An Improved Unbiased Particle Filter
Abstract
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time-discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls.
Cite
@article{arxiv.2302.09978,
title = {An Improved Unbiased Particle Filter},
author = {Ajay Jasra and Mohamed Maama and Hernando Ombao},
journal= {arXiv preprint arXiv:2302.09978},
year = {2023}
}