State estimation of discrete-time Markov jump linear systems in the environment of arbitrarily correlated noises

In this paper, the state estimation problem of discrete-time Markov jump linear systems is considered where the noises influencing the systems are arbitrarily correlated. For this, two algorithms of state estimate for the considered systems based on the estimation criterion of linear minimum mean-square error estimate are proposed. The first algorithm is an optimal algorithm which can exactly calculate the linear minimum mean-square error estimate of system states. The second algorithm is a suboptimal algorithm which is proposed to reduce the computation and storage load of the proposed optimal algorithm. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm.