基于Stiefel流形的粒子滤波器研究

Stiefel manifold particle filtering

为了解决粒子滤波的粒子退化和粒子多样性丧失问题,提出了一种基于Stiefel流形的粒子滤波算法.该算法将系统模型置于Stiefel流形上,用朗之万分布描述过程转移概率分布,用矩阵正态分布表示似然函数分布,在流形分布上进行粒子采样.在计算加权粒子的均值时,将流形嵌入到欧氏空间中,先计算欧氏空间中的粒子均值,再将计算结果投影到嵌套流形上,这就排除了噪声统计特性对粒子权重方差的影响,得到了一种受系统状态模型限制较少的重要性概率密度函数通用选择方案.仿真时选取单变量非静态增长模型,仿真结果验证了该算法的实时性、鲁棒性,滤波精度和滤波效率均比无味粒子滤波算法更好.

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.