带厚尾噪声的鲁棒Student’s t容积滤波器

Robust Student’s t based cubature filter with heavy tailed noise

为了解决带厚尾过程和量测噪声的非线性状态估计问题,本文提出了一种新的鲁棒非线性滤波器.首先,对带厚尾过程和量测噪声的非线性系统进行了数学建模,并推导了基于Student’s t近似的鲁棒非线性滤波器(RSTNF)的一般结构.其次,针对RSTNF中涉及到的含有关于Student’s t分布的多维非线性函数积分的求解问题,提出了基于Student’s t分布的球径容积准则(STSRCR),并在此基础上设计了一种新的鲁棒Student’s t容积滤波器(RSTCF).最后,利用目标跟踪仿真验证了本文提出的带厚尾噪声的RSTCF的有效性以及与现有方法相比的优越性.

In this paper,a new robust nonlinear filter is proposed to solve the problem of nonlinear state estimation with heavy tailed process and measurement noises.Firstly,the nonlinear state space model with heavy tailed process and measurement noises is constructed.On this basis,a robust Student’s t based nonlinear filter(RSTNF)can be derived.Secondly,a new third-degree Student’s t spherical radial cubature rule(STSRCR)is proposed to calculate the Student’s t weighted integral in RSTNF,from which a new robust Student’s t based cubature filter(RSTCF)can be obtained.Finally,the efficiency and superiority of the proposed RSTCF with heavy process and measurement noises,as compared with existing methods,are shown in the simulation of target tracking.