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Uniform approximations of discrete-time filters

Part of: Stochastic systems and control Distribution theory

Published online by Cambridge University Press:  01 July 2016

Kari Heine  and
Dan Crisan
Kari Heine*
Affiliation:
Tampere University of Technology
Dan Crisan*
Affiliation:
Imperial College London
*
∗ Email address: kari.heine@wire.fi
∗∗ Postal address: Department of Mathematics, Huxley Building, Imperial College, 180 Queens Gate, London SW7 2BZ, UK.
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Abstract

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Throughout recent years, various sequential Monte Carlo methods, i.e. particle filters, have been widely applied to various applications involving the evaluation of the generally intractable stochastic discrete-time filter. Although convergence results exist for finite-time intervals, a stronger form of convergence, namely, uniform convergence, is required for bounding the error on an infinite-time interval. In this paper we prove easily verifiable conditions for the filter applications that are sufficient for the uniform convergence of certain particle filters. Essentially, the conditions require the observations to be accurate enough. No mixing or ergodicity conditions are imposed on the signal process.

Keywords

Discrete-time filterparticle filterMonte Carlo filteruniform convergence

MSC classification

Primary: 93E11: Filtering
Secondary: 93E15: Stochastic stability 62E20: Asymptotic distribution theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 4 , December 2008 , pp. 979 - 1001
Copyright
Copyright © Applied Probability Trust 2008 

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