A hybrid particle-stochastic map filter

Filtering in nonlinear state-space models is known to be a challenging task due to the posterior distri-bution being either intractable or expressed in a complex form. One of the most successful methods, particle filtering (PF), although generally outperforming traditional filters, suffers from sample degener-acy. Drawing from optimal transport theory, the stochastic map filter (SMF) accommodates a solution to this problem, but its performance is influenced by the limited flexibility of nonlinear map parameterisa-tion. To alleviate these drawbacks, we propose a hybrid filter which combines the PF and SMF, and hence call it PSMF. Specifically, the PSMF splits the likelihood into two parts, which are then updated by PF and SMF, respectively. The proposed approach adopts systematic resampling and smoothing to break the par-ticle degeneracy caused by the PF. To investigate the influence of the nonlinearity of transport maps, we introduce two variants of the proposed filter, the PSMF-L and PSMF-NL, which are based on linear and nonlinear maps, respectively. The PSMF is tested on various nonlinear state-space models and a nonlinear non-Gaussian target tracking model. The proposed linear PSMF-L outperforms all the reference models for medium-to-large numbers of particles, whilst the PSMF-NL shows better resilience to parameter changes.Crown Copyright (c) 2023 Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

Filtering in nonlinear state-space models is challenging due to intractable or complex posterior distribution. Particle filtering (PF) outperforms traditional filters but suffers from sample degeneracy. Stochastic map filter (SMF) solves this problem, but is limited by nonlinear map parameterization. To overcome these limitations, we propose a hybrid filter called PSMF that combines PF and SMF. PSMF updates the likelihood using PF and SMF separately, and incorporates systematic resampling and smoothing to address particle degeneracy caused by PF. The PSMF is compared to reference models on various nonlinear state-space models and shows improved performance with linear and nonlinear map variants.