A divide and conquer sequential Monte Carlo approach to high dimensional filtering

TL;DR

This paper introduces a divide-and-conquer sequential Monte Carlo method that decomposes high-dimensional filtering problems into manageable parts, enabling broader applicability and comparable performance to existing methods.

Contribution

The proposed approach decomposes high-dimensional filtering into low-dimensional components, reducing dependence on factorization assumptions and broadening applicability.

Findings

Broadly comparable performance to state-of-the-art methods

Applicable to models where existing methods fail

Demonstrated effectiveness on benchmark problems

Abstract

We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full filtering distribution. It is less dependent upon factorization of transition densities and observation likelihoods than competing approaches and can be applied to a broader class of models. Performance is compared with state-of-the-art methods on a benchmark problem and it is demonstrated that the proposed method is broadly comparable in settings in which those methods are applicable, and that it can be applied in settings in which they cannot.