On-line estimation of hidden Markov model parameters based on the Kullback-Leibler information measure

TitleOn-line estimation of hidden Markov model parameters based on the Kullback-Leibler information measure
Publication TypeJournal Article
Year of Publication1993
AuthorsKrishnamurthy, V., and J. B. Moore
JournalSignal Processing, IEEE Transactions on
Pagination2557 -2573
Date Publishedaug.
Keywordsconvergence, deterministic signals, EM algorithm, filtering and prediction theory, filters, finite-state Markov chains, fixed-lag smoothers, hidden Markov model, hidden Markov models, HMM, Kullback-Leibler information measure, Markov state levels, noise variance, online algorithms, parameter estimation, sawtooth-lag smoothers, sequential expectation maximization, signal processing, stochastic approximations, transition probabilities, white Gaussian noise, white noise

Sequential or online hidden Markov model (HMM) signal processing schemes are derived, and their performance is illustrated by simulation. The online algorithms are sequential expectation maximization (EM) schemes and are derived by using stochastic approximations to maximize the Kullback-Leibler information measure. The schemes can be implemented either as filters or fixed-lag or sawtooth-lag smoothers. They yield estimates of the HMM parameters including transition probabilities, Markov state levels, and noise variance. In contrast to the offline EM algorithm (Baum-Welch scheme), which uses the fixed-interval forward-backward scheme, the online schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes. Similar techniques are used to derive online schemes for extracting finite-state Markov chains imbedded in a mixture of white Gaussian noise (WGN) and deterministic signals of known functional form with unknown parameters


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