Multivariable feedback particle filter

Tao Yang; Richard S. Laugesen; Prashant G. Mehta; Sean P. Meyn

doi:10.1016/j.automatica.2016.04.019

Multivariable feedback particle filter

Tao Yang, Richard S. Laugesen, Prashant G. Mehta, Sean P. Meyn

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

Abstract

This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented approach to particle filtering. The approach does not require importance sampling or resampling and offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. This paper describes new representations and algorithms for the FPF in the general multivariable nonlinear non-Gaussian setting. Theory surrounding the FPF is improved: Exactness of the FPF is established in the general setting, as well as well-posedness of the associated boundary value problem to obtain the filter gain. A Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.

Original language	English (US)
Pages (from-to)	10-23
Number of pages	14
Journal	Automatica
Volume	71
DOIs	https://doi.org/10.1016/j.automatica.2016.04.019
State	Published - Sep 1 2016

Keywords

Estimation theory
Nonlinear filtering
Particle filtering

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Online availability

10.1016/j.automatica.2016.04.019

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title = "Multivariable feedback particle filter",

abstract = "This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented approach to particle filtering. The approach does not require importance sampling or resampling and offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. This paper describes new representations and algorithms for the FPF in the general multivariable nonlinear non-Gaussian setting. Theory surrounding the FPF is improved: Exactness of the FPF is established in the general setting, as well as well-posedness of the associated boundary value problem to obtain the filter gain. A Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.",

keywords = "Estimation theory, Nonlinear filtering, Particle filtering",

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T1 - Multivariable feedback particle filter

AU - Yang, Tao

AU - Laugesen, Richard S.

AU - Mehta, Prashant G.

AU - Meyn, Sean P.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented approach to particle filtering. The approach does not require importance sampling or resampling and offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. This paper describes new representations and algorithms for the FPF in the general multivariable nonlinear non-Gaussian setting. Theory surrounding the FPF is improved: Exactness of the FPF is established in the general setting, as well as well-posedness of the associated boundary value problem to obtain the filter gain. A Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.

AB - This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented approach to particle filtering. The approach does not require importance sampling or resampling and offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. This paper describes new representations and algorithms for the FPF in the general multivariable nonlinear non-Gaussian setting. Theory surrounding the FPF is improved: Exactness of the FPF is established in the general setting, as well as well-posedness of the associated boundary value problem to obtain the filter gain. A Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.

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KW - Particle filtering

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Multivariable feedback particle filter

Abstract

Keywords

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