An Improved Unbiased Particle Filter

Ajay Jasra; Mohamed Maama; Hernando Ombao

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arXiv · 2302.09978

An Improved Unbiased Particle Filter

Ajay Jasra·Mohamed Maama·Hernando Ombao

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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.

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Ajay Jasra, Mohamed Maama, Hernando Ombao. 2023-02-20. An Improved Unbiased Particle Filter. https://arxiv.org/abs/2302.09978

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