When the input signal is correlated input signals, and the input and output signal is contaminated by Gaussian noise, the total least squares normalized subband adaptive filter (TLS-NSAF) algorithm shows good performance. However, when it is disturbed by impulse noise, the TLS-NSAF algorithm shows the rapidly deteriorating convergence performance. To solve this problem, this paper proposed the robust total minimum mean M-estimator normalized subband filter (TLMM-NSAF) algorithm. In addition, this paper also conducts a detailed theoretical performance analysis of the TLMM-NSAF algorithm and obtains the stable step size range and theoretical steady-state mean squared deviation (MSD) of the algorithm. To further improve the performance of the algorithm, we also propose a new variable step size (VSS) method of the algorithm. Finally, the robustness of our proposed algorithm and the consistency of theoretical and simulated values are verified by computer simulations of system identification and echo cancellation under different noise models.

翻译：当输入信号为相关信号，且输入与输出信号均受高斯噪声污染时，总最小二乘归一化子带自适应滤波器（TLS-NSAF）算法表现出良好性能。然而，当受到脉冲噪声干扰时，TLS-NSAF算法的收敛性能急剧恶化。针对此问题，本文提出了鲁棒总最小均值M估计归一化子带滤波器（TLMM-NSAF）算法。此外，本文还对TLMM-NSAF算法进行了详细的理论性能分析，获得了算法的稳定步长范围及理论稳态均方偏差（MSD）。为进一步提升算法性能，我们进一步提出了该算法的变步长（VSS）方法。最后，通过不同噪声模型下系统辨识与回声消除的计算机仿真验证了所提算法的鲁棒性以及理论值与仿真值的一致性。