电子学报 ›› 2016, Vol. 44 ›› Issue (1): 95-100.DOI: 10.3969/j.issn.0372-2112.2016.01.014

• 学术论文 • 上一篇    下一篇

基于径向基-Galerkin解的反馈粒子滤波器

张宏欣, 周穗华, 冯士民   

  1. 海军工程大学兵器工程系, 湖北武汉 430033
  • 收稿日期:2014-04-14 修回日期:2014-08-03 出版日期:2016-01-25 发布日期:2016-01-25
  • 作者简介:张宏欣 男,1987年12月出生,陕西汉中人. 2010年毕业于西安理工大学, 现为海军工程大学博士生,从事统计信号处理及目标跟踪相关研究. 周穗华 男,1962年10月出生,广东五华人,1984年毕业于海军工程学院,1990年在海军工程学院获得博士学位.现为海军工程大学教授,从事军用目标特性信息处理及武器系统总体设计方面研究.

Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method

ZHANG Hong-xin, ZHOU Sui-hua, FENG Shi-min   

  1. Department of Weapon Engineering, Naval University of Engineering, Wuhan, Hubei 430033, China
  • Received:2014-04-14 Revised:2014-08-03 Online:2016-01-25 Published:2016-01-25

摘要:

反馈粒子滤波器(FPF)是一种连续时间最优贝叶斯估计器.针对FPF对系统采样率要求较高的问题,提出一种基于径向基函数-Galerkin法求解的反馈粒子滤波器.该算法推导了反馈增益势函数所满足偏微分方程的弱形式,结合径向基函数对势函数进行近似,利用Galerkin法和蒙特卡罗积分得到了反馈增益近似解,并给出了一种径向基参数选取方法,从数值上分析了径向基函数参数选取对于滤波精度的影响.仿真算例表明反馈粒子滤波器在低系统采样率下会严重发散,而本文算法能够避免这一问题,且提高了FPF在低系统采样率下的滤波精度和稳定性.

关键词: 非线性滤波, 贝叶斯滤波, 反馈粒子滤波器, Galerkin法, 径向基函数

Abstract:

A radial basis function(RBF) Galerkin solution based feedback particle filter is proposed to resolve the divergency problem existing in present particle filter when the continuity of system model is violated. A weak formulation of the PDE regarding to the potential of feedback gain is firstly derived, then the RBFs are employed to approximate the potential function. Finally the feedback gain solution is obtained using Galerkin method and Monte Carlo integral, also the method for choosing RBF parameters is provided and analyzed numerically. It is demonstrated that the present FPF diverges under low system sample rate, whereas our proposed feedback particle filter is nevertheless effective, with preferable tracking accuracy and stability under low system sample rate.

Key words: nonlinear filtering, Bayesian filtering, feedback particle filer(FPF), Galerkin method, radial basis functions(RBF)

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