Recently, the nearest Kronecker product (NKP) decomposition-based normalized least mean square (NLMS-NKP) algorithm has demonstrated superior convergence performance compared to the conventional NLMS algorithm. However, its convergence rate exhibits significant degradation when processing highly correlated input signals. To address this problem, we propose a type-I NKP-based normalized subband adaptive filter (NSAF) algorithm, namely NSAF-NKP-I. Nevertheless, this algorithm incurs substantially higher computational overhead than the NLMS-NKP algorithm. Remarkably, our enhanced type-II NKP-based NSAF (NSAF-NKP-II) algorithm achieves equivalent convergence performance while substantially reducing computational complexity. Furthermore, to enhance robustness against impulsive noise interference, we develop two robust variants: the maximum correntropy criterion-based robust NSAF-NKP (RNSAF-NKP-MCC) and logarithmic criterion-based robust NSAF-NKP (RNSAF-NKP-LC) algorithms. Additionally, detailed analyses of computational complexity, step-size range, and theoretical steady-state performance are provided for theproposed algorithms. To enhance the practicability of the NSAF-NKP-II algorithm in complex nonlinear environments, we further devise two nonlinear implementations: the trigonometric functional link network-based NKP-NSAF (TFLN-NSAF-NKP) and Volterra series expansion-based NKP-NSAF (Volterra-NKP-NSAF) algorithms. In active noise control (ANC) systems, we further propose the filtered-x NSAF-NKP-II (NKP-FxNSAF) algorithm. Simulation experiments in echo cancellation, sparse system identification, nonlinear processing, and ANC scenarios are conducted to validate the superiority of the proposed algorithms over existing state-of-the-art counterparts.

翻译：最近，基于最近Kronecker积（NKP）分解的归一化最小均方（NLMS-NKP）算法相较于传统NLMS算法已展现出更优的收敛性能。然而，在处理高度相关的输入信号时，其收敛速度会出现显著下降。为解决此问题，我们提出了一种基于I型NKP的归一化子带自适应滤波器（NSAF）算法，即NSAF-NKP-I。然而，该算法的计算开销远高于NLMS-NKP算法。值得注意的是，我们增强的基于II型NKP的NSAF（NSAF-NKP-II）算法在显著降低计算复杂度的同时，实现了同等的收敛性能。此外，为增强对抗脉冲噪声干扰的鲁棒性，我们开发了两种鲁棒变体：基于最大相关熵准则的鲁棒NSAF-NKP（RNSAF-NKP-MCC）算法和基于对数准则的鲁棒NSAF-NKP（RNSAF-NKP-LC）算法。同时，对所提算法的计算复杂度、步长范围及理论稳态性能进行了详细分析。为提升NSAF-NKP-II算法在复杂非线性环境中的实用性，我们进一步设计了两种非线性实现方案：基于三角函数链接网络的NKP-NSAF（TFLN-NSAF-NKP）算法和基于Volterra级数展开的NKP-NSAF（Volterra-NKP-NSAF）算法。在主动噪声控制（ANC）系统中，我们进一步提出了滤波-x NSAF-NKP-II（NKP-FxNSAF）算法。通过在回声消除、稀疏系统辨识、非线性处理及ANC场景中进行仿真实验，验证了所提算法相较于现有先进算法的优越性。