为了解决非线性滤波中量测噪声呈厚尾分布且统计特性不确定的问题,提出一种基于Pearson Type VII 分布的自适应滤波算法.针对传统鲁棒卡尔曼滤波器因尺度矩阵和自由度参数固定不变而无法自适应调整的问题,以容积卡尔曼滤波器为基础,选择Pearson Type VII 分布对厚尾噪声进行建模,将传统鲁棒滤波固定自由度参数的估计转化为Pearson Type VII 分布中可自适应调整的双自由度参数的估计,并通过 inverse Wishart和Gamma分布描述尺度矩阵、双自由度参数和辅助参数的先验分布,利用遗忘因子对各参数进行时间更新;基于变分贝叶斯理论,对系统状态、尺度矩阵、双自由度参数和辅助参数形成的联合后验概率密度函数进行变分迭代,实现对系统状态和未知厚尾噪声的联合估计.仿真结果表明,在不确定厚尾噪声条件下,本文算法的滤波精度高于传统鲁棒容积卡尔曼滤波.

An adaptive Pearson Type VII based filter was proposed to deal with measurement noise with heavy tailed distribution and uncertain statistical characteristics in nonlinear filtering. In view of the fact that the scale matrix and degree-of-freedom (DOF) parameters of traditional robust Kalman filter are fixed, which cannot adjust adaptively. The Pearson Type VII distribution was selected to model the heavy tailed noise to realize the adaptive estimation of 2-DOF parameters based on Cubature Kalman filter (CKF). Inverse Wishart and Gamma distributions were used to describe prior distributions of the scale matrix, 2-DOF parameters, and auxiliary parameters. Besides, time updating of these parameters was performed through a forgetting factor. Based on the variational Bayesian theory, the variational iteration of joint posterior probability density function formed by states together with the 2-DOF parameters and auxiliary parameters was performed, and the states and noise parameters were estimated simultaneously. The simulation results show that this algorithm has a higher filtering accuracy than the traditional robust CKF under the condition of uncertain heavy tailed noise.