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Showing papers on "Invariant extended Kalman filter published in 1985"


Book
01 Jan 1985

652 citations


Journal ArticleDOI
TL;DR: In this article, a modified gain extended Kalman observer (MGEKO) was developed for a special class of systems and a sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square was obtained.
Abstract: A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.

287 citations


Journal ArticleDOI
Uri Shaked1
TL;DR: In this paper, a closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero.
Abstract: A closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero Simple expressions, in closed form, are obtained for the Kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the Kalman filter closed loop matrix is derived The minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure, and a remarkably different behavior of the solution in the minimum- and nonminimum-phase cases is found

82 citations


Journal ArticleDOI
TL;DR: In this paper, an extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data, and the effects of the magnitude of the rate constants and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses.

41 citations


Journal ArticleDOI
TL;DR: In this paper, a new probabilistic technique for fault classification using an adaptive Kalman filter using voltage measurements is described. But this technique assumes the features of a faulted phase while the other has features of an unfaulted phase and the condition of the phase, faulted or non-faulted, is then decided from the computed a posteriori probabilities.
Abstract: This paper describes a new probabilistic technique for fault classification to be used in digital distance protection of power systems. The new technique is based on an adaptive Kalman filter using voltage measurements. The voltage data of each phase is processed in two Kalman filter models simultaneously. One Kalman filter assumes the features of a faulted phase while the other has the features of an unfaulted phase. The condition of the phase, faulted or non-faulted, is then decided from the computed a posteriori probabilities.

39 citations


Journal ArticleDOI
TL;DR: In this paper, the performance of fixed-interval smoothing for a linear calibration graph with drifting parameters was investigated and it was shown that a considerable reduction in variance can be obtained.

33 citations


Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this paper, the optimal projection equations derived previously for reduced-order, continuous-time modelling, estimation and control are developed for the discrete-time case, and the design equations are presented in a concise and unified manner to facilitate their accessibility for the development of numerical algorithms for practical applications.
Abstract: The optimal projection equations derived previously for reduced-order, continuous-time modelling, estimation and control are developed for the discrete-time case. The design equations are presented in a concise and unified manner to facilitate their accessibility for the development of numerical algorithms for practical applications. As in the continuous-time case, the standard Kalman filter and linear-quadratic-Gaussian results are immediately obtained as special cases of the estimation and control results.

29 citations


Journal ArticleDOI
TL;DR: This approach combines simplex optimization with the adaptive Kalman filter to yield a method in which initial guesses for the adaptive filter are generated by the simplex algorithm.

28 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the impact of instrument offset from center of gravity, measurement time delays, sinusoidal disturbances and nonlinearities on the identified instrument errors using the extended Kalman Filter approach and the Maximum Likelihood method.

21 citations


Journal ArticleDOI
TL;DR: In this paper, the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process is investigated and some asymptotic properties of the state estimates and predicted values obtained by the KF with estimated parameters which converge to the true parameters with probability one.
Abstract: . State estimation and prediction problems are considered for a stochastic process represented by a state space form which involves unknown parameters. We first study the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process. Second, we consider the state estimation and prediction when the process is stationary, and show some asymptotic properties of the state estimates and predicted values obtained by the Kalman filter with estimated parameters which converge to the true parameters or to the equivalent classes of the true parameters with probability one.

20 citations



Proceedings ArticleDOI
Fred Daum1
01 Dec 1985
TL;DR: In this paper, a new nonlinear filter is derived for continuous time processes with discrete time measurements, which can be implemented in real-time with a computational complexity that is comparable to the Kalman filter.
Abstract: A new nonlinear filter is derived for continuous time processes with discrete time measurements. The filter is exact, and it can be implemented in real-time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete time version of the Bene? filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete time Bene? filters. A simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.

Journal ArticleDOI
TL;DR: In this paper, the Kalman filter gain and covariance update algorithms are illustrated geometrically for a low dimensional system, and the illustrations give an intuitive understanding of the basic filtering process.
Abstract: The Kalman filter gain and covariance update algorithms are illustrated geometrically for a low dimensional system. The illustrations give an intuitive understanding of the basic filtering process and advocate a more "natural" form of the covariance update algorithm.

Journal ArticleDOI
Bertil Ekstrand1
TL;DR: In this paper, the steady-state solution to a continuous time Kalman filter for a two-state model where both states are measured is given by a limiting operation on the known solution for the corresponding discrete time case.
Abstract: Analytical expressions are given for the steady-state solution to a continuous time Kalman filter for a two-state model where both states are measured. The solution is obtained by a limiting operation on the known solution for the corresponding discrete time case. The solution is visualized in two graphs. The filter transfer function is also given.

01 Jan 1985
TL;DR: In this article, a two-dimensional Kalman filter is described for data assimilation for making weather forecasts, which is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation.
Abstract: 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.


Journal ArticleDOI
TL;DR: A filter is introduced which is not new but less well known and suffers less with computational eomplexity and robustness problems and is shown how simultaneous state and parameter estimation can be done without using extended state techniques.

Journal ArticleDOI
TL;DR: In this article, a two-stage estimator consisting of two consecutive Kalman filters is proposed to solve the linear estimation problem, and the interconnections between this estimator structure and the more familiar one-stage optimal Kalman filter are discussed.
Abstract: The estimation algorithm described in this note solves the linear estimation problem as a two-stage estimator consisting of two consecutive Kalman filters. The interconnections between this estimator structure and the more familiar one-stage optimal Kalman filter are discussed. Applications to decentralized estimation, bias estimation, and parameter identification are described.

Proceedings ArticleDOI
01 Dec 1985
TL;DR: An adaptive target tracking scheme using two Kalman filters in series using a pseudosystem concept and the inclusion of the covariance between the state estimates of the two filters in the second filter gain and covariance algorithms.
Abstract: An adaptive target tracking scheme using two Kalman filters in series is presented. The first filter is a priori designed to cope with all possible target maneuvers, The second filter is controlled adaptively to suppress measurement noise, A pseudosystem concept is applied that have an influence on the Kalman filter algorithms of both filters. This includes the decomposition of the first filter state covariance into a system noise part and a measurement noise part and the inclusion of the covariance between the state estimates of the two filters in the second filter gain and covariance algorithms. The covariance between the state estimates is recursively calculated and accounts for the serially correlated measurement noise of the second filter. The qualitative merits of the method are discussed, Results from computer simulations are included to demonstrate performance obtained.


Journal ArticleDOI
TL;DR: Using Kalman filter theory, new non-recursive algorithms for estimating the fundamental voltage and current waveforms from noise signals are developed and investigated in this article, which have much better filter properties than Fourier algorithms, especially with increase in filter order and sampling frequency.

01 Dec 1985
TL;DR: In this paper, the feasibility of replacing the Wiener-hopf filter with a Kalman filter was evaluated by first designing an appropriate preliminary design and then testing the design through a Monte Carlo computer simulation analysis.
Abstract: : Currently, the F-4E/G uses a Wiener-Hopf filter for estimating target position, velocity, and acceleration during air combat maneuvering. As implemented, the errors between the actual target variables and the estimate of these variables are too large. The purpose of this study is to evaluate the feasibility of replacing the Wiener-Hopf filter with a Kalman filter in order to obtain better estimates. The evaluation is made by first designing an appropriate preliminary design Kalman filter and then testing the design through a Monte Carlo computer simulation analysis. The computer simulation results indicate that the Kalman filter is capable of significantly outperforming the Wiener-Hopf filter and as such should be developed into a final design. The Kalman filter contains nine states (three relative target position, three total target velocity, and three total target acceleration states). Filter propagation is based on linear time-invariant dynamics primarily because of the limited capabilities of the on-board aircraft computer. The linear dynamics permits propagation by a state transition matrix. Measurement updates use six measurements (range, range rate, azimuth angle, elevation angle, azimuth rate, and elevation rate) available on the F-4. Both continuous time sampled-data and discrete-time sampled-data designs are included. (Author)

Journal ArticleDOI
Arnold Heemink1
TL;DR: In this article, a discrete time-invariant Kalman filter for the prediction of water levels and velocities has been developed, based on a set of difference equations derived from the linearized two dimensional shallow water equations using the finite difference scheme proposed by Sielecki.

Journal ArticleDOI
TL;DR: In this article, the optimal discrete-time filtering problem for time-varying non-stationary signal models is considered and a return-difference/covariance factorisation result is derived, which has implications for both the stability and optimality of the filter.

Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this article, an optimal linear filter or predictor is described which has the feedback form of a Kalman filter but which involves only an input-output signal model within the feedback loop.
Abstract: An optimal linear filter or predictor is described which has the feedback form of a Kalman filter but which involves only an input-output signal model within the feedback loop. The Kalman gain matrix is replaced by a dynamical gain block. The solution to the problem is obtained using a polynomial system approach. This enables adaptive estimators to be constructed since the signal models are normally identified in polynomial matrix (ARMA) form.

Proceedings ArticleDOI
R. Kumar1
01 Apr 1985
TL;DR: An algorithm for optimal estimation in presence of non-Gaussian observation noise is presented and the filter is shown to be superior to the Kalman Filter when applied to the same system.
Abstract: An algorithm for optimal estimation in presence of non-Gaussian observation noise is presented. The algorithm, based on Bayes' recursion formula is implemented numerically. The filter is shown to be superior to the Kalman Filter when applied to the same system. It has been shown that the steady state estimation error is zeros. The Algorithm is a potential technique for analyzing transients in the automobile electrical environoment.

01 Jan 1985
TL;DR: In this article, the authors give an exposition of the applications Kalman filters and the related nonlinear filters offer when used in models describing tidal motion in seas and estuaries.
Abstract: This report gives an exposition of the applications Kalman filters and the related nonlinear filters offer when used in models describing tidal motion in seas and estuaries. In addition to methods that are generally used in this field, for example deterministic and black-box models, Kalman filters can provide significant contributions in particular situations. Although it is not our intention to claim that the use of Kalman filters is the most fruitful method for all problems, it will be shown that these filters exhibit some specific useful properties, not present in the above mentioned conventional methods. Before explaining the fundamental ideas of the Kalman filter and its advantages and disadvantages a short review will be given of other known methods.

Journal Article
TL;DR: In this paper, reduced-order Kalman filters designed to improve performance of the F-4E/G long range air-to-air missile capability (LRI function) are examined.
Abstract: : This study examines reduced-order Kalman filters designed to improve performance of the F-4E/G long range air-to-air missile capability (LRI function) Operational requirements dictate a high degree of accuracy and constraints imposed by existing hardware mandate minimal complexity Two linear dynamics models are proposed, one based on constant target velocity, and the other based on time-correlated target acceleration Both are defined in inertial Cartesian coordinates aligned with north, east, and down A nonlinear model is developed for measurements available in the existing F-4E/G hardware, including range, range rate, radar antenna gimbal angles, and radar antenna rates The models are implemented in extended Kalman filter formulations employing linear propagation equations to avoid on-line numerical integration Performance evaluations are performed on three test trajectories using Monte Carlo analysis Filter tuning, error budgets, adaptive techniques, and observability issues are addressed during filter evaluation Results of the evaluation indicate the filter designs can meet the requirements of the F-4E/G fire control system Recommendations are made for continued testing and for operational implementation

Journal ArticleDOI
TL;DR: In this paper, a Kalman filter bank is designed to enhance the dynamic response time for the radome error slope estimate with compensation for the seeker dynamic lag, and the bank of Kalman filters can be increased to five to enlarge the dynamic range while reducing the system response time simultaneously and to estimate the cross-plane radome estimation for three-dimensional engagement.
Abstract: Conclusion A Kalman filter bank is designed to enhance the dynamic response time for the radome error slope estimate with compensation for the seeker dynamic lag. In calculating the critical weighting coefficients (a posteriori probabilities) a measurepredict-measure technique is used when the semi-Markov statistics of a random starting process are used to make the intermediate predictive step. That is, the resulting estimated radome slope parameter is the statistical average weighted by time-varying, a posteriori hypothesis probability, which is calculated concurrently with the recursive filter scheme by using Bayesian rule. To reduce computation burden, the Kalman filter bank is digitally simulated and designed by tuning the noise processes, including the measurement and plant noise, to allow a one-time calculation of the Kalman filter gain. The simple one-state filter described above can be modified to include a correlation parameter for studying the cross-plane errors. The bank of Kalman filters can be increased to five to enlarge the dynamic range while reducing the system response time simultaneously and to estimate the cross-plane radome error slope simultaneously for three-dimensional engagement. The adaptive radome estimator design is intended to be an "add-on" compensation network that is independent of guidance computer and autopilot design. The objective is to permit relaxation of missile bandwidth requirements by reducing error due to radome at the guidance computer output, thus enhancing missile performance.

Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this article, the problem of estimating two-dimensional isotropic random fields, whose equations are expressed in terms of the Laplacian, given some noisy observations on a finite disk is shown to be equivalent to solving a countably infinite number of one-dimensional estimation problems.
Abstract: This paper considers the application of Kalman estimation theory to the problem of estimating two-dimensional isotropic random fields, whose equations are expressed in terms of the Laplacian, given some noisy observations on a finite disk. It is shown that this problem is equivalent to that of solving a countably infinite number of one-dimensional estimation problems. Markovian models for the one-dimensional processes are developed and the associated Kalman filters are shown to be asymptotically stable. The desired field estimate is then obtained by combining the smoothed estimates resulting from each of the one-dimensional problems weighted in an appropriate fashion.