Asymptotic stability of the Wonham filter: Ergodic and nonergodic signals

Peter Baxendale; Pavel Chigansky; Robert Liptser

doi:10.1137/S0363012902416924

Asymptotic stability of the Wonham filter: Ergodic and nonergodic signals

Peter Baxendale^*, Pavel Chigansky, Robert Liptser

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identiflability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure.

Original language	English
Pages (from-to)	643-669
Number of pages	27
Journal	SIAM Journal on Control and Optimization
Volume	43
Issue number	2
DOIs	https://doi.org/10.1137/S0363012902416924
State	Published - 2005
Externally published	Yes

Keywords

Nonlinear filtering
Stability
Wonham filter

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10.1137/S0363012902416924

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abstract = "The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identiflability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure.",

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AU - Liptser, Robert

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KW - Nonlinear filtering

KW - Stability

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Asymptotic stability of the Wonham filter: Ergodic and nonergodic signals

Abstract

Keywords

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