Optimal Linear State Estimation for Discrete-time Systems with Time-correlated Multiplicative Noises and Delays

This brief is concerned with the filtering problem for discrete-time measurement-delay systems with time-correlated multiplicative noise. First, by using the reorganized innovation approach, the original system is transformed into a delay-free system. Then, several new recursive terms are added in the initial estimation of the new algorithm, including the estimation for the product of multiplicative measurement noise and state along with the corresponding error covariances. Based on the well-known projection theorem, a new algorithm for optimal filtering of the system under consideration is proposed.