最大相关熵准则下的因式分解形式类卡尔曼实现
Factored-form Kalman-like implementations under maximum correntropy criterion
AI总结：
针对MCC-KF估计器有限精度运算下数值稳定性研究不足的问题，本文推导了其及改进变体的因式分解形式（含UD、SVD基等）算法，重点研究阵列算法，通过理论分析与数值比较确定最可靠的实现方式，丰富了相关算法族。
摘要：
最大相关熵准则（MCC）方法被公认为一种针对异常值的鲁棒滤波策略，且在存在非高斯噪声的情况下，其估计精度优于经典卡尔曼滤波器（KF）。然而，新提出的MCC-KF估计器在有限精度运算中的数值稳定性很少被研究。本文分别为MCC-KF及其改进变体推导了一族因式分解形式（平方根）算法。该族算法传统上包含三种因式分解形式的实现：（i）基于Cholesky分解的算法，（ii）改进Cholesky分解即基于UD的方法，以及（iii）近期建立的基于SVD的滤波方法。所有这些策略通常被认为能够增强传统滤波针对舍入误差的数值鲁棒性，因此在解决具有高可靠性要求的应用时，它们是首选的实现方式。此前，仅设计了基于Cholesky分解的IMCC-KF算法。本文还引入了基于UD和SVD的方法，丰富了因式分解形式算法族。本文特别关注阵列算法，这类算法被证明数值稳定性最高，此外还适合并行实现。文中讨论了理论性质，并给出了数值比较以确定最可靠的实现方式。
英文摘要：
The maximum correntropy criterion (MCC) methodology is recognized to be a robust filtering strategy with respect to outliers and shown to outperform the classical Kalman filter (KF) for estimation accuracy in the presence of non-Gaussian noise. However, the numerical stability of the newly proposed MCC-KF estimators in finite precision arithmetic is seldom addressed. In this paper, a family of {\it factored-form} (square-root) algorithms is derived for the MCC-KF and its improved variant, respectively. The family traditionally consists of three factored-form implementations: (i) Cholesky factorization-based algorithms, (ii) modified Cholesky, i.e. UD-based methods, and (iii) the recently established SVD-based filtering. All these strategies are commonly recognized to enhance the numerical robustness of conventional filtering with respect to roundoff errors and, hence, they are the preferred implementations when solving applications with high reliability requirements. Previously, only Cholesky-based IMCC-KF algorithms have been designed. This paper enriches a factored-form family by introducing the UD- and SVD-based methods as well. A special attention is paid to {\it array} algorithms that are proved to be the most numerically stable and, additionally, suitable for parallel implementations. The theoretical properties are discussed and numerical comparison is presented for determining the most reliable implementations.
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