt to maximize tracking performance. For these scenarios, we compare and contrast the acquisition time and mean-squared tracking error performance characteristics of particle filters and MHEKF via Monte Carlo simulation.
Nenov, Valeriy; Bergsneider, Marvin; Glenn, Thomas C.; Vespa, Paul; Martin, Neil
2007-01-01
Impeded by the rigid skull, assessment of physiological variables of the intracranial system is difficult. A hidden state estimation approach is used in the present work to facilitate the estimation of unobserved variables from available clinical measurements including intracranial pressure (ICP) and cerebral blood flow velocity (CBFV). The estimation algorithm is based on a modified nonlinear intracranial mathematical model, whose parameters are first identified in an offline stage using a nonlinear optimization paradigm. Following the offline stage, an online filtering process is performed using a nonlinear Kalman filter (KF)-like state estimator that is equipped with a new way of deriving the Kalman gain satisfying the physiological constraints on the state variables. The proposed method is then validated by comparing different state estimation methods and input/output (I/O) configurations using simulated data. It is also applied to a set of CBFV, ICP and arterial blood pressure (ABP) signal segments from brain injury patients. The results indicated that the proposed constrained nonlinear KF achieved the best performance among the evaluated state estimators and that the state estimator combined with the I/O configuration that has ICP as the measured output can potentially be used to estimate CBFV continuously. Finally, the state estimator combined with the I/O configuration that has both ICP and CBFV as outputs can potentially estimate the lumped cerebral arterial radii, which are not measurable in a typical clinical environment. PMID:17281533
Towards denoising XMCD movies of fast magnetization dynamics using extended Kalman filter.
Kopp, M; Harmeling, S; Schütz, G; Schölkopf, B; Fähnle, M
2015-01-01
The Kalman filter is a well-established approach to get information on the time-dependent state of a system from noisy observations. It was developed in the context of the Apollo project to see the deviation of the true trajectory of a rocket from the desired trajectory. Afterwards it was applied to many different systems with small numbers of components of the respective state vector (typically about 10). In all cases the equation of motion for the state vector was known exactly. The fast dissipative magnetization dynamics is often investigated by x-ray magnetic circular dichroism movies (XMCD movies), which are often very noisy. In this situation the number of components of the state vector is extremely large (about 10(5)), and the equation of motion for the dissipative magnetization dynamics (especially the values of the material parameters of this equation) is not well known. In the present paper it is shown by theoretical considerations that - nevertheless - there is no principle problem for the use of the Kalman filter to denoise XMCD movies of fast dissipative magnetization dynamics. PMID:25461588
Flight test development and evaluation of a Kalman filter state estimator for low-altitude flight
NASA Technical Reports Server (NTRS)
Zelenka, Richard E.; Yee, Zee; Zirkler, Andre
1993-01-01
Flight operations dependent on digitized terrain elevation data for navigational reference or trajectory generation are constrained in minimum flight altitude, due to airborne navigation errors and inaccuracies of the reference terrain elevation data. This limitation is not restrictive in traditional medium-altitude implementations of such databases, such as in unmanned aerial vehicles, missiles, or high-performance, high-speed aircraft. In low-altitude, lower speed terrain hugging helicopter missions, however, such constraints on minimum flight altitudes greatly reduce the effectiveness of their missions and diminish the benefits of employing terrain elevation maps. A Kalman filter state estimator has been developed which blends airborne navigation, stored terrain elevation data, and a radar altimeter in estimating above-ground-level (AGL) altitude. This AGL state estimator was integrated in a near-terrain guidance system aboard a research helicopter and flight tested in moderately rugged terrain over a variety of flight and system conditions. The minimum operating altidude of the terrain database referenced guidance system was reduced from 300 ft to 150 ft with the addition of the Kalman filter state estimator.
Kalman Filters in Geotechnical Monitoring of Ground Subsidence Using Data from MEMS Sensors.
Li, Cheng; Azzam, Rafig; Fernández-Steeger, Tomás M
2016-01-01
The fast development of wireless sensor networks and MEMS make it possible to set up today real-time wireless geotechnical monitoring. To handle interferences and noises from the output data, Kalman filter can be selected as a method to achieve a more realistic estimate of the observations. In this paper, a one-day wireless measurement using accelerometers and inclinometers was deployed on top of a tunnel section under construction in order to monitor ground subsidence. The normal vectors of the sensors were firstly obtained with the help of rotation matrices, and then be projected to the plane of longitudinal section, by which the dip angles over time would be obtained via a trigonometric function. Finally, a centralized Kalman filter was applied to estimate the tilt angles of the sensor nodes based on the data from the embedded accelerometer and the inclinometer. Comparing the results from two sensor nodes deployed away and on the track respectively, the passing of the tunnel boring machine can be identified from unusual performances. Using this method, the ground settlement due to excavation can be measured and a real-time monitoring of ground subsidence can be realized. PMID:27447630
Kalman Filters in Geotechnical Monitoring of Ground Subsidence Using Data from MEMS Sensors
Li, Cheng; Azzam, Rafig; Fernández-Steeger, Tomás M.
2016-01-01
The fast development of wireless sensor networks and MEMS make it possible to set up today real-time wireless geotechnical monitoring. To handle interferences and noises from the output data, Kalman filter can be selected as a method to achieve a more realistic estimate of the observations. In this paper, a one-day wireless measurement using accelerometers and inclinometers was deployed on top of a tunnel section under construction in order to monitor ground subsidence. The normal vectors of the sensors were firstly obtained with the help of rotation matrices, and then be projected to the plane of longitudinal section, by which the dip angles over time would be obtained via a trigonometric function. Finally, a centralized Kalman filter was applied to estimate the tilt angles of the sensor nodes based on the data from the embedded accelerometer and the inclinometer. Comparing the results from two sensor nodes deployed away and on the track respectively, the passing of the tunnel boring machine can be identified from unusual performances. Using this method, the ground settlement due to excavation can be measured and a real-time monitoring of ground subsidence can be realized. PMID:27447630
Enhanced tracking of airborne targets using a correlator-Kalman filter
NASA Astrophysics Data System (ADS)
Millner, P. P.
1982-12-01
Over the past four years considerable work has been accomplished at the Air Force Institute of Technology to improve the tracking capability of the high energy laser weapon against airborne targets. In this research, many of the prior concepts are incorporated into a correlator/Kalman filter to develop a tracker capable of providing precise target position estimates in a dynamic shortrange environment using a Forward Looking Infrared sensor (FLIR) to provide measurement data. Digital signal processing in employed on the FLIR data to identify the underlying target intensity shape function when the target under consideration has either single or multiple hot spots. The estimated target shape function is then used as the template in a correlation algorithm, where spatial and frequency domain correlation techniques were explored, to determine the offsets between the template and the incoming measurement. These offsets are used as pseudomeasurements in a linear Kalman filter which exploits knowledge of the process dynamics and statistical knowledge of the correlator error to enhance the position estimates.
Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation
NASA Astrophysics Data System (ADS)
Bocquet, M.; Raanes, P. N.; Hannart, A.
2015-07-01
The ensemble Kalman filter (EnKF) is a powerful data assimilation method meant for high-dimensional nonlinear systems. But its implementation requires fixes such as localization and inflation. The recently developed finite-size ensemble Kalman filter (EnKF-N) does not require multiplicative inflation meant to counteract sampling errors. Aside from the practical interest of avoiding the tuning of inflation in perfect model data assimilation experiments, it also offers theoretical insights and a unique perspective on the EnKF. Here, we revisit, clarify and correct several key points of the EnKF-N derivation. This simplifies the use of the method, and expands its validity. The EnKF is shown to not only rely on the observations and the forecast ensemble but also on an implicit prior assumption, termed hyperprior, that fills in the gap of missing information. In the EnKF-N framework, this assumption is made explicit through a Bayesian hierarchy. This hyperprior has been so far chosen to be the uninformative Jeffreys' prior. Here, this choice is revisited to improve the performance of the EnKF-N in the regime where the analysis strongly relaxes to the prior. Moreover, it is shown that the EnKF-N can be extended with a normal-inverse-Wishart informative hyperprior that additionally introduces climatological error statistics. This can be identified as a hybrid 3D-Var/EnKF counterpart to the EnKF-N.
Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation
NASA Astrophysics Data System (ADS)
Bocquet, M.; Raanes, P. N.; Hannart, A.
2015-11-01
The ensemble Kalman filter (EnKF) is a powerful data assimilation method meant for high-dimensional nonlinear systems. But its implementation requires somewhat ad hoc procedures such as localization and inflation. The recently developed finite-size ensemble Kalman filter (EnKF-N) does not require multiplicative inflation meant to counteract sampling errors. Aside from the practical interest in avoiding the tuning of inflation in perfect model data assimilation experiments, it also offers theoretical insights and a unique perspective on the EnKF. Here, we revisit, clarify and correct several key points of the EnKF-N derivation. This simplifies the use of the method, and expands its validity. The EnKF is shown to not only rely on the observations and the forecast ensemble, but also on an implicit prior assumption, termed hyperprior, that fills in the gap of missing information. In the EnKF-N framework, this assumption is made explicit through a Bayesian hierarchy. This hyperprior has so far been chosen to be the uninformative Jeffreys prior. Here, this choice is revisited to improve the performance of the EnKF-N in the regime where the analysis is strongly dominated by the prior. Moreover, it is shown that the EnKF-N can be extended with a normal-inverse Wishart informative hyperprior that introduces additional information on error statistics. This can be identified as a hybrid EnKF-3D-Var counterpart to the EnKF-N.
Adaptive Kalman filter based state of charge estimation algorithm for lithium-ion battery
NASA Astrophysics Data System (ADS)
Zheng, Hong; Liu, Xu; Wei, Min
2015-09-01
In order to improve the accuracy of the battery state of charge (SOC) estimation, in this paper we take a lithium-ion battery as an example to study the adaptive Kalman filter based SOC estimation algorithm. Firstly, the second-order battery system model is introduced. Meanwhile, the temperature and charge rate are introduced into the model. Then, the temperature and the charge rate are adopted to estimate the battery SOC, with the help of the parameters of an adaptive Kalman filter based estimation algorithm model. Afterwards, it is verified by the numerical simulation that in the ideal case, the accuracy of SOC estimation can be enhanced by adding two elements, namely, the temperature and charge rate. Finally, the actual road conditions are simulated with ADVISOR, and the simulation results show that the proposed method improves the accuracy of battery SOC estimation under actual road conditions. Thus, its application scope in engineering is greatly expanded. Project supported by the National Natural Science Foundation of China (Grant Nos. 61004048 and 61201010).
Recursive starlight and bias estimation for high-contrast imaging with an extended Kalman filter
NASA Astrophysics Data System (ADS)
Riggs, A. J. Eldorado; Kasdin, N. Jeremy; Groff, Tyler D.
2016-01-01
For imaging faint exoplanets and disks, a coronagraph-equipped observatory needs focal plane wavefront correction to recover high contrast. The most efficient correction methods iteratively estimate the stellar electric field and suppress it with active optics. The estimation requires several images from the science camera per iteration. To maximize the science yield, it is desirable both to have fast wavefront correction and to utilize all the correction images for science target detection. Exoplanets and disks are incoherent with their stars, so a nonlinear estimator is required to estimate both the incoherent intensity and the stellar electric field. Such techniques assume a high level of stability found only on space-based observatories and possibly ground-based telescopes with extreme adaptive optics. In this paper, we implement a nonlinear estimator, the iterated extended Kalman filter (IEKF), to enable fast wavefront correction and a recursive, nearly-optimal estimate of the incoherent light. In Princeton's High Contrast Imaging Laboratory, we demonstrate that the IEKF allows wavefront correction at least as fast as with a Kalman filter and provides the most accurate detection of a faint companion. The nonlinear IEKF formalism allows us to pursue other strategies such as parameter estimation to improve wavefront correction.
NASA Astrophysics Data System (ADS)
Jesussek, Mathias; Ellermann, Katrin
2014-12-01
Reliability and dependability in complex mechanical systems can be improved by fault detection and isolation (FDI) methods. These techniques are key elements for maintenance on demand, which could decrease service cost and time significantly. This paper addresses FDI for a railway vehicle: the mechanical model is described as a multibody system, which is excited randomly due to track irregularities. Various parameters, like masses, spring- and damper-characteristics, influence the dynamics of the vehicle. Often, the exact values of the parameters are unknown and might even change over time. Some of these changes are considered critical with respect to the operation of the system and they require immediate maintenance. The aim of this work is to detect faults in the suspension system of the vehicle. A Kalman filter is used in order to estimate the states. To detect and isolate faults the detection error is minimised with multiple Kalman filters. A full-scale train model with nonlinear wheel/rail contact serves as an example for the described techniques. Numerical results for different test cases are presented. The analysis shows that for the given system it is possible not only to detect a failure of the suspension system from the system's dynamic response, but also to distinguish clearly between different possible causes for the changes in the dynamical behaviour.
Switching Kalman filter based methods for apnea bradycardia detection from ECG signals.
Montazeri Ghahjaverestan, Nasim; Shamsollahi, Mohammad B; Ge, Di; Hernández, Alfredo I
2015-09-01
Apnea bradycardia (AB) is an outcome of apnea occurrence in preterm infants and is an observable phenomenon in cardiovascular signals. Early detection of apnea in infants under monitoring is a critical challenge for the early intervention of nurses. In this paper, we introduce two switching Kalman filter (SKF) based methods for AB detection using electrocardiogram (ECG) signal.The first SKF model uses McSharry's ECG dynamical model integrated in two Kalman filter (KF) models trained for normal and AB intervals. Whereas the second SKF model is established by using only the RR sequence extracted from ECG and two AR models to be fitted in normal and AB intervals. In both SKF approaches, a discrete state variable called a switch is considered that chooses one of the models (corresponding to normal and AB) during the inference phase. According to the probability of each model indicated by this switch, the model with larger probability determines the observation label at each time instant.It is shown that the method based on ECG dynamical model can be effectively used for AB detection. The detection performance is evaluated by comparing statistical metrics and the amount of time taken to detect AB compared with the annotated onset. The results demonstrate the superiority of this method, with sensitivity and specificity 94.74[Formula: see text] and 94.17[Formula: see text], respectively. The presented approaches may therefore serve as an effective algorithm for monitoring neonates suffering from AB. PMID:26235524
Relationships between observer and Kalman Filter models for human dynamic spatial orientation.
Selva, Pierre; Oman, Charles M
2012-01-01
How does the central nervous system (CNS) combine sensory information from semicircular canal, otolith, and visual systems into perceptions of rotation, translation and tilt? Over the past four decades, a variety of input-output ("black box") mathematical models have been proposed to predict human dynamic spatial orientation perception and eye movements. The models have proved useful in vestibular diagnosis, aircraft accident investigation, and flight simulator design. Experimental refinement continues. This paper briefly reviews the history of two widely known model families, the linear "Kalman Filter" and the nonlinear "Observer". Recent physiologic data supports the internal model assumptions common to both. We derive simple 1-D and 3-D examples of each model for vestibular inputs, and show why - despite apparently different structure and assumptions - the linearized model predictions are dynamically equivalent when the four free model parameters are adjusted to fit the same empirical data, and perceived head orientation remains near upright. We argue that the motion disturbance and sensor noise spectra employed in the Kalman Filter formulation may reflect normal movements in daily life and perceptual thresholds, and thus justify the interpretation that the CNS cue blending scheme may well minimize least squares angular velocity perceptual errors. PMID:23000607
An O(N(2)) square root unscented Kalman Filter for visual simultaneous localization and mapping.
Holmes, Steven A; Klein, Georg; Murray, David W
2009-07-01
This paper develops a Square Root Unscented Kalman Filter (SRUKF) for performing video-rate visual simultaneous localization and mapping (SLAM) using a single camera. The conventional UKF has been proposed previously for SLAM, improving the handling of nonlinearities compared with the more widely used Extended Kalman Filter (EKF). However, no account was taken of the comparative complexity of the algorithms: In SLAM, the UKF scales as O(N;{3}) in the state length, compared to the EKF's O(N;{2}), making it unsuitable for video-rate applications with other than unrealistically few scene points. Here, it is shown that the SRUKF provides the same results as the UKF to within machine accuracy and that it can be reposed with complexity O(N;{2}) for state estimation in visual SLAM. This paper presents results from video-rate experiments on live imagery. Trials using synthesized data show that the consistency of the SRUKF is routinely better than that of the EKF, but that its overall cost settles at an order of magnitude greater than the EKF for large scenes. PMID:19443923
NASA Astrophysics Data System (ADS)
Dong, Gangqi; Zhu, Zheng H.
2016-05-01
This paper presents a real-time, vision-based algorithm for the pose and motion estimation of non-cooperative targets and its application in visual servo robotic manipulator to perform autonomous capture. A hybrid approach of adaptive extended Kalman filter and photogrammetry is developed for the real-time pose and motion estimation of non-cooperative targets. Based on the pose and motion estimates, the desired pose and trajectory of end-effector is defined and the corresponding desired joint angles of the robotic manipulator are derived by inverse kinematics. A close-loop visual servo control scheme is then developed for the robotic manipulator to track, approach and capture the target. Validating experiments are designed and performed on a custom-built six degrees of freedom robotic manipulator with an eye-in-hand configuration. The experimental results demonstrate the feasibility, effectiveness and robustness of the proposed adaptive extended Kalman filter enabled pose and motion estimation and visual servo strategy.
A Preliminary Application of Ensemble Transform Kalman Filter System to Rainfall Forecast
NASA Astrophysics Data System (ADS)
Tie, Wang
2014-05-01
WangTie(1,2),YangXiaofeng(1),ZangXin(1),GengLining(1),ZhouYan(1) (1)NanJing China-Spacenet Satellite Telecom CO., Ltd, Nanjing, 210061, China,(2)Institute of Atmospheric Physics, Chinese Academy of Sciences, LASG, Beijing, 100029, China The Ensemble Transform Kalman Filter(ETKF) method is applied to WRF model(Weather Research & Forecast Model system) Version 3.5.1, and the ETKF based data assimilation system is constructed. The accurate of forecast result and the sensitivity of initial data error on a heavy rainfall from 5th to 7th July 2003 in Jiangsu province China are investigated. The numerical result indicated that the ETKF method could decrease the forecast error and improves the forecast result either the synoptic scale system and the meso-scale system, the RMSEs of wind decrease less than 18 percent, while the temperature and humidity decrease about 6 precent. The forecast of precipitation, especially the 12h accumulated precipitation is improved significant after ETKF assimilation. Keywords: intense rainfall, prediction error, Ensemble Transform Kalman Filter(ETKF), WRF model
NASA Astrophysics Data System (ADS)
Kang, Ji-Sun; Kalnay, Eugenia; Liu, Junjie; Fung, Inez; Miyoshi, Takemasa; Ide, Kayo
2011-05-01
In ensemble Kalman filter, space localization is used to reduce the impact of long-distance sampling errors in the ensemble estimation of the forecast error covariance. When two variables are not physically correlated, their error covariance is still estimated by the ensemble and, therefore, it is dominated by sampling errors. We introduce a "variable localization" method, zeroing out such covariances between unrelated variables to the problem of assimilating carbon dioxide concentrations into a dynamical model using the local ensemble transform Kalman filter (LETKF) in an observing system simulation experiments (OSSE) framework. A system where meteorological and carbon variables are simultaneously assimilated is used to estimate surface carbon fluxes that are not directly observed. A range of covariance structures are explored for the LETKF, with emphasis on configurations allowing nonzero error covariance between carbon variables and the wind field, which affects transport of atmospheric CO2, but not between CO2 and the other meteorological variables. Such variable localization scheme zeroes out the background error covariance among prognostic variables that are not physically related, thus reducing sampling errors. Results from the identical twin experiments show that the performance in the estimation of surface carbon fluxes obtained using variable localization is much better than that using a standard full covariance approach. The relative improvement increases when the surface fluxes change with time and model error becomes significant.
Markov models and the ensemble Kalman filter for estimation of sorption rates.
Vugrin, Eric D.; McKenna, Sean Andrew; Vugrin, Kay White
2007-09-01
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude.
NASA Astrophysics Data System (ADS)
Hoteit, I.; Korres, G.; Triantafyllou, G.
2007-05-01
Two assimilation systems based on a suboptimal extended Kalman filter have been developed to simultaneously assimilate physical and biochemical data into a complex ecosystem model of the Eastern Mediterranean. The three-dimensional ecosystem model is composed of two on-line coupled sub-models: the Princeton Ocean Model (POM) and the European Regional Seas Ecosystem Model (ERSEM). The filter is a variant of the extended Kalman filter which operates with low-rank error covariance matrices to reduce computational burden. Two different approaches have been considered: the "joint approach" and the "dual approach". In the first approach, one filter is used in which the state vector of the filter is composed of all prognostic variables of POM and ERSEM models. Basically, the numerical models are integrated forward in time to produce the (physical and biochemical) forecasts. The observations are then assimilated jointly to correct all forecast variables using the cross-correlations between all physical and biochemical forecast errors, which simultaneously provides the analyses for the physics and for the ecology. The dual approach consists of two filters, operating separately on the physics and on the ecology. We describe the two assimilation systems and discuss results of assimilation experiments.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. PMID:27085426
A novel Kalman filter based video image processing scheme for two-photon fluorescence microscopy
NASA Astrophysics Data System (ADS)
Sun, Wenqing; Huang, Xia; Li, Chunqiang; Xiao, Chuan; Qian, Wei
2016-03-01
Two-photon fluorescence microscopy (TPFM) is a perfect optical imaging equipment to monitor the interaction between fast moving viruses and hosts. However, due to strong unavoidable background noises from the culture, videos obtained by this technique are too noisy to elaborate this fast infection process without video image processing. In this study, we developed a novel scheme to eliminate background noises, recover background bacteria images and improve video qualities. In our scheme, we modified and implemented the following methods for both host and virus videos: correlation method, round identification method, tree-structured nonlinear filters, Kalman filters, and cell tracking method. After these procedures, most of noises were eliminated and host images were recovered with their moving directions and speed highlighted in the videos. From the analysis of the processed videos, 93% bacteria and 98% viruses were correctly detected in each frame on average.
Olivares, Alberto; Górriz, J M; Ramírez, J; Olivares, G
2016-05-01
With the advent of miniaturized inertial sensors many systems have been developed within the last decade to study and analyze human motion and posture, specially in the medical field. Data measured by the sensors are usually processed by algorithms based on Kalman Filters in order to estimate the orientation of the body parts under study. These filters traditionally include fixed parameters, such as the process and observation noise variances, whose value has large influence in the overall performance. It has been demonstrated that the optimal value of these parameters differs considerably for different motion intensities. Therefore, in this work, we show that, by applying frequency analysis to determine motion intensity, and varying the formerly fixed parameters accordingly, the overall precision of orientation estimation algorithms can be improved, therefore providing physicians with reliable objective data they can use in their daily practice. PMID:26337122
Estimation of the Chandler wobble parameters by the use of the Kalman deconvolution filter
NASA Astrophysics Data System (ADS)
Brzezinski, A.; Rajner, M.
2014-12-01
We estimate the Chandler wobble (CW) parameters, the period T and the quality factor Q, based on the stochastic models of polar motion and geophysical excitation data. We apply the Kalman deconvolution filter developed by Brzezinski (1992). This filter can be used to analyze either the polar motion data alone, or simultaneously the polar motion and the excitation data, in order to estimate the unknown residual excitation. By imposing the minimum variance constraint upon the estimated unknown excitation we can find the best value of the resonant parameters T and Q. The CW parameters estimated from different sets of polar motion and geophysical excitation data are compared to each other as well as to the earlier results derived by the alternative algorithms.
Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks.
Gao, Shouwan; Chen, Pengpeng; Huang, Dan; Niu, Qiang
2016-01-01
This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples. PMID:27104541
Optimal interpolation and the Kalman filter. [for analysis of numerical weather predictions
NASA Technical Reports Server (NTRS)
Cohn, S.; Isaacson, E.; Ghil, M.
1981-01-01
The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.
Kalman filtering applied to real-time monitoring of apogee maneuvers
NASA Technical Reports Server (NTRS)
Deboer, Frederic; Barbier, Christian
1993-01-01
Part of the Space Mathematics Division in CNES, the Flight Dynamics Center provides attitude and orbit determinations and maneuvers during the Launch and Early Operation Phase (LEOP) of geostationary satellites. Orbit determination is based on a Kalman filter method; when the 2 GHz CNES/NASA network is used, Doppler measurements are available and allow orbit determination during the apogee maneuvers. This method was used for TELE-X and TDF 2 LEOP (3-axis controlled satellites) and also for TELECOM 2 and HISPASAT (spun satellites): it enables us to follow the evolution of the maneuver and gives out a quite accurate estimation of the reached orbit. In this paper, we briefly describe the dynamic models of the orbit evolution in both cases, '3-axis' and 'inertial' thrust. Then, we present the results obtained for each case. Afterwards, we present some cases to show the robustness of the filter.
Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks
Gao, Shouwan; Chen, Pengpeng; Huang, Dan; Niu, Qiang
2016-01-01
This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples. PMID:27104541
Kalman filter based range estimation for autonomous navigation using imaging sensors
NASA Technical Reports Server (NTRS)
Sridhar, B.; Cheng, V. H. L.; Phatak, A. V.
1990-01-01
The ability to detect and locate obstacles using on-board sensors and modify the nominal trajectory is necessary for safe landing of an autonomous lander on Mars. This paper examines some of the issues in the location of objects using a sequence of images from a passive sensor, and describes a Kalman filter approach to improve the range estimation to obstacles. The filter is also used to track features in the images leading to a significant reduction of search effort in the feature extraction step of the algorithm. The lack of suitable flight imagery data presents a problem in the verification of concepts for obstacle detection. An experiment is designed to acquire a sequence of images along with sensor motion parameters and the range estimation results using this imagery are presented.
Neural Network Aided Adaptive Extended Kalman Filtering Approach for DGPS Positioning
NASA Astrophysics Data System (ADS)
Jwo, Dah-Jing; Huang, Hung-Chih
2004-09-01
The extended Kalman filter, when employed in the GPS receiver as the navigation state estimator, provides optimal solutions if the noise statistics for the measurement and system are completely known. In practice, the noise varies with time, which results in performance degradation. The covariance matching method is a conventional adaptive approach for estimation of noise covariance matrices. The technique attempts to make the actual filter residuals consistent with their theoretical covariance. However, this innovation-based adaptive estimation shows very noisy results if the window size is small. To resolve the problem, a multilayered neural network is trained to identify the measurement noise covariance matrix, in which the back-propagation algorithm is employed to iteratively adjust the link weights using the steepest descent technique. Numerical simulations show that based on the proposed approach the adaptation performance is substantially enhanced and the positioning accuracy is substantially improved.
NASA Astrophysics Data System (ADS)
Yan, Jun; Yu, Kegen; Wu, Lenan
2014-12-01
To mitigate the non-line-of-sight (NLOS) effect, a three-step positioning approach is proposed in this article for target tracking. The possibility of each distance measurement under line-of-sight condition is first obtained by applying the truncated triangular probability-possibility transformation associated with fuzzy modeling. Based on the calculated possibilities, the measurements are utilized to obtain intermediate position estimates using the maximum likelihood estimation (MLE), according to identified measurement condition. These intermediate position estimates are then filtered using a linear Kalman filter (KF) to produce the final target position estimates. The target motion information and statistical characteristics of the MLE results are employed in updating the KF parameters. The KF position prediction is exploited for MLE parameter initialization and distance measurement selection. Simulation results demonstrate that the proposed approach outperforms the existing algorithms in the presence of unknown NLOS propagation conditions and achieves a performance close to that when propagation conditions are perfectly known.
Beghi, Alessandro; Belfi, Jacopo; Beverini, Nicolò; Bouhadef, B; Cuccato, D; Di Virgilio, Angela; Ortolan, Antonello
2012-11-01
He-Ne ring-laser gyroscopes are, at present, the most precise devices for absolute angular velocity measurements. Limitations to their performance come from the nonlinear dynamics of the laser. Following Lamb semiclassical theory, we find a set of critical parameters affecting the time stability of the system. We propose a method for estimating the long-term drift of the laser parameters and for filtering out the laser dynamics effects from the rotation measurement. The parameter estimation procedure, based on the perturbative solutions of the laser dynamics, allows us to apply Kalman filter theory for the estimation of the angular velocity. Results of a comprehensive Monte Carlo simulation and results of a preliminary analysis on experimental data from the ring-laser prototype G-Pisa are shown and discussed. PMID:23128698
Compensation of the laser parameter fluctuations in large ring-laser gyros: a Kalman filter approach
NASA Astrophysics Data System (ADS)
Beghi, Alessandro; Belfi, Jacopo; Beverini, Nicolò; Bouhadef, B.; Cuccato, D.; Di Virgilio, Angela; Ortolan, Antonello
2012-11-01
He-Ne ring laser gyroscopes are, at present, the most precise devices for absolute angular velocity measurements. Limitations to their performance come from the non--linear dynamics of the laser. Following the Lamb semi-classical theory, we find a set of critical parameters affecting the time stability of the system. We propose a method for estimating the long term drift of the laser parameters and for filtering out the laser dynamics effects from the rotation measurement. The parameter estimation procedure, based on the perturbative solutions of the laser dynamics, allow us to apply Kalman Filter theory for the estimation of the angular velocity. Results of a comprehensive Monte Carlo simulation and results of a preliminary analysis on experimental data from the ring laser prototype G-Pisa are shown and discussed.
Xie, XianMing; Li, YingHui
2014-06-20
This paper presents an enhanced phase unwrapping algorithm by combining an unscented Kalman filter, an enhanced local phase gradient estimator based on an amended matrix pencil model, and a path-following strategy. This technology is able to accurately unwrap seriously noisy wrapped phase images by applying the unscented Kalman filter to simultaneously perform noise suppression and phase unwrapping along the path from the high-quality region to the low-quality region of the wrapped phase images. Results obtained with synthetic data and real data validate the effectiveness of the proposed method and show improved performance of this new algorithm with respect to some of the most used algorithms. PMID:24979440
Emulation of an ensemble Kalman filter algorithm on a flood wave propagation model
NASA Astrophysics Data System (ADS)
Barthélémy, S.; Ricci, S.; Pannekoucke, O.; Thual, O.; Malaterre, P. O.
2013-06-01
This study describes the emulation of an Ensemble Kalman Filter (EnKF) algorithm on a 1-D flood wave propagation model. This model is forced at the upstream boundary with a random variable with gaussian statistics and a correlation function in time with gaussian shape. This allows for, in the case without assimilation, the analytical study of the covariance functions of the propagated signal anomaly. This study is validated numerically with an ensemble method. In the case with assimilation with one observation point, where synthetical observations are generated by adding an error to a true state, the dynamic of the background error covariance functions is not straightforward and a numerical approach using an EnKF algorithm is prefered. First, those numerical experiments show that both background error variance and correlation length scale are reduced at the observation point. This reduction of variance and correlation length scale is propagated downstream by the dynamics of the model. Then, it is shown that the application of a Best Linear Unbiased Estimator (BLUE) algorithm using the background error covariance matrix converged from the EnKF algorithm, provides the same results as the EnKF but with a cheaper computational cost, thus allowing for the use of data assimilation in the context of real time flood forecasting. Moreover it was demonstrated that the reduction of background error correlation length scale and variance at the observation point depends on the error observation statistics. This feature is quantified by abacus built from linear regressions over a limited set of EnKF experiments. These abacus that describe the background error variance and the correlation length scale in the neighboring of the observation point combined with analytical expressions that describe the background error variance and the correlation length scale away from the observation point provide parametrized models for the variance and the correlation length scale. Using this
A Kalman filter implementation for precision improvement in low-cost GPS positioning of tractors.
Gomez-Gil, Jaime; Ruiz-Gonzalez, Ruben; Alonso-Garcia, Sergio; Gomez-Gil, Francisco Javier
2013-01-01
Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain. PMID:24217355
Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
NASA Astrophysics Data System (ADS)
Kelly, D. T. B.; Law, K. J. H.; Stuart, A. M.
2014-10-01
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so for small ensemble size. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with respect to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise.
A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors
Gomez-Gil, Jaime; Ruiz-Gonzalez, Ruben; Alonso-Garcia, Sergio; Gomez-Gil, Francisco Javier
2013-01-01
Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain. PMID:24217355
The role of model dynamics in ensemble Kalman filter performance for chaotic systems
Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.
2011-01-01
The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.
Ligorio, Gabriele; Sabatini, Angelo Maria
2013-01-01
In this paper measurements from a monocular vision system are fused with inertial/magnetic measurements from an Inertial Measurement Unit (IMU) rigidly connected to the camera. Two Extended Kalman filters (EKFs) were developed to estimate the pose of the IMU/camera sensor moving relative to a rigid scene (ego-motion), based on a set of fiducials. The two filters were identical as for the state equation and the measurement equations of the inertial/magnetic sensors. The DLT-based EKF exploited visual estimates of the ego-motion using a variant of the Direct Linear Transformation (DLT) method; the error-driven EKF exploited pseudo-measurements based on the projection errors from measured two-dimensional point features to the corresponding three-dimensional fiducials. The two filters were off-line analyzed in different experimental conditions and compared to a purely IMU-based EKF used for estimating the orientation of the IMU/camera sensor. The DLT-based EKF was more accurate than the error-driven EKF, less robust against loss of visual features, and equivalent in terms of computational complexity. Orientation root mean square errors (RMSEs) of 1° (1.5°), and position RMSEs of 3.5 mm (10 mm) were achieved in our experiments by the DLT-based EKF (error-driven EKF); by contrast, orientation RMSEs of 1.6° were achieved by the purely IMU-based EKF. PMID:23385409
Bearings only tracking using a set of range parameterised extended Kalman filters
NASA Astrophysics Data System (ADS)
Peach, Nigel G.
Bearings only tracking using the Extended Kalman Filter (EKF) configured in Cartesian and modified polar coordinate systems is reviewed. A new tracking approach is proposed which consists of a set of weighted EKFs each with a different initial range estimate and this is referred to as the Range Parameterised (RP) tracker. This new approach overcomes the problems exhibited with existing EKP trackers when the bearing rate is very high or near zero. In addition, it allows a more natural implementation for the prior knowledge of the target velocity, which can allow the range to be inferred even before the first observer manoeuvre. Results are presented for a typical tracking scenario, involving a manoeuvring observer and a constant velocity target. The results show that the RP tracker gives stable, consistent and unbiased estimates in all the cases considered, whereas the same is not true for the Cartesian and Modified Polar EKF trackers. The RP tracker has been extended to allow for manoeuvring targets by adding a manoeuvre detection and correction procedure based on a Generalised Likelihood Ratio (GLR) test. The GLR threshold has been set to 3.0 as this gives a good compromise between a reasonably low false alarm rate and a short detection delay for typical target manoeuvres. However, the selection of a particular threshold is not critical as the proposed procedure is robust to false alarms, since it only results in increased computation without long term loss in tracking accuracy. The tracking performance of the GLR procedure has been compared with the standard technique of adding plant noise to allow for unmodelled target dynamics. This comparison has illustrated that the GLR procedure provides better tracking performance before and after a target manoeuvre and, in particular, the track estimates for the GLR procedure are consistent with the estimated covariance matrix. The tracking performance of the RP tracker has been shown to approach the Cramer Rao Lower Bound
Predicting Ground Based Magnetometer Measurements Using the Ensemble Transform Kalman Filter
NASA Astrophysics Data System (ADS)
Lynch, E. M.; Sharma, A. S.; Kalnay, E.; Ide, K.
2015-12-01
Ensemble data assimilation techniques, including the Ensemble Transform Kalman Filter (ETKF), have been successfully used to improve prediction skill in cases where a numerical model for forecasting has been developed. These techniques for systems for which no model exists are developed using the reconstruction of phase space from time series data. For many natural systems, the complete set of equations governing their evolution are not known and observational data of only a limited number of physical variables are available However, for a dissipative system in which the variables are coupled nonlinearly, the dimensionality of the phase space is greatly reduced, and it is possible to reconstruct the details of the phase space from a single scalar time series of observations. A combination of the phase phase reconstruction with ETKF yields a new technique of forecasting using only time series data. This technique is used to forecast magnetic field variations in th magnetosphere, which exhibits low dimensional behavior on the substorm time scale. The time series data of the magnetic field variations monitored by the network of groundbased magnetometers in the auroral region are used for forecasting at two stages.. In the first stage, the auroral electrojet indices computed from the data from the magnetometers are used for forecasting and yields forecasts that are better than persistence. In the second stage, the multivariate time series from several auroral region magnetometers is used to reconstruct the phase space of the magnetosphere-solar wind system using Multi-channel Singular Spectrum Analysis. The ETKF is applied to ensemble forecasts made using model data constructed from long time series of the data from each magnetometer and observations of the magnetometer measurements. The improved prediction skill, e.g., with respect to persistence, is achieved from the use of the dynamical behavior of nearby trajectories. The near-real time forecasts of space weather
Achieving High Contrast for Exoplanet Imaging with a Kalman Filter and Stroke Minimization
NASA Astrophysics Data System (ADS)
Eldorado Riggs, A. J.; Groff, T. D.; Kasdin, N. J.; Carlotti, A.; Vanderbei, R. J.
2014-01-01
High contrast imaging requires focal plane wavefront control and estimation to correct aberrations in an optical system; non-common path errors prevent the use of conventional estimation with a separate wavefront sensor. The High Contrast Imaging Laboratory (HCIL) at Princeton has led the development of several techniques for focal plane wavefront control and estimation. In recent years, we developed a Kalman filter for optimal wavefront estimation. Our Kalman filter algorithm is an improvement upon DM Diversity, which requires at least two images pairs each iteration and does not utilize any prior knowledge of the system. The Kalman filter is a recursive estimator, meaning that it uses the data from prior estimates along with as few as one new image pairs per iteration to update the electric field estimate. Stroke minimization has proven to be a feasible controller for achieving high contrast. While similar to a variation of Electric Field Conjugation (EFC), stroke minimization achieves the same contrast with less stroke on the DMs. We recently utilized these algorithms to achieve high contrast for the first time in our experiment at the High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Laboratory (JPL). Our HCIT experiment was also the first demonstration of symmetric dark hole correction in the image plane using two DMs--this is a major milestone for future space missions. Our ongoing work includes upgrading our optimal estimator to include an estimate of the incoherent light in the system, which allows for simultaneous estimation of the light from a planet along with starlight. The two-DM experiment at the HCIT utilized a shaped pupil coronagraph. Those tests utilized ripple style, free-standing masks etched out of silicon, but our current work is in designing 2-D optimized reflective shaped pupils. In particular, we have created several designs for the AFTA telescope, whose pupil presents major hurdles because of its atypical pupil obstructions. Our
AMA- and RWE- Based Adaptive Kalman Filter for Denoising Fiber Optic Gyroscope Drift Signal.
Yang, Gongliu; Liu, Yuanyuan; Li, Ming; Song, Shunguang
2015-01-01
An improved double-factor adaptive Kalman filter called AMA-RWE-DFAKF is proposed to denoise fiber optic gyroscope (FOG) drift signal in both static and dynamic conditions. The first factor is Kalman gain updated by random weighting estimation (RWE) of the covariance matrix of innovation sequence at any time to ensure the lowest noise level of output, but the inertia of KF response increases in dynamic condition. To decrease the inertia, the second factor is the covariance matrix of predicted state vector adjusted by RWE only when discontinuities are detected by adaptive moving average (AMA).The AMA-RWE-DFAKF is applied for denoising FOG static and dynamic signals, its performance is compared with conventional KF (CKF), RWE-based adaptive KF with gain correction (RWE-AKFG), AMA- and RWE- based dual mode adaptive KF (AMA-RWE-DMAKF). Results of Allan variance on static signal and root mean square error (RMSE) on dynamic signal show that this proposed algorithm outperforms all the considered methods in denoising FOG signal. PMID:26512665
AMA- and RWE- Based Adaptive Kalman Filter for Denoising Fiber Optic Gyroscope Drift Signal
Yang, Gongliu; Liu, Yuanyuan; Li, Ming; Song, Shunguang
2015-01-01
An improved double-factor adaptive Kalman filter called AMA-RWE-DFAKF is proposed to denoise fiber optic gyroscope (FOG) drift signal in both static and dynamic conditions. The first factor is Kalman gain updated by random weighting estimation (RWE) of the covariance matrix of innovation sequence at any time to ensure the lowest noise level of output, but the inertia of KF response increases in dynamic condition. To decrease the inertia, the second factor is the covariance matrix of predicted state vector adjusted by RWE only when discontinuities are detected by adaptive moving average (AMA).The AMA-RWE-DFAKF is applied for denoising FOG static and dynamic signals, its performance is compared with conventional KF (CKF), RWE-based adaptive KF with gain correction (RWE-AKFG), AMA- and RWE- based dual mode adaptive KF (AMA-RWE-DMAKF). Results of Allan variance on static signal and root mean square error (RMSE) on dynamic signal show that this proposed algorithm outperforms all the considered methods in denoising FOG signal. PMID:26512665
NASA Technical Reports Server (NTRS)
Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.
2013-01-01
In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.
A Two-Stage Kalman Filter Approach for Robust and Real-Time Power System State Estimation
Zhang, Jinghe; Welch, Greg; Bishop, Gary; Huang, Zhenyu
2014-04-01
As electricity demand continues to grow and renewable energy increases its penetration in the power grid, realtime state estimation becomes essential for system monitoring and control. Recent development in phasor technology makes it possible with high-speed time-synchronized data provided by Phasor Measurement Units (PMU). In this paper we present a two-stage Kalman filter approach to estimate the static state of voltage magnitudes and phase angles, as well as the dynamic state of generator rotor angles and speeds. Kalman filters achieve optimal performance only when the system noise characteristics have known statistical properties (zero-mean, Gaussian, and spectrally white). However in practice the process and measurement noise models are usually difficult to obtain. Thus we have developed the Adaptive Kalman Filter with Inflatable Noise Variances (AKF with InNoVa), an algorithm that can efficiently identify and reduce the impact of incorrect system modeling and/or erroneous measurements. In stage one, we estimate the static state from raw PMU measurements using the AKF with InNoVa; then in stage two, the estimated static state is fed into an extended Kalman filter to estimate the dynamic state. Simulations demonstrate its robustness to sudden changes of system dynamics and erroneous measurements.
Fuzzy State Transition and Kalman Filter Applied in Short-Term Traffic Flow Forecasting
Ming-jun, Deng; Shi-ru, Qu
2015-01-01
Traffic flow is widely recognized as an important parameter for road traffic state forecasting. Fuzzy state transform and Kalman filter (KF) have been applied in this field separately. But the studies show that the former method has good performance on the trend forecasting of traffic state variation but always involves several numerical errors. The latter model is good at numerical forecasting but is deficient in the expression of time hysteretically. This paper proposed an approach that combining fuzzy state transform and KF forecasting model. In considering the advantage of the two models, a weight combination model is proposed. The minimum of the sum forecasting error squared is regarded as a goal in optimizing the combined weight dynamically. Real detection data are used to test the efficiency. Results indicate that the method has a good performance in terms of short-term traffic forecasting. PMID:26779258
Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique.
Cheng, Zhongtao; Liu, Dong; Yang, Yongying; Ling, Tong; Chen, Xiaoyu; Zhang, Lei; Bai, Jian; Shen, Yibing; Miao, Liang; Huang, Wei
2015-12-14
A phase unwrapping algorithm for interferometric fringes based on the unscented Kalman filter (UKF) technique is proposed. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the UKF process. Simulations indicate that the proposed algorithm has better accuracy than some widely employed phase unwrapping approaches in the same noise condition. Also, the time consumption of the algorithm is reasonably acceptable. Applications of the algorithm in our different optical interferometer systems are provided to demonstrate its practicability with good performance. We hope this algorithm can be a practical approach that can help to reduce the systematic errors significantly induced by phase unwrapping process for interferometric measurements such as wavefront distortion testing, surface figure testing of optics, etc. PMID:26699024
The Local Ensemble Transform Kalman Filter (LETKF) with a Global NWP Model on the Cubed Sphere
NASA Astrophysics Data System (ADS)
Shin, Seoleun; Kang, Ji-Sun; Jo, Youngsoon
2016-04-01
We develop an ensemble data assimilation system using the four-dimensional local ensemble transform kalman filter (LEKTF) for a global hydrostatic numerical weather prediction (NWP) model formulated on the cubed sphere. Forecast-analysis cycles run stably and thus provide newly updated initial states for the model to produce ensemble forecasts every 6 h. Performance of LETKF implemented to the global NWP model is verified using the ECMWF reanalysis data and conventional observations. Global mean values of bias and root mean square difference are significantly reduced by the data assimilation. Besides, statistics of forecast and analysis converge well as the forecast-analysis cycles are repeated. These results suggest that the combined system of LETKF and the global NWP formulated on the cubed sphere shows a promising performance for operational uses.
Fang, Joyce; Savransky, Dmitry
2016-08-01
Automation of alignment tasks can provide improved efficiency and greatly increase the flexibility of an optical system. Current optical systems with automated alignment capabilities are typically designed to include a dedicated wavefront sensor. Here, we demonstrate a self-aligning method for a reconfigurable system using only focal plane images. We define a two lens optical system with 8 degrees of freedom. Images are simulated given misalignment parameters using ZEMAX software. We perform a principal component analysis on the simulated data set to obtain Karhunen-Loève modes, which form the basis set whose weights are the system measurements. A model function, which maps the state to the measurement, is learned using nonlinear least-squares fitting and serves as the measurement function for the nonlinear estimator (extended and unscented Kalman filters) used to calculate control inputs to align the system. We present and discuss simulated and experimental results of the full system in operation. PMID:27505378
NASA Astrophysics Data System (ADS)
Fang, Joyce; Savransky, Dmitry
2016-08-01
Automation of alignment tasks can provide improved efficiency and greatly increase the flexibility of an optical system. Current optical systems with automated alignment capabilities are typically designed to include a dedicated wavefront sensor. Here, we demonstrate a self-aligning method for a reconfigurable system using only focal plane images. We define a two lens optical system with eight degrees of freedom. Images are simulated given misalignment parameters using ZEMAX software. We perform a principal component analysis (PCA) on the simulated dataset to obtain Karhunen-Lo\\`eve (KL) modes, which form the basis set whose weights are the system measurements. A model function which maps the state to the measurement is learned using nonlinear least squares fitting and serves as the measurement function for the nonlinear estimator (Extended and Unscented Kalman filters) used to calculate control inputs to align the system. We present and discuss both simulated and experimental results of the full system in operation.
The Local Ensemble Transform Kalman Filter (LETKF) with a Global NWP Model on the Cubed Sphere
NASA Astrophysics Data System (ADS)
Shin, Seoleun; Kang, Ji-Sun; Jo, Youngsoon
2016-07-01
We develop an ensemble data assimilation system using the four-dimensional local ensemble transform kalman filter (LEKTF) for a global hydrostatic numerical weather prediction (NWP) model formulated on the cubed sphere. Forecast-analysis cycles run stably and thus provide newly updated initial states for the model to produce ensemble forecasts every 6 h. Performance of LETKF implemented to the global NWP model is verified using the ECMWF reanalysis data and conventional observations. Global mean values of bias and root mean square difference are significantly reduced by the data assimilation. Besides, statistics of forecast and analysis converge well as the forecast-analysis cycles are repeated. These results suggest that the combined system of LETKF and the global NWP formulated on the cubed sphere shows a promising performance for operational uses.
New efficient optimizing techniques for Kalman filters and numerical weather prediction models
NASA Astrophysics Data System (ADS)
Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis
2016-06-01
The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.
Fuzzy State Transition and Kalman Filter Applied in Short-Term Traffic Flow Forecasting.
Deng, Ming-jun; Qu, Shi-ru
2015-01-01
Traffic flow is widely recognized as an important parameter for road traffic state forecasting. Fuzzy state transform and Kalman filter (KF) have been applied in this field separately. But the studies show that the former method has good performance on the trend forecasting of traffic state variation but always involves several numerical errors. The latter model is good at numerical forecasting but is deficient in the expression of time hysteretically. This paper proposed an approach that combining fuzzy state transform and KF forecasting model. In considering the advantage of the two models, a weight combination model is proposed. The minimum of the sum forecasting error squared is regarded as a goal in optimizing the combined weight dynamically. Real detection data are used to test the efficiency. Results indicate that the method has a good performance in terms of short-term traffic forecasting. PMID:26779258
NASA Astrophysics Data System (ADS)
Zhang, Y.
2015-12-01
Accurate forecasting the solar photospheric magnetic field distribution play an important role in the estimates of the inner boundary conditions of the coronal and solar wind model. Forecasting solar photospheric magnetic field using the solar flux transport (SFT) model can achieve an acceptable match to the actual field. The observations from ground-based or spacecraft instruments can be assimilated to update the modeled flux. The local ensemble Kalman filtering (LEnKF) method is utilized to improve forecasts and characterize their uncertainty by propagating the SFT model with different model parameters forward in time to control the evolution of the solar photospheric magnetic field. Optimal assimilation of measured data into the ensemble produces an improvement in the fit of the forecast to the actual field. Our approach offers a method to improve operational forecasting of the solar photospheric magnetic field. The LEnKF method also allows sensitivity analysis of the SFT model to noise and uncertainty within the physical representation.
NASA Astrophysics Data System (ADS)
Zhang, Ying; Du, Aimin; Feng, Xueshang
2015-04-01
Accurate forecasting the solar photospheric magnetic field distribution play an important role in the estimates of the inner boundary conditions of the coronal and solar wind model. Forecasting solar photospheric magnetic field using the solar flux transport (SFT) model can achieve an acceptable match to the actual field. The observations from ground-based or spacecraft instruments can be assimilated to update the modeled flux. The local ensemble Kalman filtering (LEnKF) method is utilized to improve forecasts and characterize their uncertainty by propagating the SFT model with different model parameters forward in time to control the evolution of the solar photospheric magnetic field. Optimal assimilation of measured data into the ensemble produces an improvement in the fit of the forecast to the actual field. Our approach offers a method to improve operational forecasting of the solar photospheric magnetic field. The LEnKF method also allows sensitivity analysis of the SFT model to noise and uncertainty within the physical representation.
Adaptive UAV Attitude Estimation Employing Unscented Kalman Filter, FOAM and Low-Cost MEMS Sensors
de Marina, Héctor García; Espinosa, Felipe; Santos, Carlos
2012-01-01
Navigation employing low cost MicroElectroMechanical Systems (MEMS) sensors in Unmanned Aerial Vehicles (UAVs) is an uprising challenge. One important part of this navigation is the right estimation of the attitude angles. Most of the existent algorithms handle the sensor readings in a fixed way, leading to large errors in different mission stages like take-off aerobatic maneuvers. This paper presents an adaptive method to estimate these angles using off-the-shelf components. This paper introduces an Attitude Heading Reference System (AHRS) based on the Unscented Kalman Filter (UKF) using the Fast Optimal Attitude Matrix (FOAM) algorithm as the observation model. The performance of the method is assessed through simulations. Moreover, field experiments are presented using a real fixed-wing UAV. The proposed low cost solution, implemented in a microcontroller, shows a satisfactory real time performance. PMID:23012559
Extended Kalman filtering for joint mitigation of phase and amplitude noise in coherent QAM systems.
Pakala, Lalitha; Schmauss, Bernhard
2016-03-21
We numerically investigate our proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extend Kalman filter (EKF) for joint mitigation of linear and non-linear phase noise as well as amplitude noise on 4, 16 and 64 polarization multiplexed (PM) quadrature amplitude modulation (QAM) 224 Gb/s systems. The results are compared to decision directed (DD) carrier phase estimation (CPE), DD phase locked loop (PLL) and universal CPE (U-CPE) algorithms. Besides eliminating the necessity of phase unwrapping function, EKF-CPANE shows improved performance for both back-to-back (BTB) and transmission scenarios compared to the aforementioned algorithms. We further propose a weighted innovation approach (WIA) of the EKF-CPANE which gives an improvement of 0.3 dB in the Q-factor, compared to the original algorithm. PMID:27136830
Development and validation of a Kalman filter-based model for vehicle slip angle estimation
NASA Astrophysics Data System (ADS)
Gadola, M.; Chindamo, D.; Romano, M.; Padula, F.
2014-01-01
It is well known that vehicle slip angle is one of the most difficult parameters to measure on a vehicle during testing or racing activities. Moreover, the appropriate sensor is very expensive and it is often difficult to fit to a car, especially on race cars. We propose here a strategy to eliminate the need for this sensor by using a mathematical tool which gives a good estimation of the vehicle slip angle. A single-track car model, coupled with an extended Kalman filter, was used in order to achieve the result. Moreover, a tuning procedure is proposed that takes into consideration both nonlinear and saturation characteristics typical of vehicle lateral dynamics. The effectiveness of the proposed algorithm has been proven by both simulation results and real-world data.
Yoon, Paul K; Zihajehzadeh, Shaghayegh; Bong-Soo Kang; Park, Edward J
2015-08-01
This paper proposes a novel indoor localization method using the Bluetooth Low Energy (BLE) and an inertial measurement unit (IMU). The multipath and non-line-of-sight errors from low-power wireless localization systems commonly result in outliers, affecting the positioning accuracy. We address this problem by adaptively weighting the estimates from the IMU and BLE in our proposed cascaded Kalman filter (KF). The positioning accuracy is further improved with the Rauch-Tung-Striebel smoother. The performance of the proposed algorithm is compared against that of the standard KF experimentally. The results show that the proposed algorithm can maintain high accuracy for position tracking the sensor in the presence of the outliers. PMID:26736389
An adaptive Kalman filter technique for context-aware heart rate monitoring.
Xu, Min; Goldfain, Albert; Dellostritto, Jim; Iyengar, Satish
2012-01-01
Traditional physiological monitoring systems convert a person's vital sign waveforms, such as heart rate, respiration rate and blood pressure, into meaningful information by comparing the instant reading with a preset threshold or a baseline without considering the contextual information of the person. It would be beneficial to incorporate the contextual data such as activity status of the person to the physiological data in order to obtain a more accurate representation of a person's physiological status. In this paper, we proposed an algorithm based on adaptive Kalman filter that describes the heart rate response with respect to different activity levels. It is towards our final goal of intelligent detection of any abnormality in the person's vital signs. Experimental results are provided to demonstrate the feasibility of the algorithm. PMID:23367423
Adaptive UAV attitude estimation employing unscented Kalman Filter, FOAM and low-cost MEMS sensors.
de Marina, Héctor García; Espinosa, Felipe; Santos, Carlos
2012-01-01
Navigation employing low cost MicroElectroMechanical Systems (MEMS) sensors in Unmanned Aerial Vehicles (UAVs) is an uprising challenge. One important part of this navigation is the right estimation of the attitude angles. Most of the existent algorithms handle the sensor readings in a fixed way, leading to large errors in different mission stages like take-off aerobatic maneuvers. This paper presents an adaptive method to estimate these angles using off-the-shelf components. This paper introduces an Attitude Heading Reference System (AHRS) based on the Unscented Kalman Filter (UKF) using the Fast Optimal Attitude Matrix (FOAM) algorithm as the observation model. The performance of the method is assessed through simulations. Moreover, field experiments are presented using a real fixed-wing UAV. The proposed low cost solution, implemented in a microcontroller, shows a satisfactory real time performance. PMID:23012559
Espinosa, Felipe; Santos, Carlos; Marrón-Romera, Marta; Pizarro, Daniel; Valdés, Fernando; Dongil, Javier
2011-01-01
This paper describes a relative localization system used to achieve the navigation of a convoy of robotic units in indoor environments. This positioning system is carried out fusing two sensorial sources: (a) an odometric system and (b) a laser scanner together with artificial landmarks located on top of the units. The laser source allows one to compensate the cumulative error inherent to dead-reckoning; whereas the odometry source provides less pose uncertainty in short trajectories. A discrete Extended Kalman Filter, customized for this application, is used in order to accomplish this aim under real time constraints. Different experimental results with a convoy of Pioneer P3-DX units tracking non-linear trajectories are shown. The paper shows that a simple setup based on low cost laser range systems and robot built-in odometry sensors is able to give a high degree of robustness and accuracy to the relative localization problem of convoy units for indoor applications. PMID:22164079
Real time estimation of the heaving and pitching motions of a ship, using a Kalman filter
NASA Technical Reports Server (NTRS)
Triantafyllou, M.; Athans, M.
1981-01-01
In the present study the estimation of the heave and pitch motion of a ship is considered, using Kalman filtering techniques. A significant part of the study is devoted to constructing appropriate models for the sea and the ship. 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 numerical application is considered for a DD-963 destroyer.
Experiments with the assimilation of fine aerosols using an ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Pagowski, Mariusz; Grell, Georg A.
2012-11-01
In a series of experiments we issue forecasts of fine aerosol concentration over the coterminous USA and southern Canada using the Weather Research and Forecasting - Chemistry model initialized with 3D-VAR or ensemble Kalman filter (EnKF) assimilation methods. Assimilated observations include surface measurements of fine aerosols from the United States Environmental Protection Agency AIRNow Data Exchange program. Evaluation statistics calculated over a month-and-half-long summer period demonstrate the advantage of EnKF over 3D-VAR and point to the limitations of applying a simple aerosol parameterization for predicting air quality over the forecast area. Strategies for further improvement of forecasting aerosol concentrations are discussed.
Time scale algorithm: Definition of ensemble time and possible uses of the Kalman filter
NASA Technical Reports Server (NTRS)
Tavella, Patrizia; Thomas, Claudine
1990-01-01
The comparative study of two time scale algorithms, devised to satisfy different but related requirements, is presented. They are ALGOS(BIPM), producing the international reference TAI at the Bureau International des Poids et Mesures, and AT1(NIST), generating the real-time time scale AT1 at the National Institute of Standards and Technology. In each case, the time scale is a weighted average of clock readings, but the weight determination and the frequency prediction are different because they are adapted to different purposes. The possibility of using a mathematical tool, such as the Kalman filter, together with the definition of the time scale as a weighted average, is also analyzed. Results obtained by simulation are presented.
Real time estimation and prediction of ship motions using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Triantafyllou, M. A.; Bodson, M.; Athans, M.
1982-01-01
A landing scheme for landing V/STOL aircraft on rolling ships was sought using computerized simulations. The equations of motion as derived from hydrodynamics, their form and the physical mechanisms involved and the general form of the approximation are discussed. The modeling of the sea is discussed. The derivation of the state-space equations for the DD-963 destroyer is described. Kalman filter studies are presented and the influence of the various parameters is assessed. The effect of various modeling parameters on the rms error is assessed and simplifying conclusions are drawn. An upper bound for prediction time of about five seconds is established, with the exception of roll, which can be predicted up to ten seconds ahead.
Real-time acquisition and tracking system with multiple Kalman filters
NASA Astrophysics Data System (ADS)
Beard, Gary C.; McCarter, Timothy G.; Spodeck, Walter; Fletcher, James E.
1994-07-01
The design of a real-time, ground-based, infrared tracking system with proven field success in tracking boost vehicles through burnout is presented with emphasis on the software design. The system was originally developed to deliver relative angular positions during boost, and thrust termination time to a sensor fusion station in real-time. Autonomous target acquisition and angle-only tracking features were developed to ensure success under stressing conditions. A unique feature of the system is the incorporation of multiple copies of a Kalman filter tracking algorithm running in parallel in order to minimize run-time. The system is capable of updating the state vector for an object at measurement rates approaching 90 Hz. This paper will address the top-level software design, details of the algorithms employed, system performance history in the field, and possible future upgrades.
Espinosa, Felipe; Santos, Carlos; Marrón-Romera, Marta; Pizarro, Daniel; Valdés, Fernando; Dongil, Javier
2011-01-01
This paper describes a relative localization system used to achieve the navigation of a convoy of robotic units in indoor environments. This positioning system is carried out fusing two sensorial sources: (a) an odometric system and (b) a laser scanner together with artificial landmarks located on top of the units. The laser source allows one to compensate the cumulative error inherent to dead-reckoning; whereas the odometry source provides less pose uncertainty in short trajectories. A discrete Extended Kalman Filter, customized for this application, is used in order to accomplish this aim under real time constraints. Different experimental results with a convoy of Pioneer P3-DX units tracking non-linear trajectories are shown. The paper shows that a simple setup based on low cost laser range systems and robot built-in odometry sensors is able to give a high degree of robustness and accuracy to the relative localization problem of convoy units for indoor applications. PMID:22164079
NASA Astrophysics Data System (ADS)
Hoffman, Matthew J.; Greybush, Steven J.; John Wilson, R.; Gyarmati, Gyorgyi; Hoffman, Ross N.; Kalnay, Eugenia; Ide, Kayo; Kostelich, Eric J.; Miyoshi, Takemasa; Szunyogh, Istvan
2010-10-01
The local ensemble transform Kalman filter (LETKF) is applied to the GFDL Mars general circulation model (MGCM) to demonstrate the potential benefit of an advanced data assimilation method. In perfect model (aka identical twin) experiments, simulated observations are used to assess the performance of the LETKF-MGCM system and to determine the dependence of the assimilation on observational data coverage. Temperature retrievals are simulated at locations that mirror the spatial distribution of the Thermal Emission Spectrometer (TES) retrievals from the Mars Global Surveyor (MGS). The LETKF converges quickly and substantially reduces the analysis and subsequent forecast errors in both temperature and velocity fields, even though only temperature observations are assimilated. The LETKF is also found to accurately estimate the magnitude of forecast uncertainties, notably those associated with the phase and amplitude of baroclinic waves along the boundary of the polar ice cap during Northern Hemisphere winter.
Calibrating Multi-machine Power System Parameters with the Extended Kalman Filter
Kalsi, Karanjit; Sun, Yannan; Huang, Zhenyu; Du, Pengwei; Diao, Ruisheng; Anderson, Kevin K.; Li, Yulan; Lee, Barry
2012-07-24
Large-scale renewable resources and novel smart-grid technologies continue to increase the complexity of power systems. As power systems continue to become more complex, accurate modeling for planning and operation becomes a necessity. Inaccurate system models would result in an unreliable assessment of system security conditions and could cause large-scale blackouts. This motivates the need for model parameter calibration, since some or all of the model parameters could be unknown or inaccurate. In this paper, the extended Kalman filter is used to calibrate the parameters of a multi-machine power system. The calibration performance is tested under varying fault locations, parameter errors and measurement noise giving an insight into how many generators and which generators could be difficult to calibrate.
Dynamic State Estimation and Parameter Calibration of DFIG based on Ensemble Kalman Filter
Fan, Rui; Huang, Zhenyu; Wang, Shaobu; Diao, Ruisheng; Meng, Da
2015-07-30
With the growing interest in the application of wind energy, doubly fed induction generator (DFIG) plays an essential role in the industry nowadays. To deal with the increasing stochastic variations introduced by intermittent wind resource and responsive loads, dynamic state estimation (DSE) are introduced in any power system associated with DFIGs. However, sometimes this dynamic analysis canould not work because the parameters of DFIGs are not accurate enough. To solve the problem, an ensemble Kalman filter (EnKF) method is proposed for the state estimation and parameter calibration tasks. In this paper, a DFIG is modeled and implemented with the EnKF method. Sensitivity analysis is demonstrated regarding the measurement noise, initial state errors and parameter errors. The results indicate this EnKF method has a robust performance on the state estimation and parameter calibration of DFIGs.
NASA Astrophysics Data System (ADS)
Heidari, Leila; Gervais, Véronique; Ravalec, Mickaële Le; Wackernagel, Hans
2013-06-01
The Ensemble Kalman Filter (EnKF) has been successfully applied in petroleum engineering during the past few years to constrain reservoir models to production or seismic data. This sequential assimilation method provides a set of updated static variables (porosity, permeability) and dynamic variables (pressure, saturation) at each assimilation time. However, several limitations can be pointed out. In particular, the method does not prevent petrophysical realizations from departing from prior information. In addition, petrophysical properties can reach extreme (non-physical) values. In this work, we propose to combine the EnKF with two parameterization methods designed to preserve second-order statistical properties: pilot points and gradual deformation. The aim is to prevent the departure of the constrained petrophysical property distributions from prior information. Over/under estimations should also be avoided. The two algorithms are applied to a synthetic case. Several parameter configurations are investigated in order to identify solutions improving the performance of the method.
NASA Technical Reports Server (NTRS)
Deutschmann, Julie; Harman, Rick; Bar-Itzhack, Itzhack
1998-01-01
An innovative approach to autonomous attitude and trajectory estimation is available using only magnetic field data and rate data. The estimation is performed simultaneously using an Extended Kalman Filter, a well known algorithm used extensively in onboard applications. The magnetic field is measured on a satellite by a magnetometer, an inexpensive and reliable sensor flown on virtually all satellites in low earth orbit. Rate data is provided by a gyro, which can be costly. This system has been developed and successfully tested in a post-processing mode using magnetometer and gyro data from 4 satellites supported by the Flight Dynamics Division at Goddard. In order for this system to be truly low cost, an alternative source for rate data must be utilized. An independent system which estimate spacecraft rate has been successfully developed and tested using only magnetometer data or a combination of magnetometer data and sun sensor data, which is less costly than a gyro. This system also uses an Extended Kalman Filter. Merging the two systems will provide an extremely low cost, autonomous approach to attitude and trajectory estimation. In this work we provide the theoretical background of the combined system. The measurement matrix is developed by combining the measurement matrix of the orbit and attitude estimation EKF with the measurement matrix of the rate estimation EKF, which is composed of a pseudo-measurement which makes the effective measurement a function of the angular velocity. Associated with this is the development of the noise covariance matrix associated with the original measurement combined with the new pseudo-measurement. In addition, the combination of the dynamics from the two systems is presented along with preliminary test results.
Estimation of thermospheric zonal and meridional winds using a Kalman filter technique
NASA Astrophysics Data System (ADS)
Lomidze, Levan; Scherliess, Ludger
2015-11-01
Knowledge of the thermospheric neutral wind and its horizontal components is critical for an improved understanding of F region dynamics and morphology. However, to date their reliable estimation remains a challenge because of difficulties in both measurement and modeling. We present a new method to estimate the climatology of the zonal and meridional components of thermospheric neutral wind at low and middle latitudes using a Kalman filter technique. First, the climatology of the magnetic meridional wind is obtained by assimilating seasonal maps of F region ionosphere peak parameters (NmF2 and hmF2), obtained from Constellation Observing System for Meteorology, Ionosphere, and Climate radio occultation data, into the Global Assimilation of Ionospheric Measurements Full Physics (GAIM-FP) model. GAIM-FP provides the 3-D electron density throughout the ionosphere, together with the magnetic meridional wind. Next, the global zonal and meridional wind components are estimated using a newly developed Thermospheric Wind Assimilation Model (TWAM). TWAM combines magnetic meridional wind data obtained from GAIM-FP with a physics-based 3-D thermospheric neutral wind model using an implicit Kalman filter technique. Ionospheric drag and ion diffusion velocities, needed for the wind calculation, are also taken from GAIM-FP. The obtained wind velocities are in close agreement with measurements made by interferometers and with wind values from the Horizontal Wind Model 93 (HWM93) over Millstone Hill, Arecibo, and Arequipa during December and June solstices, and March equinox. In addition, it is shown that compared to HWM93 the winds from TWAM significantly improve the accuracy of the Ionosphere/Plasmasphere Model in reproducing the observed electron density variation over the Weddell Sea Anomaly.
Monthly Climatology of Thermospheric Zonal and Meridional Winds Obtained from a Kalman Filter Model
NASA Astrophysics Data System (ADS)
Scherliess, L.; Lomidze, L.
2015-12-01
Knowledge of the thermospheric neutral wind and its meridional and zonal components is critical for an improved understanding of the low- and mid-latitude F-region dynamics and morphology. To date, the reliable estimation of the wind and its components remains a challenge because of difficulties in both measurement and modeling. Previous methods that use ionospheric measurements to deduce winds provide their values only in the direction of the magnetic meridian. We will present the monthly climatology of the zonal and meridional components of thermospheric neutral wind at low and mid-latitudes obtained by a Kalman Filter technique. First, the climatology of the magnetic meridional wind is obtained by assimilating monthly maps of F-region ionosphere peak parameters (NmF2 and hmF2), obtained from COSMIC radio occultation data, into the Global Assimilation of Ionospheric Measurements Full Physics (GAIM-FP) model. The model provides the 3-D electron density throughout the ionosphere, together with the magnetic meridional wind. Next, the estimation of the global zonal and meridional wind components is performed using the newly developed Thermospheric Wind Assimilation Model (TWAM). TWAM combines magnetic meridional wind data obtained from GAIM-FP with a physics-based 3-D thermospheric neutral wind model using an implicit Kalman Filter technique. The ionospheric drag and ion diffusion velocities, needed for the wind calculation, are also taken from the GAIM-FP model. We present the monthly climatology of our wind estimation and compare individual horizontal wind components to their corresponding empirical model values and to measurements made by interferometers.
Markov Models and the Ensemble Kalman Filter for Estimation of Sorption Rates
NASA Astrophysics Data System (ADS)
Vugrin, E. D.; McKenna, S. A.; White Vugrin, K.
2007-12-01
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude. Sandia is a multi program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000. This work was supported under the Sandia Laboratory Directed Research and Development program.
Tracking magma volume recovery at okmok volcano using GPS and an unscented kalman filter
Fournier, T.; Freymueller, Jeffrey T.; Cervelli, Peter
2009-01-01
Changes beneath a volcano can be observed through position changes in a GPS network, but distinguishing the source of site motion is not always straightforward. The records of continuous GPS sites provide a favorable data set for tracking magma migration. Dense campaign observations usually provide a better spatial picture of the overall deformation field, at the expense of an episodic temporal record. Combining these observations provides the best of both worlds. A Kalman filter provides a means for integrating discrete and continuous measurements and for interpreting subtle signals. The unscented Kalman filter (UKF) is a nonlinear method for time-dependent observations. We demonstrate the application of this technique to deformation data by applying it to GPS data collected at Okmok volcano. Seven years of GPS observations at Okmok are analyzed using a Mogi source model and the UKF. The deformation source at Okmok is relatively stable at 2.5 km depth below sea level, located beneath the center of the caldera, which means the surface deformation is caused by changes in the strength of the source. During the 7 years of GPS observations more than 0.5 m of uplift has occurred, a majority of that during the time period January 2003 to July 2004. The total volume recovery at Okmok since the last eruption in 1997 is ??60-80%. The UKF allows us to solve simultaneously for the time-dependence of the source strength and for the location without a priori information about the source. ?? 2009 by the American Geophysical Union.
Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Slojkowski, Steven; Lowe, Jonathan; Woodburn, James
2015-01-01
Orbit determination (OD) analysis results are presented for the Lunar Reconnaissance Orbiter (LRO) using a commercially available Extended Kalman Filter, Analytical Graphics' Orbit Determination Tool Kit (ODTK). Process noise models for lunar gravity and solar radiation pressure (SRP) are described and OD results employing the models are presented. Definitive accuracy using ODTK meets mission requirements and is better than that achieved using the operational LRO OD tool, the Goddard Trajectory Determination System (GTDS). Results demonstrate that a Vasicek stochastic model produces better estimates of the coefficient of solar radiation pressure than a Gauss-Markov model, and prediction accuracy using a Vasicek model meets mission requirements over the analysis span. Modeling the effect of antenna motion on range-rate tracking considerably improves residuals and filter-smoother consistency. Inclusion of off-axis SRP process noise and generalized process noise improves filter performance for both definitive and predicted accuracy. Definitive accuracy from the smoother is better than achieved using GTDS and is close to that achieved by precision OD methods used to generate definitive science orbits. Use of a multi-plate dynamic spacecraft area model with ODTK's force model plugin capability provides additional improvements in predicted accuracy.
NASA Technical Reports Server (NTRS)
Deutschmann, Julie; Bar-Itzhack, Itzhack Y.; Rokni, Mohammad
1990-01-01
The testing and comparison of two Extended Kalman Filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS) is described. One EKF updates the attitude quaternion using a four component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. A brief development of the multiplicative algorithm is included. The mathematical development of the additive EKF was presented in the 1989 Flight Mechanics/Estimation Theory Symposium along with some preliminary testing results using real spacecraft data. A summary of the additive EKF algorithm is included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases. Sensitivity studies are performed on the estimation of sensor calibration states. The potential application of the EKF for real time and non-real time ground attitude determination and sensor calibration for future missions such as the Gamma Ray Observatory (GRO) and the Small Explorer Mission (SMEX) is also presented.
Abrecht, David G.; Schwantes, Jon M.; Kukkadapu, Ravi K.; McDonald, Benjamin S.; Eiden, Gregory C.; Sweet, Lucas E.
2015-02-01
Spectrum-processing software that incorporates a gaussian smoothing kernel within the statistics of first-order Kalman filtration has been developed to provide cross-channel spectral noise reduction for increased real-time signal-to-noise ratios for Mossbauer spectroscopy. The filter was optimized for the breadth of the gaussian using the Mossbauer spectrum of natural iron foil, and comparisons between the peak broadening, signal-to-noise ratios, and shifts in the calculated hyperfine parameters are presented. The results of optimization give a maximum improvement in the signal-to-noise ratio of 51.1% over the unfiltered spectrum at a gaussian breadth of 27 channels, or 2.5% of the total spectrum width. The full-width half-maximum of the spectrum peaks showed an increase of 19.6% at this optimum point, indicating a relatively weak increase in the peak broadening relative to the signal enhancement, leading to an overall increase in the observable signal. Calculations of the hyperfine parameters showed no statistically significant deviations were introduced from the application of the filter, confirming the utility of this filter for spectroscopy applications.
Gao, Wei; Zhang, Ya; Wang, Jianguo
2014-01-01
The integrated navigation system with strapdown inertial navigation system (SINS), Beidou (BD) receiver and Doppler velocity log (DVL) can be used in marine applications owing to the fact that the redundant and complementary information from different sensors can markedly improve the system accuracy. However, the existence of multisensor asynchrony will introduce errors into the system. In order to deal with the problem, conventionally the sampling interval is subdivided, which increases the computational complexity. In this paper, an innovative integrated navigation algorithm based on a Cubature Kalman filter (CKF) is proposed correspondingly. A nonlinear system model and observation model for the SINS/BD/DVL integrated system are established to more accurately describe the system. By taking multi-sensor asynchronization into account, a new sampling principle is proposed to make the best use of each sensor's information. Further, CKF is introduced in this new algorithm to enable the improvement of the filtering accuracy. The performance of this new algorithm has been examined through numerical simulations. The results have shown that the positional error can be effectively reduced with the new integrated navigation algorithm. Compared with the traditional algorithm based on EKF, the accuracy of the SINS/BD/DVL integrated navigation system is improved, making the proposed nonlinear integrated navigation algorithm feasible and efficient. PMID:24434842
Rigatos, G; Rigatou, E; Djida, J D
2015-01-01
The derivative-free nonlinear Kalman filter is proposed for state estimation and fault diagnosis in distributed parameter systems of the wave-type and particularly in the Peyrard-Bishop-Dauxois model of DNA dynamics. At a first stage, a nonlinear filtering approach is introduced for estimating the dynamics of the Peyrard-Bishop-Dauxois 1D nonlinear wave equation, through the processing of a small number of measurements. It is shown that the numerical solution of the associated partial differential equation results in a set of nonlinear ordinary differential equations. With the application of a diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical (Brunovsky) form. This transformation enables to obtain local estimates about the state vector of the DNA model through the application us of the standard Kalman filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for this distributed parameter system by processing with statistical tools the differences (residuals) between the output of the Kalman filter and the measurements obtained from the distributed parameter system. Optimal selection of the fault threshold is succeeded by using the local statistical approach to fault diagnosis. The efficiency of the proposed filtering approach in the problem of fault diagnosis for parametric change detection, in nonlinear wave-type models of DNA dynamics, is confirmed through simulation experiments. PMID:25294023
Unscented KALMAN Filtering for Spacecraft Attitude and Rate Determination Using Magnetometer
NASA Astrophysics Data System (ADS)
Kim, Sung-Woo; Abdelrahman, Mohammed; Park, Sang-Young; Choi, Kyu-Hong; Park, Sang-Young; Choi, Kyu-Hong
2009-03-01
An Unscented Kalman Filter (UKF) for estimation of the attitude and rate of a spacecraft using only magnetometer vector measurement is developed. The attitude dynamics used in the estimation is the nonlinear Euler's rotational equation which is augmented with the quaternion kinematics to construct a process model. The filter is designed for small satellite in low Earth orbit, so the disturbance torques include gravity-gradient torque, magnetic disturbance torque, and aerodynamic drag torque. The magnetometer measurements are simulated based on time-varying position of the spacecraft. The filter has been tested not only in the standby mode but also in the detumbling mode. Two types of actuators have been modeled and applied in the simulation. The PD controller is used for the two types of actuators (reaction wheels and thrusters) to detumble the spacecraft. The estimation error converged to within 5 deg for attitude and 0.1 deg/s for rate respectively when the two types of actuators were used. A joint state parameter estimation has been tested and the effect of the process noise covariance on the parameter estimation has been indicated. Also, Monte-Carlo simulations have been performed to test the capability of the filter to converge with the initial conditions sampled from a uniform distribution. Finally, the UKF performance has been compared to that of the EKF and it demonstrates that UKF slightly outperforms EKF. The developed algorithm can be applied to any type of small satellites that are actuated by magnetic torquers, reaction wheels or thrusters with a capability of magnetometer vector measurements for attitude and rate estimation.
Oster, Julien; Behar, Joachim; Sayadi, Omid; Nemati, Shamim; Johnson, Alistair E W; Clifford, Gari D
2015-09-01
Automatic processing and accurate diagnosis of pathological electrocardiogram (ECG) signals remains a challenge. As long-term ECG recordings continue to increase in prevalence, driven partly by the ease of remote monitoring technology usage, the need to automate ECG analysis continues to grow. In previous studies, a model-based ECG filtering approach to ECG data from healthy subjects has been applied to facilitate accurate online filtering and analysis of physiological signals. We propose an extension of this approach, which models not only normal and ventricular heartbeats, but also morphologies not previously encountered. A switching Kalman filter approach is introduced to enable the automatic selection of the most likely mode (beat type), while simultaneously filtering the signal using appropriate prior knowledge. Novelty detection is also made possible by incorporating a third mode for the detection of unknown (not previously observed) morphologies, and denoted as X-factor. This new approach is compared to state-of-the-art techniques for the ventricular heartbeat classification in the MIT-BIH arrhythmia and Incart databases. F1 scores of 98.3% and 99.5% were found on each database, respectively, which are superior to other published algorithms' results reported on the same databases. Only 3% of all the beats were discarded as X-factor, and the majority of these beats contained high levels of noise. The proposed technique demonstrates accurate beat classification in the presence of previously unseen (and unlearned) morphologies and noise, and provides an automated method for morphological analysis of arbitrary (unknown) ECG leads. PMID:25680203
NASA Astrophysics Data System (ADS)
Loizu, Javier; Massari, Christian; Álvarez-Mozos, Jesús; Casalí, Javier; Goñi, Mikel
2016-04-01
Assimilation of Surface Soil Moisture (SSM) observations obtained from remote sensing techniques have been shown to improve streamflow prediction at different time scales of hydrological modeling. Different sensors and methods have been tested for their application in SSM estimation, especially in the microwave region of the electromagnetic spectrum. The available observation devices include passive microwave sensors such as the Advanced Microwave Scanning Radiometer - Earth Observation System (AMSR-E) onboard the Aqua satellite and the Soil Moisture and Ocean Salinity (SMOS) mission. On the other hand, active microwave systems include Scatterometers (SCAT) onboard the European Remote Sensing satellites (ERS-1/2) and the Advanced Scatterometer (ASCAT) onboard MetOp-A satellite. Data assimilation (DA) include different techniques that have been applied in hydrology and other fields for decades. These techniques include, among others, Kalman Filtering (KF), Variational Assimilation or Particle Filtering. From the initial KF method, different techniques were developed to suit its application to different systems. The Ensemble Kalman Filter (EnKF), extensively applied in hydrological modeling improvement, shows its capability to deal with nonlinear model dynamics without linearizing model equations, as its main advantage. The objective of this study was to investigate whether data assimilation of SSM ASCAT observations, through the EnKF method, could improve streamflow simulation of mediterranean catchments with TOPLATS hydrological complex model. The DA technique was programmed in FORTRAN, and applied to hourly simulations of TOPLATS catchment model. TOPLATS (TOPMODEL-based Land-Atmosphere Transfer Scheme) was applied on its lumped version for two mediterranean catchments of similar size, located in northern Spain (Arga, 741 km2) and central Italy (Nestore, 720 km2). The model performs a separated computation of energy and water balances. In those balances, the soil