A hybrid particle-stochastic map filter

Abstract

Filtering in nonlinear state-space models is known to be a challenging task due to the posterior distribution 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 degeneracy. 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 parameterisation. 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 particle 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.