Particle Flow Particle Filter using Gromov's method

Particle flow filters obtain impressive results in challenging high dimensional, non-linear sequential state estimation problems. In contrast to a particle filter, which uses importance sampling to approximate the posterior distribution of the state, the flow based algorithms solve a differential equation to migrate the particles from the prior to the posterior distribution. However, the particles after the flow are not true samples of the posterior distribution due to strong model assumptions required for the derivation of the flow and the approximations associated with the numerical solution. This affects performance adversely in many highly non-linear, non-Gaussian filtering problems. Particle Flow Particle Filters (PFPF) adapt the particle flow procedure to construct a proposal density inside the particle filter. These techniques can outperform the underlying particle flow algorithms by compensating for the approximations in the flow calculations via update of importance weights after the flow, at the cost of a negligible increase in the computational complexity. Most of the PFPF approaches have focused on using a deterministic particle flow. In this paper, we develop a PFPF algorithm using a stochastic particle flow based on Gromov's method. Numerical simulations are conducted to examine when the proposed method offers advantages compared to existing techniques.