While the filtered-x normalized least mean square (FxNLMS) algorithm is widely applied due to its simple structure and easy implementation for active noise control system, it faces two critical limitations: the fixed step-size causes a trade-off between convergence rate and steady-state residual error, and its performance deteriorates significantly in impulsive noise environments. To address the step-size constraint issue, we propose the switched \mbox{step-size} FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the \mbox{mean-square} deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different \mbox{step-sizes}, the optimal step-size for each iteration is selected. Furthermore, to enhance the algorithm's robustness in impulsive noise scenarios, we integrate a robust strategy into the SSS-FxNLMS algorithm, resulting in a robust variant of it. The effectiveness and superiority of the proposed algorithms has been confirmed through computer simulations in different noise scenarios.

翻译：滤波x归一化最小均方算法因其结构简单、易于实现而广泛应用于主动噪声控制系统，但它面临两个关键限制：固定步长导致收敛速度与稳态残差之间的权衡，且在脉冲噪声环境中其性能显著恶化。为解决步长约束问题，我们提出了切换步长滤波x NLMS算法。具体而言，我们推导了滤波x NLMS算法的均方偏差趋势，然后通过比较不同步长对应的均方偏差趋势，为每次迭代选择最优步长。此外，为增强算法在脉冲噪声场景中的鲁棒性，我们将鲁棒策略集成到切换步长滤波x NLMS算法中，从而得到其鲁棒变体。通过在不同噪声场景下的计算机仿真，所提算法的有效性和优越性得到了验证。