MAP state sequence estimation for jump Markov linear systems via the expectation-maximization algorithm

TitleMAP state sequence estimation for jump Markov linear systems via the expectation-maximization algorithm
Publication TypeConference Paper
Year of Publication1997
AuthorsLogothetis, A., and V. Krishnamurthy
Conference NameDecision and Control, 1997., Proceedings of the 36th IEEE Conference on
Pagination1700 -1705 vol.2
Date Publisheddec.
Keywordscovariance matrices, expectation-maximization algorithm, hidden Markov models, iterative method, iterative methods, jump Markov systems, Kalman filters, linear systems, Markov chain, noise covariance matrix, observation matrix, optimisation, state estimation, state matrix, state sequence estimation, stochastic systems
Abstract

In a jump Markov linear system the state matrix, observation matrix and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. In this paper, we present three expectation maximization (EM) algorithms for state estimation to obtain maximum a posteriori state sequence estimates (MAPSE). Our first EM algorithm yields the MAPSE for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAPSE of the (continuous) state of the jump linear system. Our third EM algorithm computes the joint MAPSE 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 MAPSEs

URLhttp://dx.doi.org/10.1109/CDC.1997.657796
DOI10.1109/CDC.1997.657796

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