Error Analysis for the Linear Feedback Particle Filter

Amirhossein Taghvaei, Prashant G. Mehta

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the control law is designed to solve the nonlinear filtering problem. For the linear Gaussian case, certain simplifications arise whereby the linear FPF reduces to one form of the ensemble Kalman filter. For this and for the more general nonlinear non-Gaussian case, it has been an open problem to relate the convergence and error properties of the finite-N algorithm to the mean-field limit (where the exactness results have been obtained). In this paper, the equations for empirical mean and covariance are derived for the finite-N linear FPF. Remarkably, for a certain deterministic form of FPF, the equations for mean and variance are identical to the Kalman filter. This allows strong conclusions on convergence and error properties based on the classical filter stability theory for the Kalman filter. It is shown that the error converges to zero even with finite number of particles. The paper also presents propagation of chaos estimates for the finite-N linear filter. The error estimates are illustrated with numerical experiments.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4261-4266
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Taghvaei, A., & Mehta, P. G. (2018). Error Analysis for the Linear Feedback Particle Filter. In 2018 Annual American Control Conference, ACC 2018 (pp. 4261-4266). [8430867] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8430867