State estimation for Markov switching systems with modal observations

This paper considers state estimation for a discrete-time, jump linear system with parameter switching governed by a finite state Markov chain. The observation history includes noisy measurements of the Markov chain as well as the standard noisy state observations. A recursion for the optimal state estimate is derived and the solution is shown to have computational and memory costs which grow exponentially with the data length. A suboptimal algorithm with fixed memory requirements and low computational cost is then proposed and studied in numerical examples. The new filter is an extension of the interacting multiple model algorithm to incorporate the modal observations.