Optimal estimate and intercepting algorithm for state estimation of discrete-time Markov jump linear systems

In this paper, the state estimation problem for discrete-time Markov jump linear systems is considered. For this, two algorithms are presented. The first algorithm is an optimal algorithm for state estimate in the sense of minimum mean-square error estimate. The second algorithm is a suboptimal algorithm, called intercepting algorithm, which is based on the approximation for the proposed optimal algorithm. The intercepting algorithm is finite-dimensionally computable, and does not require ever-increasing computation and storage load with the length of the noise observation sequence. A numerical example is given to demonstrate the performance of the intercepting algorithm.