An Improved Unbiased Particle Filter

TL;DR

This paper introduces a modified unbiased particle filter estimator that reduces discretization bias and variance, leading to more efficient filtering of multi-dimensional diffusion processes observed discretely.

Contribution

It presents a new unbiased estimator based on recent methods, improving bias removal and variance control in particle filtering for discretized diffusion processes.

Findings

Unbiased estimator with finite variance demonstrated.

Numerical simulations show reduced computational cost.

Significant gains in mean square error efficiency.

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.