Discrete-Time Expectation Maximization Algorithms for Markov-Modulated Poisson Processes

In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of our model in either an online configuration...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 53; no. 1; pp. 247 - 256
Main Authors: Elliott, R.J., Malcolm, W.P.
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Australia Council
Change of measure
Communications technology
counting processes
Estimators
expectation maximization (EM) algorithm
Filtering
Filters
Integrals
martingales
Mathematical models
Maximization
On-line systems
Parameter estimation
Recursive estimation
Robustness
Signal processing
Signal processing algorithms
State estimation
Stochastic processes
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Description
Summary:In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of our model in either an online configuration or an offline configuration. Further, our estimator dynamics do not involve stochastic integrals and our new formulas, in terms of time integrals, are easily discretized, and are written in numerically stable forms in W. P. Malcolm, R. J. Elliott, and J. van der Hoek, ldquoOn the numerical stability of time-discretized state estimation via clark transformations,rdquo presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.914305