On the asymptotic variance in the Central Limit Theorem for particle filters

Abstract : Particle filters algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. Given a set of observations, the asymptotic behaviour of particle filters, as the number of particles tends to infinity, has been studied: a central limit theorem holds with an asymptotic variance depending on the fixed set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations. The case of the Kalman filter is treated separately.
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Pré-publication, Document de travail
MAP5 2009-14. 2009
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Contributeur : Benjamin Favetto <>
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Dernière modification le : mardi 11 octobre 2016 - 13:25:05
Document(s) archivé(s) le : mardi 15 juin 2010 - 18:01:38

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  • HAL Id : hal-00401670, version 1

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Benjamin Favetto. On the asymptotic variance in the Central Limit Theorem for particle filters. MAP5 2009-14. 2009. <hal-00401670>

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