With the help of Information Theory Learning (ITL) theory, a kind of increasingly popular non-Gaussian filtering method has been designed in the sense of the maximum correntropy (MC) criterion or minimum error entropy (MEE) criterion. In MC or MEE criterion, Gaussian kernel function is usually chosen as the kernel function. Compared to the Gaussian kernel function, the Cauchy kernel function has a wider range of action and is insensitive to the kernel parameters. In this paper, a new Cauchy kernel MEE criterion is defined. In the sense of the new defined criterion, two kinds of non-Gaussian centralized fusion filtering algorithms are proposed with the help of fixed-point theory, which are Cauchy kernel minimum error entropy parallel centralized fusion filter and Cauchy kernel minimum error entropy sequential centralized fusion filter. The propagation equation is used to calculate the prior estimates of the state and covariance, and then the fixed-point iteration is used to calculate the posterior estimates of the state and covariance. The convergence of the iteration process included in the two proposed methods is analyzed by using Banach fixed-point theorem. The final two experimental simulations verify the superior performance of the two proposed fusion filtering algorithms.

中文翻译：

---

柯西核最小误差熵集中式融合滤波器

借助信息论学习（ITL）理论，设计了一种日益流行的最大熵（MC）准则或最小误差熵（MEE）准则意义上的非高斯滤波方法。在MC或MEE准则中，通常选择高斯核函数作为核函数。与高斯核函数相比，柯西核函数的作用范围更广，并且对核参数不敏感。本文定义了一种新的柯西核MEE准则。在新定义准则的意义上，借助不动点理论，提出了两种非高斯集中式融合滤波算法：柯西核最小误差熵并行集中式融合滤波器和柯西核最小误差熵顺序集中式融合滤波器。筛选。使用传播方程计算状态和协方差的先验估计，然后使用定点迭代计算状态和协方差的后验估计。利用Banach不动点定理分析了两种方法中迭代过程的收敛性。最后的两个实验模拟验证了两种提出的融合滤波算法的优越性能。