Toward Practical N2 Monte Carlo: the Marginal Particle Filter

TL;DR

This paper introduces the Marginal Particle Filter, a Sequential Monte Carlo method that directly targets the marginal distribution to reduce variance and computational cost in state estimation for non-linear, non-Gaussian models.

Contribution

It presents a novel marginal particle filtering algorithm that operates directly on the marginal distribution, reducing variance and computational complexity compared to traditional methods.

Findings

Reduces variance over conventional particle filtering.

Achieves computational complexity reduction from O(N^2) to O(N logN).

Demonstrates effectiveness through theoretical and empirical results.

Abstract

Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework, the dimension of the target distribution grows with each time step, thus it is necessary to introduce some resampling steps to ensure that the estimates provided by the algorithm have a reasonable variance. In many applications, we are only interested in the marginal filtering distribution which is defined on a space of fixed dimension. We present a Sequential Monte Carlo algorithm called the Marginal Particle Filter which operates directly on the marginal distribution, hence avoiding having to perform importance sampling on a space of growing dimension. Using this idea, we also derive an improved version of the auxiliary particle filter. We show theoretic and empirical results which demonstrate a reduction in variance over conventional particle filtering, and present techniques for reducing the cost of the marginal particle filter with N particles from O(N2) to O(N logN).