This paper presents a robust error variance estimation rule for the nonparametric variable step-size normalized least mean square (NPVSS-NLMS) algorithm. The proposed variance estimation rule accurately estimates the variance of the error signal. This is achieved by the variable exponential windowing parameter depending on the standard deviations of the sequential error signals. The accurate estimation of the error signal variance in the NPVSS-NLMS algorithm considerably improves the performance of the adaptive filter when compared to the classical NPVSS-NLMS algorithm. Moreover, the convergence and steady-state performances of the NPVSS-NLMS based on the proposed rule are analyzed in this study. The performance of the proposed algorithm is evaluated on system identification and acoustic echo canceling experiments and compared with that the classical NPVSS-NLMS algorithm. As a result, simulations show that the proposed algorithm with the help of the novel robust error variance estimation rule not only yields a dramatically reduced steady-state error but also achieves a faster convergence rate as compared with the classical counterparts. Furthermore, the theoretical results of the variable exponential windowing parameter used in the proposed rule are in very good agreement with its simulation results.

中文翻译：

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非参数VSS-NLMS算法的新误差方差估计规则

本文提出了非参数可变步长归一化最小均方 (NPVSS-NLMS) 算法的鲁棒误差方差估计规则。提出的方差估计规则准确地估计了误差信号的方差。这是通过取决于顺序误差信号的标准偏差的可变指数加窗参数来实现的。与经典的 NPVSS-NLMS 算法相比，NPVSS-NLMS 算法中误差信号方差的准确估计大大提高了自适应滤波器的性能。此外，本研究还分析了基于所提出规则的 NPVSS-NLMS 的收敛性和稳态性能。通过系统识别和声学回声消除实验评估了所提出算法的性能，并与经典的 NPVSS-NLMS 算法进行了比较。结果，仿真表明，与经典算法相比，所提出的算法在新的鲁棒误差方差估计规则的帮助下不仅显着降低了稳态误差，而且实现了更快的收敛速度。此外，所提出的规则中使用的可变指数加窗参数的理论结果与其模拟结果非常吻合。仿真表明，与经典算法相比，所提出的算法在新的鲁棒误差方差估计规则的帮助下不仅显着降低了稳态误差，而且实现了更快的收敛速度。此外，所提出的规则中使用的可变指数加窗参数的理论结果与其模拟结果非常吻合。仿真表明，与经典算法相比，所提出的算法在新的鲁棒误差方差估计规则的帮助下不仅显着降低了稳态误差，而且实现了更快的收敛速度。此外，所提出的规则中使用的可变指数加窗参数的理论结果与其仿真结果非常吻合。