Maximum likelihood state estimation for Markov jump systems with uncertain mode-dependent delays

This paper presents a recursive maximum likelihood state estimator based on the expectation maximization algorithm for Markov jump linear systems with uncertain mode-dependent delays. To calculate the posterior probability of each possible candidate time delay, a recursive algorithm is derived within the Bayesian framework conditioned on the likelihood density function of state with respect to the candidate time delay related to the reference mode. By combining the optimal principle of expectation maximization and the interacting multiple mode approximation, we propose a double-reweight interacting multiple model (D-RIMM) algorithm to obtain the maximum a posterior estimator of state that is of low computational complexity. An example is given to demonstrate the effectiveness and potential of the proposed D-RIMM algorithm.