Optimal filter for discrete-time Markov jump systems with measurement-delays and packet dropouts

This paper is concerned with the optimal filter for discrete-time linear jump system with delayed measurement and packet losses. The Markov chain is assumed to be directly accessible. The delayed measurement system is transformed into an equivalent delay-free one by employing the reorganized observation technique. Then the filtering problem is translated to one of the delay-free system with jumping parameters and diagonal matrix multiplicative noise. An optimal linear Markov jump filter is derived by using the mean squared method, where the filter gains are developed by solving a set of filtering coupled difference Riccati equations (CDREs) based on a set of coupled Lyapunov equations. Stability and steady-state property of the proposed filter is analyzed. The CDREs converge to the stationary ones under appropriate conditions. Finally, a numerical example illustrates the effectiveness of the proposed algorithm.