An EM algorithm for Markov modulated Markov processes

Authors:
Yariv Ephraim;William J. J. Roberts
Affiliations:
Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA;Atlantic Coast Technologies, Inc., Silver Spring, MD
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

An expectation-maximization (EM) algorithm for estimating the parameter of a Markov modulated Markov process in the maximum likelihood sense is developed. This is a doubly stochastic random process with an underlying continuous-time finite-state homogeneous Markov chain. Conditioned on that chain, the observable process is a continuous-time finite-state nonhomogeneous Markov chain. The generator of the observable process at any given time is determined by the state of the underlying Markov chain at that time. The parameter of the process comprises the set of generators for the underlying and conditional Markov chains. The proposed approach generalizes an earlier approach by Rydén for estimating the parameter of a Markov modulated Poisson process.