Non-Gaussian noise processing is a difficult and hot spot in the study of filters. A currently effective method to deal with non-Gaussian noise is replacing the minimum mean square error criterion with the maximum correntropy criterion. Based on the maximum correntropy criterion, maximum correntropy Kalman filter, which usually uses the Gaussian kernel function to define the distance between vectors, is developed. However, when the non-Gaussian noise is multi-dimensional, maximum correntropy Kalman filter tends to break down due to the appearance of singular matrices. To overcome the drawback, a novel filter named Cauchy kernel-based maximum correntropy Kalman filter is proposed, which utilises the Cauchy kernel function to define the distance between vectors. Due to the insensitive feature to the kernel bandwidth and thick-tailed characteristic of the Cauchy kernel function, Cauchy kernel-based maximum correntropy Kalman filter can effectively avoid filter faults and has a better stability. Simulation results demonstrate the excellent performance of the proposed algorithm by comparing it with other conventional methods, such as Kalman filter, ideal Kalman filter, Huber-based filter, Gaussian sum filter and maximum correntropy Kalman filter.

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基于柯西核的最大相关熵卡尔曼滤波器

非高斯噪声处理是滤波器研究中的难点和热点。目前处理非高斯噪声的有效方法是用最大相关熵准则代替最小均方误差准则。基于最大相关熵准则，开发了通常使用高斯核函数来定义向量间距离的最大相关熵卡尔曼滤波器。然而，当非高斯噪声为多维时，由于奇异矩阵的出现，最大相关熵卡尔曼滤波器往往会崩溃。为了克服这个缺点，提出了一种新的滤波器，称为基于柯西核的最大相关熵卡尔曼滤波器，它利用柯西核函数来定义向量之间的距离。由于柯西核函数对核带宽的不敏感特性和厚尾特性，基于柯西核的最大相关熵卡尔曼滤波器可以有效避免滤波器故障并具有更好的稳定性。仿真结果通过与其他传统方法如卡尔曼滤波器、理想卡尔曼滤波器、基于Huber 的滤波器、高斯和滤波器和最大相关熵卡尔曼滤波器进行比较，证明了该算法的优异性能。