@inproceedings{4a79a1e382fd4c40a37ba49cc36127a6,
title = "Error estimates for the kernel gain function approximation in the feedback particle filter",
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.",
author = "Amirhossein Taghvaei and Mehta, {Prashant G.} and Meyn, {Sean P.}",
note = "Publisher Copyright: {\textcopyright} 2017 American Automatic Control Council (AACC).; 2017 American Control Conference, ACC 2017 ; Conference date: 24-05-2017 Through 26-05-2017",
year = "2017",
month = jun,
day = "29",
doi = "10.23919/ACC.2017.7963661",
language = "English (US)",
series = "Proceedings of the American Control Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4576--4582",
booktitle = "2017 American Control Conference, ACC 2017",
address = "United States",
}