Abstract This paper proposes a new robust learning strategy, which is based on a Weibull M-transform function. The suitability of the Weibull M-transform function as a robust norm has been investigated for different shape and scale parameters, and a Weibull M-transform least mean square (WMLMS) algorithm has been developed. Further, the bound of learning rate has been derived for the proposed algorithm. The proposed WMLMS algorithm has been evaluated for the problem of system identification and simulation studies carried out demonstrate its robustness. In addition, a filtered-x WMLMS (Fx-WMLMS) algorithm has been developed for robust room equalization and has been shown to offer stable room equalization even in the presence of strong disturbances picked up by the microphone.

中文翻译：

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Weibull M 变换最小均方算法

摘要 本文提出了一种新的鲁棒学习策略，它基于威布尔 M 变换函数。已经针对不同的形状和尺度参数研究了 Weibull M 变换函数作为稳健范数的适用性，并开发了 Weibull M 变换最小均方 (WMLMS) 算法。此外，已经为所提出的算法导出了学习率的界限。所提出的 WMLMS 算法已经针对系统识别问题进行了评估，并且进行的仿真研究证明了其鲁棒性。此外，已开发出一种已过滤的 x WMLMS (Fx-WMLMS) 算法以实现稳健的房间均衡，并且即使在麦克风拾取的强烈干扰存在的情况下也能提供稳定的房间均衡。