A High-Dimensional Particle Filter Algorithm

TL;DR

This paper introduces a novel high-dimensional particle filter algorithm that uses local interactions and MCMC techniques to improve online data assimilation in large spatial models, achieving more uniform error distribution.

Contribution

The paper presents a new particle filter method leveraging local dependencies and MCMC, addressing spatial inhomogeneity and error bias in high-dimensional filtering.

Findings

Error is uniform in space and time

Lower bias compared to previous algorithms

Higher variance observed

Abstract

Online data assimilation in time series models over a large spatial extent is an important problem in both geosciences and robotics. Such models are intrinsically high-dimensional, rendering traditional particle filter algorithms ineffective. Though methods that begin to address this problem exist, they either rely on additional assumptions or lead to error that is spatially inhomogeneous. I present a novel particle-based algorithm for online approximation of the filtering problem on such models, using the fact that each locus affects only nearby loci at the next time step. The algorithm is based on a Metropolis-Hastings-like MCMC for creating hybrid particles at each step. I show simulation results that suggest the error of this algorithm is uniform in both space and time, with a lower bias, though higher variance, as compared to a previously-proposed algorithm.