Error estimates for the kernel gain function approximation in the feedback particle filter

Amirhossein Taghvaei, Prashant G. Mehta, Sean P. Meyn

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

Abstract

This paper is concerned with the analysis of the kernel-based algorithm for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The kernel-based method - introduced in our prior work - allows one to approximate this solution using only particles sampled from the probability distribution. This paper describes new representations and algorithms based on the kernel-based method. Theory surrounding the approximation is improved and a novel formula for the gain function approximation is derived. A procedure for carrying out error analysis of the approximation is introduced. Certain asymptotic bounds for bias and variance are derived for the general nonlinear non-Gaussian case. Comparison with the constant gain function approximation is provided. The results are illustrated with the aid of numerical experiments.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4576-4582
Number of pages7
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Publication series

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

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Taghvaei, A., Mehta, P. G., & Meyn, S. P. (2017). Error estimates for the kernel gain function approximation in the feedback particle filter. In 2017 American Control Conference, ACC 2017 (pp. 4576-4582). [7963661] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2017.7963661