Stochastic stability of the discrete-time extended Kalman filter

The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

[1]  T. Morozan.  Stability of stochastic discrete systems , 1968 .

[2]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[3]  E. Jury,et al.  ALMOST SURE BOUNDEDNESS OF RANDOMLY SAMPLED SYSTEMS , 1971 .

[4]  T. Morozan.  Boundedness properties for stochastic systems , 1972 .

[5]  John M. Fitts.  On the observability of non-linear systems with applications to non-linear regression analysis , 1972, Inf. Sci..

[6]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[7]  T. Tarn,et al.  Observers for nonlinear stochastic systems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[8]  Eduardo Sontag.  On the Observability of Polynomial Systems. , 1977 .

[9]  B. Ursin.  Asymptotic convergence properties of the extended Kalman filter using filtered state estimates , 1980 .

[10]  T. Westerlund,et al.  Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems" , 1980 .

[11]  Michael G. Safonov,et al.  Stability and Robustness of Multivariable Feedback Systems , 1980 .

[12]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[13]  H. Nijmeijer.  Observability of autonomous discrete-time nonlinear systems: a geometric approach : Preprint , 1982 .

[14]  P. Krishnaprasad,et al.  Dynamic observers as asymptotic limits of recursive filters , 1982, CDC 1982.

[15]  J. Speyer,et al.  A stochastic analysis of a modified gain extended Kalman filter with applications to estimation with bearings only measurements , 1983 .

[16]  Chaw-Bing Chang,et al.  Application of state estimation to target tracking , 1984 .

[17]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[18]  Jerry M. Mendel,et al.  Lessons in digital estimation theory , 1986 .

[19]  S. Falk,et al.  Matrizen und ihre Anwendungen für Angewandte Mathematiker, Physiker und Ingenieure , 1986 .

[20]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .

[21]  S. Zacks,et al.  Introduction to stochastic differential equations , 1988 .

[22]  J. Hedrick,et al.  Nonlinear Observers—A State-of-the-Art Survey , 1989 .

[23]  H. Triebel.  Analysis und mathematische Physik , 1989 .

[24]  Lei Guo.  Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence , 1990 .

[25]  H. Heuser.  Lehrbuch der Analysis , 2022 .

[26]  Peggy Galkowski,et al.  An alternative derivation of the modified gain function of Song and Speyer , 1991 .

[27]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[28]  J. Gauthier,et al.  High gain estimation for nonlinear systems , 1992 .

[29]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[30]  E. Yaz,et al.  Observer design for discrete and continuous non-linear stochastic systems , 1993 .

[31]  J. Spall.  THE DISTRIBUTION OF NONSTATIONARY AUTOREGRESSIVE PROCESSES UNDER GENERAL NOISE CONDITIONS , 1993 .

[32]  P. Bougerol.  Kalman filtering with random coefficients and contractions , 1993 .

[33]  F. W. Cathey,et al.  The iterated Kalman filter update as a Gauss-Newton method , 1993, IEEE Trans. Autom. Control..

[34]  Lee A. Feldkamp,et al.  Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks , 1994, IEEE Trans. Neural Networks.

[35]  Bradley M. Bell,et al.  The Iterated Kalman Smoother as a Gauss-Newton Method , 1994, SIAM J. Optim..

[36]  D. Bertsekas.  Incremental least squares methods and the extended Kalman filter , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[37]  Mohamed Darouach,et al.  Convergence analysis of the extended Kalman filter as an observer for nonlinear discrete-time systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[38]  James C. Spall,et al.  Uncertainties for recursive estimators in nonlinear state-space models, with applications to epidemiology , 1995, Autom..

[39]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[40]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systemsy , 1995 .

[41]  Rolf Unbehauen,et al.  Modification of the extended Kalman filter with an additive term of instability , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[42]  R. Unbehauen,et al.  Linearisation Along Trajectories and the Extended Kalman Filter , 1996 .

[43]  V. Solo,et al.  Stability of the Kalman filter with stochastic time-varying parameters , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[44]  R. Unbehauen,et al.  An Observer for Nonlinear Systems Based on H,-Filtering Techniques , 1997 .

[45]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[46]  R. Unbehauen,et al.  An observer for nonlinear systems based on H/sub /spl infin//-filtering techniques , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[47]  M. Boutayeb,et al.  Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems , 1997, IEEE Trans. Autom. Control..

[48]  Konrad Reif,et al.  An EKF-Based Nonlinear Observer with a Prescribed Degree of Stability , 1998, Autom..

[49]  Konrad Reif,et al.  Nonlinear state observation using H∞-filtering Riccati design , 1999, IEEE Trans. Autom. Control..

[50]  R. Unbehauen,et al.  Stochastic stability of the continuous-time extended Kalman filter , 2000 .