Optimal filtering for discrete‐time linear systems with multiplicative and time‐correlated additive measurement noises

Abstract

The filtering problem for discrete‐time linear systems with multiplicative and time‐correlated additive measurement noises is considered where the multiplicative noises are zero‐mean white noise sequences, and the time‐correlated additive measurement noise is described by a linear system model with white noise. Using the method of measurement differencing and some results obtained in this study, a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean‐square error. The proposed algorithm is recursive, and does not increase computation and storage load with time. The convergence of the proposed algorithm is investigated. Computer simulations are carried out to demonstrate the performance of the proposed algorithm. The simulation results show the superiority of the proposed algorithm.