Time discretization of continuous-time filters for hidden Markov model parameter estimation

TitleTime discretization of continuous-time filters for hidden Markov model parameter estimation
Publication TypeConference Paper
Year of Publication1992
AuthorsJames, M. R., V. Krishnamurthy, and F. Le Gland
Conference NameDecision and Control, 1992., Proceedings of the 31st IEEE Conference on
Pagination3305 -3310 vol.4
Keywordscomputational complexity, continuous-time filters, EM algorithm, expectation-maximization algorithm, fast-sampled homogeneous Markov chains, filtering and prediction theory, hidden Markov model parameter estimation, hidden Markov models, maximum likelihood parameter estimation, MLE, numerical analysis, numerical techniques, parameter estimation, robust discretization, time discretization, white Gaussian noise, white noise

The authors propose numerical techniques for parameter estimation of fast-sampled homogeneous Markov chains observed in white Gaussian noise. Continuous-time filters that estimate the quantities used in the expectation-maximization (EM) algorithm for maximum likelihood parameter estimation have been obtained by R.J. Elliott (1991, 1992). The numerical work is based on the robust discretization of these filters. The advantage of using filters in the EM algorithm is that they have negligible memory requirements, independent of the number of observations. In comparison, standard discrete-time EM algorithms (Baum-Welch re-estimation equations) are based on smoothers and require the use of the forward-backward algorithm, which is a fixed-interval algorithm and has memory requirements proportional to the number of observations. Although the computational complexity of the filters at each time instant is O(N4) (for a N state Markov) compared to O(N2) for the forward-backward scheme, the filters are suitable for parallel implementation. Simulations are presented to illustrate the satisfactory performance of the algorithms


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