Stein Particle Filter for Nonlinear, Non-Gaussian State Estimation

TL;DR

This paper introduces the Stein particle filter, a scalable deterministic particle filtering method for nonlinear, non-Gaussian state estimation that leverages differentiability and reproducing kernel Hilbert spaces to improve over traditional sampling methods.

Contribution

The paper presents the Stein particle filter, a novel deterministic particle filtering approach that scales to higher dimensions using kernel methods and particle interactions.

Findings

Outperforms traditional sequential Monte Carlo in complex localization tasks.

Scales effectively to higher-dimensional state spaces.

Demonstrates robustness in simulation and real-world scenarios.

Abstract

Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and Gaussian noise problems, the general nonlinear and non-Gaussian noise case is significantly more complicated, typically relying on sampling strategies that are limited to low-dimensional state spaces. In this paper we devise a general inference procedure for filtering of nonlinear, non-Gaussian dynamical systems that exploits the differentiability of both the update and prediction models to scale to higher dimensional spaces. Our method, Stein particle filter, can be seen as a deterministic flow of particles, embedded in a reproducing kernel Hilbert space, from an initial state to the desirable posterior. The particles evolve jointly to conform to a posterior approximation while interacting with each other through a repulsive force. We evaluate the method in simulation and in complex localization tasks while comparing it to sequential Monte Carlo solutions.