State Estimation for Two-Dimensional Systems with Time-Correlated Multiplicative Measurement Noises

This paper addresses the state estimation problem for a class of two-dimensional discrete-time linear systems with additive noises and time-correlated multiplicative measurement noises. The time-correlated multiplicative noises are described by a linear system model with white noises. The main objective of this paper is to construct a recursive estimator that achieves the minimum error variance of the state estimation at each step. By introducing the method of the line of cross-cut and geometric to deal with second-order variables, a recursive algorithm is proposed for the system under consideration in the sense of linear minimum mean-square error.