Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.