基于径向基-Galerkin解的反馈粒子滤波器  

Feedback Particle Filter Using Radial Basis Functions Based Galerkin Method

作　　者：张宏欣[1] 周穗华[1] 冯士民[1] 

机构地区：[1]海军工程大学兵器工程系,湖北武汉430033

出　　处：《电子学报》2016年第1期95-100,共6页Acta Electronica Sinica

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.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 lowsystem sample rate,whereas our proposed feedback particle filter is nevertheless effective,with preferable tracking accuracy and stability under lowsystem sample rate.

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 

分 类 号：TP202[自动化与计算机技术—检测技术与自动化装置]