Optimal Markov jump linear filter for discrete-time jumping parameter systems with multi-channel observation delays and packet losses

This paper is concerned with the optimal Markov jump linear filter problem for Markov jumping parameter system with multi-channel observation delays and packet losses, where the jumping parameters are assumed to be known up to the present time. Firstly, by defining an equivalent delay-free observation sequence, the optimal jumping filter problem is transformed into the one of delay-free system which is just with jumping parameters and multi-channel multiplicative noises. Then an optimal Markov jump linear filter is presented based on the mean squared method, in which the filter gains are determined by solving a set of generalized coupled Riccati equations based on a set of coupled Lyapunov equations. And the Riccati equations developed in this paper are not only relevant to the transition probability of the jumping parameters but also concerned with the probability of the packet losses. This is the main difference btween the result proposed in this paper and our previous works.