Stein Particle Filter for Nonlinear, Non-Gaussian State Estimation
This work addresses a critical problem in robotics for state estimation under sensor noise and model inaccuracies, offering a novel approach that is incremental in building upon existing particle filter methods.
The paper tackles the problem of state estimation in nonlinear, non-Gaussian dynamical systems, which is challenging for existing methods like Kalman filters and sampling strategies in high-dimensional spaces. It introduces the Stein particle filter, a deterministic flow-based method that scales to higher dimensions and shows improved performance in simulations and complex localization tasks compared to sequential Monte Carlo solutions.
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.