Particle Filtering for Large Dimensional State Spaces with Multimodal Observation Likelihoods

TL;DR

This paper develops importance sampling techniques for particle filtering in high-dimensional spaces with multimodal or heavy-tailed observation likelihoods, addressing challenges in large-scale spatial tracking problems.

Contribution

It generalizes existing particle filtering methods to handle multimodal optimal importance densities conditioned on parts of the state, and proposes solutions for high-dimensional tracking.

Findings

Derived conditions for testing unimodality of conditional posteriors.

Addressed the increase in particle number with state dimension, proposing partial solutions.

Applied techniques to spatially varying physical quantity tracking with sensor networks.

Abstract

We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. The number of particles, N, to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. We propose a solution that partially addresses this problem. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have non-negligible failure probabilities.