Abstract
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.
Highlights
The particle filter (PF), which is used to estimate the current state of a system, has been demonstrated to be a potential technique for nonlinear and non-Gaussian environments [1]–[4]
To facilitate the discussion of this special problem caused by the narrow observation noise, the concepts of importance region (IR) and particle density (PD) are defined as follows: Definition 1: Suppose X is a d × N matrix, each of its columns being a sample from the multidimensional distribution function F (x), where the dimension of x is d
We focus on developing a SVR algorithm into a general PF (GPF) to form a new PF framework to overcome the problem caused by narrow observation noise
Summary
The particle filter (PF), which is used to estimate the current state of a system, has been demonstrated to be a potential technique for nonlinear and non-Gaussian environments [1]–[4]. X. Qiang et al.: SVRPF: Improved PF for a Nonlinear/Non-Gaussian Environment resampling technique involves discarding low-weighted particles and replicating high-weighted ones, thereby effectively alleviating the degeneracy problem. Qiang et al.: SVRPF: Improved PF for a Nonlinear/Non-Gaussian Environment resampling technique involves discarding low-weighted particles and replicating high-weighted ones, thereby effectively alleviating the degeneracy problem All these improved techniques can be divided into two categories:. (2) Region amplification and the particle migration technique based on the SVR probability density estimation is proposed. In this procedure, particles are placed uniformly in the IR without changing the PDF of the original particles.
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