基于稳定Cholesky分解的最大相关熵准则卡尔曼滤波方法研究
On the stable Cholesky factorization-based method for the maximum correntropy criterion Kalman filtering
AI总结：
本文针对最大相关熵准则卡尔曼滤波，提出首个基于Cholesky分解的鲁棒数值稳定平方根实现方法，采用协方差矩阵平方根因子与迭代正交变换，实验显示其性能优于传统及现有Cholesky基变体。
摘要：
本文延续了针对最大相关熵准则卡尔曼滤波（MCC-KF）的数值稳定平方根实现设计的研究。与以往所得结果不同，本文提出了基于Cholesky分解方法中首个（针对舍入误差）鲁棒的方法。该方法以协方差矩阵的平方根因子表述，即属于协方差型滤波方法体系。此外，算法的每次迭代都采用数值稳定的正交变换，以准确传播所涉及的Cholesky因子。数值实验结果表明，新型MCC-KF实现的性能优于传统算法及其此前公布的基于Cholesky的变体。
英文摘要：
This paper continues the research devoted to the design of numerically stable square-root implementations for the maximum correntropy criterion Kalman filtering (MCC-KF). In contrast to the previously obtained results, here we reveal the first robust (with respect to round-off errors) method within the Cholesky factorization-based approach. The method is formulated in terms of square-root factors of the {\it covariance} matrices, i.e. it belongs to the covariance-type filtering methodology. Additionally, a numerically stable orthogonal transformation is utilized at each iterate of the algorithm for accurate propagation of the Cholesky factors involved. The results of numerical experiments illustrate a superior performance of the novel MCC-KF implementation compared to both the conventional algorithm and its previously published Cholesky-based variant.
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