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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Vydáno v:	IEEE transactions on automatic control Ročník 53; číslo 1; s. 247 - 256
Hlavní autoři:	Elliott, R.J., Malcolm, W.P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.02.2008 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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
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Abstract	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.
AbstractList	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. 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, "On the numerical stability of time-discretized state estimation via clark transformations," presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.
Author	Elliott, R.J. Malcolm, W.P.
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References	ref12 ref14 ref31 ref30 ref11 malcolm (ref16) 2003 royden (ref20) 1988 ref10 ref1 ref19 ref18 malcolm (ref13) 1999 ref24 ref23 ref26 ref25 ref22 ref21 mclachlan (ref17) 1997 ref28 bremaud (ref5) 1981 elliott (ref2) 1982 ref27 ref29 elliott (ref15) 2001 ref7 ref9 ref4 ref3 ref6 demster (ref8) 1997; b 39
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SubjectTerms	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
Title	Discrete-Time Expectation Maximization Algorithms for Markov-Modulated Poisson Processes
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