State estimation for discrete-time Markov jump linear systems with time-correlated measurement noise

In this paper, the state estimation problem for discrete-time Markov jump linear systems affected by time-correlated measurement noise is considered where the time-correlated measurement noise is described by a linear system model with white noise. As a result, two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence. The first algorithm is optimal in the sense of minimum mean-square error, which is obtained based on the measurement differencing method, Bayes' rule and some results derived in this paper. The second algorithm is a suboptimal algorithm obtained by using a lot of Gaussian hypotheses. The proposed suboptimal algorithm is finite-dimensionally computable and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm.