Robust filtering for systems with stochastic nonlinearities and deterministic uncertainties

In this paper, we consider the robust finite-horizon filter design problem for a class of discrete time varying systems with both stochastic nonlinearities and deterministic uncertainties. The description of the stochastic nonlinearities is quite general, which comprises the state-multiplicative noises and the random sequences whose powers depend on either the sector-bound nonlinear function of the state or the sign of a nonlinear function of the state. The norm bounded parameter uncertainties are allowed to enter both the system and the output matrices. We aim to design a robust filter that guarantees an optimized upper bound on the state estimation error variance, for all stochastic nonlinearities and admissible deterministic uncertainties. The existence conditions for the desired robust filters are first derived, and the filter parameters are then determined in terms of the solutions to two recursive Riccati-like difference equations. A numerical example is presented to show the applicability of the proposed method.

[1]  Bor-Sen Chen,et al.  Minimax robust deconvolution filters under stochastic parametric and noise uncertainties , 1994, IEEE Trans. Signal Process..

[2]  Edwin Engin Yaz,et al.  On LMI formulations of some problems arising in nonlinear stochastic system analysis , 1999, IEEE Trans. Autom. Control..

[3]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[4]  Edwin Engin Yaz,et al.  State estimation of uncertain nonlinear stochastic systems with general criteria , 2001, Appl. Math. Lett..

[5]  Zhi-Quan Luo,et al.  Finite-horizon robust Kalman filter design , 2001, IEEE Trans. Signal Process..

[6]  Keith J. Burnham,et al.  Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation , 2001, IEEE Trans. Signal Process..

[7]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[8]  Fuwen Yang,et al.  Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises , 2002, IEEE Trans. Autom. Control..

[9]  Lihua Xie,et al.  Robust Kalman filter design , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  Lihua Xie,et al.  Design and analysis of discrete-time robust Kalman filters , 2002, Autom..

[11]  Uri Shaked,et al.  Robust discrete-time minimum-variance filtering , 1996, IEEE Trans. Signal Process..

[12]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

[13]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[14]  Fan Wang,et al.  Robust steady-state filtering for systems with deterministic and stochastic uncertainties , 2003, IEEE Trans. Signal Process..

[15]  Fuwen Yang,et al.  Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty , 2003, Autom..

[16]  D. Jacobson.  A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria , 1974 .