  The performance of a particle filter (PF) in nonlinear and non-Gaussian
environments is often affected by particle degeneracy and impoverishment
problems. In this paper, these two problems are re-assessed using the concepts
of importance region (IR) selection and particle density (PD), where IR
describes the distribution region of particles, and PD describes the density of
particles in IR. Based on these two factors, a support vector regression PF
(SVRPF) is proposed to overcome the problems from nonlinear and non-Gaussian
environments, especially in regard to narrow observation noise. Furthermore,
the consistency of the SVRPF and Bayes' filtering is demonstrated. A numerical
simulation shows that the performance of the SVRPF is more stable than other
filter algorithms. Provided that other conditions are the same, when the
observation noise variance is 0.1 and 5, the root-mean-square errors of the
SVRPF decrease by 0.5 and 0.03, respectively, compared with that of a general
PF.
