标题： 基于Chandrasekhar的最大核相关性卡尔曼滤波与自适应核大小选择 显示英文标题

标题： Chandrasekhar-based maximum correntropy Kalman filtering with the adaptive kernel size selection

摘要： 本技术备注旨在推导最大互信息准则（MCC）卡尔曼滤波（KF）的 Chandrasekhar 型递归公式。 对于经典的 KF，第一个 Chandrasekhar 差分方程是在 1970 年代初提出的。 这是对传统使用的 Riccati 递归的替代方法，并产生了所谓的快速实现，称为 Morf-Sidhu-Kailath-Sayed KF 算法。 它们被证明在计算上是廉价的，因为其在 Riccati 递归中传播的矩阵尺寸小于$n \times n$误差协方差矩阵。 在工程文献中，尚未提出在 MCC 估计方法论内推导 Chandrasekhar 型递归的问题。 在本技术备注中，我们迈出了第一步，并推导了自适应核大小选择策略情况下的 Chandrasekhar MCC-KF 估计器，这表示一个常数标量调整权重。 数值示例验证了新提出的 MCC-KF 实现的实用性以及所呈现理论推导的正确性。 显示英文摘要

摘要： This technical note is aimed to derive the Chandrasekhar-type recursion for the maximum correntropy criterion (MCC) Kalman filtering (KF). For the classical KF, the first Chandrasekhar difference equation was proposed at the beginning of 1970s. This is the alternative to the traditionally used Riccati recursion and it yields the so-called fast implementations known as the Morf-Sidhu-Kailath-Sayed KF algorithms. They are proved to be computationally cheap because of propagating the matrices of a smaller size than $n \times n$ error covariance matrix in the Riccati recursion. The problem of deriving the Chandrasekhar-type recursion within the MCC estimation methodology has never been raised yet in engineering literature. In this technical note, we do the first step and derive the Chandrasekhar MCC-KF estimators for the case of adaptive kernel size selection strategy, which implies a constant scalar adjusting weight. Numerical examples substantiate a practical feasibility of the newly suggested MCC-KF implementations and correctness of the presented theoretical derivations.