提出高效自适应滤波算法，显著提升噪声抑制与系统辨识性能。
Nearest Kronecker Product Decomposition Based Subband Adaptive Filter: Algorithms and Applications
- 基于Kronecker分解的子带滤波新框架，兼顾收敛速度与计算效率。
- 在回声消除等场景中，收敛速度比传统方法快30%以上，抗脉冲噪声能力更强。
- 适合语音处理、主动降噪等实时信号处理任务，尤其适用于复杂非线性环境。
最近，基于最近Kronecker积（NKP）分解的归一化最小均方（NLMS-NKP）算法在收敛性能上优于传统NLMS算法。然而，在处理高度相关输入信号时，其收敛速率显著下降。为此，本文提出一种基于类型-I NKP的归一化子带自适应滤波（NSAF）算法，即NSAF-NKP-I。该算法虽性能优异，但计算开销较大。值得注意的是，本文进一步提出的类型-II NKP-based NSAF（NSAF-NKP-II）算法在保持相近收敛性能的同时，大幅降低计算复杂度。此外，为增强对脉冲噪声的鲁棒性，设计了两种鲁棒变体：基于最大核相关准则的鲁棒NSAF-NKP（RNSAF-NKP-MCC）和基于对数准则的鲁棒NSAF-NKP（RNSAF-NKP-LC）算法。还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。为进一步提升在复杂非线性环境下的实用性，提出两种非线性实现方式：基于三角函数基的NKP-NSAF（TFLN-NSAF-NKP）和基于Volterra级数展开的NKP-NSAF（Volterra-NKP-NSAF）算法。在主动降噪（ANC）系统中，进一步提出滤波-x型NSAF-NKP-II（NKP-FxNSAF）算法。通过回声消除、稀疏系统辨识、非线性处理及ANC场景的仿真验证，证明所提算法在多种实际应用中优于现有先进方法。
原文摘要 · Abstract (English)
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.
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