Stochastic Particle Flow for Nonlinear High-Dimensional Filtering Problems

TL;DR

This paper introduces Stochastic Particle Flow, a novel filtering method combining Monte Carlo and local parametric solutions to improve nonlinear high-dimensional Bayesian filtering, outperforming existing methods in benchmark problems.

Contribution

The paper presents a new stochastic particle flow filter that addresses limitations of traditional methods using a hybrid approach with local Fokker-Planck solutions.

Findings

Outperforms state-of-the-art nonlinear high-dimensional filters

Effective in multi-target multi-sensor tracking scenarios

Demonstrates utility through benchmark problem evaluations

Abstract

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to nonlinear filtering problems. They do so by defining a continuum of densities between the prior probability density and the posterior, i.e. the filtering density. Building on these methods' successes, we propose a novel filter. The new filter aims to address the shortcomings of sequential Monte Carlo methods when applied to important nonlinear high-dimensional filtering problems. The novel filter uses equally weighted samples, each of which is associated with a local solution of the Fokker-Planck equation. This hybrid of Monte Carlo and local parametric approximation gives rise to a global approximation of the filtering density of interest. We show that, when compared with state-of-the-art methods, the Gaussian-mixture implementation of the new filtering technique, which we call Stochastic Particle Flow, has utility in the context of benchmark nonlinear high-dimensional filtering problems. In addition, we extend the original particle flow filters for tackling multi-target multi-sensor tracking problems to enable a comparison with the new filter.