A filtered EM algorithm for joint hidden Markov model and sinusoidal parameter estimation

TitleA filtered EM algorithm for joint hidden Markov model and sinusoidal parameter estimation
Publication TypeJournal Article
Year of Publication1995
AuthorsKrishnamurthy, V., and R. J. Elliott
JournalSignal Processing, IEEE Transactions on
Pagination353 -358
Date Publishedjan.
Keywordsamplitudes, autoregressive moving average processes, deterministic interference, deterministic signals, discrete time filters, discrete-time finite-state Markov chains, expectation-maximization algorithm, filtered EM algorithm, filtering theory, finite-dimensional discrete-time filters, forward-backward variables, frequency components, Gaussian noise, Gaussian white noise, hidden Markov model, hidden Markov models, maximum likelihood estimation, memory requirements, Multidimensional digital filters, multiprocessor implementation, parameter estimation, periodic signals, phases, polynomial drift, sinusoidal parameter estimation, smoothed variables, state levels, transition probabilities, white noise

Derives finite-dimensional discrete-time filters for estimating the parameters of discrete-time finite-state Markov chains imbedded in a mixture of Gaussian white noise and deterministic signals of known functional form with unknown parameters. The filters that are derived estimate quantities used in the expectation-maximization (EM) algorithm for maximum likelihood (ML) estimation of the Markov chain parameters (transition probabilities and state levels) as well as the parameters of the deterministic interference. Two types of deterministic signals are considered: periodic or almost periodic signals with unknown frequency components, amplitudes, and phases, and polynomial drift in the states of the Markov process with the coefficients of the polynomial unknown. The filter-based EM algorithm has negligible memory requirements. In comparison, implementing the EM algorithm using smoothed variables (forward-backward variables) requires memory proportional to the number of observations. In addition, the filters are suitable for multiprocessor implementation unlike the forward-backward algorithm


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