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		Gang George YIN,Qing ZHANG,Yuanjin LIU.[en_title][J].Control Theory and Technology,2004,2(1):1~10.[Copy]

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GangGeorgeYIN,QingZHANG,YuanjinLIU
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Received:January 12, 2004

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Discrete-time approximation of Wonhain filters

Gang George YIN, Qing ZHANG, Yuanjin LIU

(Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.; Department of Mathematics, Boyd GSRC, The University of Georgia, Athens, GA 30602-7403; Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.)

Abstract:

A continuous-rime finite-state Markov chain observed in white noise is considered. The well-known result of Wonham filter provides a formula for obtaining posterior probabilities. Although the filter is of finite dimension, numerical schemes are needed in applications because of the nonlinearity and because the observations are frequently collected in discrete moments. In this work, we develop approximation schemes of Wonham filters by constructing discrete-time recursive algorithms. We prove the convergence of the algorithm by weak convergence method and martingale averaging techniques. Numerical experiments are also famished to demonstrate the performance of our algorithms.

Key words: Wonham filter Approximation Weak convergence