Expectation maximization algorithms for MAP estimation of jump Markov linear systems (Q2723863)

This paper presents three expectation maximization (EM) algorithms for state estimation to compute maximum a posteriori (MAP) state sequence estimates (Bayes maximum likelihood state sequence estimates). The first EM algorithm yields the MAP estimate for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAP estimate of the continuous state of the jump linear system. The third EM algorithm computes the joint MAP estimate of the finite and continuous states. The three EM algorithms optimally combine a hidden Markov model estimator and a Kalman smoother in three different ways to compute the desired MAP state sequence estimates. The proposed iterative schemes are linear in the data length.