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 {\em 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 estimates 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 some numerical experiments.
Cite
@article{arxiv.1612.05606,
title = {Error Estimates for the Kernel Gain Function Approximation in the Feedback Particle Filter},
author = {Amirhossein Taghvaei and Prashant G. Mehta and Sean P. Meyn},
journal= {arXiv preprint arXiv:1612.05606},
year = {2016}
}