Design and analysis of discrete-time robust Kalman filters

• Published in: Automatica (Oxford) Vol. 38; no. 6; pp. 1069 - 1077
• Main Authors: Zhu, Xing, Soh, Yeng Chai, Xie, Lihua
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.06.2002; Elsevier
• Subjects: Applied sciences; Asymptotic analysis; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Kalman filtering; Mathematics; Probability and statistics; Probability theory and stochastic processes; Robust state estimation; Sciences and techniques of general use; Stochastic processes; Uncertain discrete-time systems; Kalman filtering; Asymptotic analysis; Uncertain discrete-time systems; Robust state estimation; Filtering; Kalman filter; Non linear filter; Discrete system; Variance; Finite horizon; Time varying system; Upper bound; Uncertain system; Linear filter; Discrete time; Infinite horizon; Riccati equation
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/S0005-1098(01)00298-9

In this paper, the problem of finite and infinite horizon robust Kalman filtering for uncertain discrete-time systems is studied. The system under consideration is subject to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty. A novel technique is developed for robust filter design. This technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized Riccati equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed.