Uniform time average consistency of Monte Carlo particle filters

Ramon van Handel

doi:10.1016/j.spa.2009.09.004

Uniform time average consistency of Monte Carlo particle filters

Ramon van Handel

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

25 Scopus citations

Abstract

We prove that bootstrap-type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.

Original language	English (US)
Pages (from-to)	3835-3861
Number of pages	27
Journal	Stochastic Processes and their Applications
Volume	119
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2009.09.004
State	Published - Nov 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Bootstrap Monte Carlo filter
Interacting particles
Nonlinear filter
Uniform convergence

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10.1016/j.spa.2009.09.004

Cite this

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abstract = "We prove that bootstrap-type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.",

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AB - We prove that bootstrap-type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.

KW - Bootstrap Monte Carlo filter

KW - Interacting particles

KW - Nonlinear filter

KW - Uniform convergence

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

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ER -

Uniform time average consistency of Monte Carlo particle filters

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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