Stiefel manifold particle filtering

Abstract

In order to solve the problems of particle degeneration and lackness of diversity of particle filter, a new particle filter based on Stiefel manifold (SMPF) is proposed in this paper. In the SMPF the system model is based on Stiefel manifold, Langevin distribution is used as a prior density, the matrix normal distribution serves a as likelihood function, and particle is sampled on the manifold distribution. First, manifold is embedded in Euclidean space, then the mean of particles is calculated in Euclidean space and its result is projected back to embedded manifold. So the influence on variance of particle weight caused by statistic characteristics of noise is removed, and a kind of universal selecting scheme of important probability density function is acquired which is hardly restrained to system state model. The simulation results based on univariate nonstationary growth model nonlinear system indicate that the SMPF works much better than scentless particle filter in real-time performance, robustness, filtering precision and filtering efficiency.