Optimal stationary linear filtering for systems with Markov switching parameters

The stationary minimum mean square error estimator for discrete time linear systems with Markov switching parameters is considered for the case when the output sequence and mode of operation of the system are directly observable. It is shown that the solution of this problem is associated to a set of coupled algebraic Riccati-like equations. Conditions for the existence and uniqueness of a positive semi-definite solution are obtained via the convergence of a sequence of solutions of Lyapunov-like equations.<>