Particle filter with extrapolation by crossover for nonlinear state estimation

This paper proposes a new particle filter (PF) named the particle filter with extrapolation by crossover (PF-XC) for estimating state vectors of dynamical systems. Estimating state vectors of dynamical systems is one of the most important problems that often appears in the wide area of engineering such as robotics, statistics and marine meteorology. The particle filter with interpolation by crossover (PF-IC) is one of the most promising PFs that overcomes a problem of the original PF. PF-IC interpolates particles to obtain an ensemble with high density around the true state. PF-IC shows better performance than PF especially when the number of particles in an ensemble is small. However, PF-IC has a serious problem in that the performance of PF-IC deteriorates when the ensemble does not cover the true state. We believe that this is because PF-IC cannot create particles around the true state when the ensemble does not cover the true state. In order to remedy the problem of PF-IC, PF-XC extrapolates particles to obtain an expanded ensemble in an isotropic manner that covers the true state. In order to investigate that PF-XC effectively works even if ensembles do not cover true states, we compared the performance of PF-XC and that of PF-IC, PF and the merging particle filter (MPF) which is one of the most famous extensions of PF on two benchmark problems that have nonlinear dynamics models. As the result, we confirmed that PF-XC outperformed PF-IC, PF and MPF. PF-XC showed up to about eight times better performance than that of PF-IC in terms of the median root mean squared error.