# Stein Particle Filter for Nonlinear, Non-Gaussian State Estimation

arXiv: https://arxiv.org/abs/2202.04213 · HTML: https://mlsanity.com/paper/2202.04213/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2022.

## Built on by (most cited first, 4 of 4)

- [Resampling-free Particle Filters in High-dimensions](https://mlsanity.com/paper/2404.13698/) (2024)
- [Permutation Invariant Learning with High-Dimensional Particle Filters](https://mlsanity.com/paper/2410.22695/) (2024)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)
- [Denoising Particle Filters: Learning State Estimation with Single-Step Objectives](https://mlsanity.com/paper/2602.19651/) (2026)

## Abstract (arXiv)

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.