Optimal state estimation for Markov jump linear systems subject to transmission delays and data losses

This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear systems subject to unknown Markov chain modes, multi-channel observation delays, and data losses. Firstly, the original system is transformed into an extended system by defining a new state variable. The new state variable is concerned with the indicator function of the Markov chain and the original state. Via the reorganized observation method, the extended transmission delayed system is further transformed into the delay free one which is just with Markov jumping parameters and multi-channel multiplicative noises. Based on the obtained system, the linear state estimation is derived by using the innovation analysis method together with geometric arguments in Hilbert space. An analytical solution to the filter is given in terms of a set of generalized Riccati difference equations based on a set of Lyapunov equations, and hence is very simple in computation. It should be noted that 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.