Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Output Observations

We investigate the design of optimal state estimators for Markovian Jump Linear Systems. We consider that the output observations and the mode observations are affected by delays not necessarily identical. Our objective is to design optimal estimators for the current state, given current and past observations. We provide a solution to this paradigm by giving an optimal recursive estimator for the state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output. We also show that if the output delay is less then the one in observing the mode, then the optimal state estimation becomes nonlinear in the output observations.