The Filtered-x Normalized Least Mean Square (FxNLMS) algorithm suffers from slow convergence and a risk of divergence, although it can achieve low steady-state errors after sufficient adaptation. In contrast, the Generative Fixed-Filter Active Noise Control (GFANC) method offers fast response speed, but its lack of adaptability may lead to large steady-state errors. This paper proposes a hybrid GFANC-FxNLMS algorithm to leverage the complementary advantages of both approaches. In the hybrid GFANC-FxNLMS algorithm, GFANC provides a frame-level control filter as an initialization for FxNLMS, while FxNLMS performs continuous adaptation at the sampling rate. Small variations in the GFANC-generated filter may repeatedly reinitialize FxNLMS, interrupting its adaptation process and destabilizing the system. An online clustering module is introduced to avoid unnecessary re-initializations and improve system stability. Simulation results show that the proposed algorithm achieves fast response, very low steady-state error, and high stability, requiring only one pre-trained broadband filter.

翻译：滤波-x归一化最小均方（FxNLMS）算法在充分自适应后能够实现较低的稳态误差，但其收敛速度较慢且存在发散风险。相比之下，生成式固定滤波器主动噪声控制（GFANC）方法响应速度快，但其缺乏自适应性可能导致较大的稳态误差。本文提出一种混合GFANC-FxNLMS算法，以融合两种方法的互补优势。在该混合算法中，GFANC提供帧级控制滤波器作为FxNLMS的初始化条件，而FxNLMS则以采样率进行连续自适应。GFANC生成滤波器的微小变化可能反复重新初始化FxNLMS，从而中断其自适应过程并导致系统失稳。为此引入在线聚类模块以避免不必要的重新初始化，从而提升系统稳定性。仿真结果表明，所提算法仅需一个预训练的宽带滤波器即可实现快速响应、极低稳态误差和高稳定性。