Importance Sampling With Stochastic Particle Flow and Diffusion Optimization

TL;DR

This paper introduces a stochastic particle flow-based importance sampling method that improves particle filtering by reducing ODE stiffness and enhancing estimation accuracy through optimized diffusion, demonstrated in a nonlinear 3-D source localization task.

Contribution

It presents a novel importance sampling approach using stochastic particle flow with optimized diffusion, enabling asymptotically optimal proposals and better accuracy-complexity tradeoffs.

Findings

Reduced ODE stiffness compared to deterministic PFL

Improved estimation accuracy in nonlinear scenarios

Effective optimization of the diffusion matrix

Abstract

Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. Recently proposed stochastic PFL introduces a diffusion term in the ordinary differential equation (ODE) that describes particle motion. This diffusion term reduces the stiffness of the ODE and makes it possible to perform PFL with a lower number of numerical integration steps compared to traditional deterministic PFL. In this work, we introduce a general approach to perform importance sampling (IS) based on stochastic PFL. Our method makes it possible to evaluate a "flow-induced" proposal probability density function (PDF) after the parameters of a Gaussian mixture model (GMM) have been migrated by stochastic PFL. Compared to conventional stochastic PFL, the resulting processing step is asymptotically optimal. Within our method, it is possible to optimize the diffusion matrix that describes the diffusion term of the ODE to improve the accuracy-computational complexity tradeoff. Our simulation results in a highly nonlinear 3-D source localization scenario showcase a reduced stiffness of the ODE and an improved estimating accuracy compared to state-of-the-art deterministic and stochastic PFL.