The kernel adaptive filters (KAFs) based on the minimum mean square error (MMSE) criterion in reproducing kernel Hilbert space (RKHS) improve the performance of linear adaptive filters but result in instability issues and large burdens of computation and memory in impulsive noises. To this end, a novel Nyström kernel recursive generalized maximum correntropy (NKRGMC) with probability density rank-based quantization (PRQ) sampling (NKRGMC-PRQ) algorithm is proposed to improve filtering performance, robustness, and computational efficiency of the traditional KAFs in this letter. In a fixed dimensional network structure, the proposed NKRGMC-PRQ algorithm can achieve a comparable performance to KAFs with low computational complexity. Monte Carlo simulations are conducted to validate the superiorities of NKRGMC-PRQ in terms of filtering accuracy, computational complexity, and robustness.

中文翻译：

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广义最大相关熵准则下的 Nystrom 核算法

在再现内核希尔伯特空间 (RKHS) 中，基于最小均方误差 (MMSE) 准则的内核自适应滤波器 (KAF) 提高了线性自适应滤波器的性能，但会导致不稳定问题以及脉冲噪声中的大量计算和内存负担。为此，提出了一种新的 Nyström 核递归广义最大相关熵（NKRGMC）和概率密度基于秩的量化（PRQ）采样（NKRGMC-PRQ）算法，以提高传统 KAF 的滤波性能、鲁棒性和计算效率。信件。在固定维网络结构中，所提出的 NKRGMC-PRQ 算法可以在计算复杂度较低的情况下实现与 KAF 相当的性能。进行蒙特卡罗模拟以验证 NKRGMC-PRQ 在过滤精度方面的优越性，