Prediction–Correction Filtering for Discrete-Time Markov Jump Linear Systems

This paper deals with the finite and infinite horizon filtering problems for discrete-time Markov jump linear systems. We assume that only an output and the jump parameters are available to the filter and the goal is to obtain a “prediction–correction” formula which is optimal among the Markovian filters. As in the case with no jumps, we show that an optimal filter can be obtained from a set of coupled Riccati difference and algebraic equations associated with the filtering problem. When there is only one mode of operation, our results coincide with the traditional Kalman filter for discrete-time linear systems.