Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises

• Published in: IEEE transactions on automatic control Vol. 47; no. 7; pp. 1179 - 1183
• Main Authors: Fuwen Yang, Zidong Wang, Hung, Y.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Automatic control; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Difference equations; Exact sciences and technology; Filtering; Kalman filtering; Kalman filters; Mathematical models; Mathematics; Noise; Noise robustness; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; State estimation; Stochastic processes; Stochastic resonance; Stochastic systems; Sufficient conditions; Time varying systems; Uncertain systems; Uncertainty; Upper bounds; Additive noise; Estimation error; Filtering; Probabilistic approach; Error estimation; Kalman filter; Numerical method; Difference equation; Finite horizon; Time varying system; Upper bound; Multiplicative noise; Uncertain system; Discrete time; System identification; Riccati equation; Deterministic approach; State estimation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.800668

In this paper, a robust finite-horizon Kalman filter is designed for discrete time-varying uncertain systems with both additive and multiplicative noises. The system under consideration is subject to both deterministic and stochastic uncertainties. Sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete Riccati difference equations. A numerical example is given to show the applicability of the presented method.