Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method

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

doi:10.3969/j.issn.0372-2112.2016.01.014

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Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method

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- Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method
- Acta Electronica Sinica Vol. 44, Issue 1, Pages: 95-100(2016)
- 作者机构：
  
  海军工程大学兵器工程系,湖北,武汉,430033
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2016.01.014
  CLC： TP202
- Published Online：25 January 2016，
  
  Published：2016
- 稿件说明：
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ZHANG Hong-xin, ZHOU Sui-hua, FENG Shi-min. Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method[J]. Acta Electronica Sinica, 2016, 44(1): 95-100.
DOI：

ZHANG Hong-xin, ZHOU Sui-hua, FENG Shi-min. Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method[J]. Acta Electronica Sinica, 2016, 44(1): 95-100. DOI： 10.3969/j.issn.0372-2112.2016.01.014.

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.

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.

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