A Two-stage Particle Filter in High Dimension

Particle Filter (PF) is a popular sequential Monte Carlo method to deal with non-linear non-Gaussian filtering problems. However, it suffers from the so-called curse of dimensionality in the sense that the required number of particle (needed for a reasonable performance) grows exponentially with the dimension of the system. One of the techniques found in the literature to tackle this is to split the high-dimensional state in to several lower dimensional (sub)spaces and run a particle filter on each subspace, the so-called multiple particle filter (MPF). It is also well-known from the literature that a good proposal density can help to improve the performance of a particle filter. In this article, we propose a new particle filter consisting of two stages. The first stage derives a suitable proposal density that incorporates the information from the measurements. In the second stage a PF is employed with the proposal density obtained in the first stage. Through a simulated example we show that in high-dimensional systems, the proposed two-stage particle filter performs better than the MPF with much fewer number of particles.