Enhanced SAF algorithm with Tukey’s biweight loss

In contrast to the normalized least mean square (NLMS) algorithm, the normalized subband adaptive filtering (NSAF) algorithm exhibits considerable improvement within the convergence for colored input signals. However, the presence of impulsive noise in the system output has a significant negative influence on its performance. To address this issue, the Tukey’s biweight function is integrated into the NSAF algorithm to suppress the influence from impulsive noise, as the Tukey’s biweight function possesses the capability to discriminate outlier values. This paper presents the Tukey’s biweight-based NSAF (Tb-NSAF) algorithm, provides the relation expression of energy conservation for the Tb-NSAF algorithm. The computational complexity and stability requirements for the Tb-NSAF algorithm are provided. Furthermore, the Tb-NSAF algorithm of adaptive parameter $b$ (ATb-NSAF) algorithm is proposed to enhance performance in actual speech input environments. Extensive experimental results confirm the effectiveness of both the Tb-NSAF and ATb-NSAF algorithms.