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 reassessed 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.

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