The errors-in-variables (EIV) model is widely used in linear systems where both input and output signals are contaminated with noise. For the parameter estimation in the EIV model, the adaptive filtering algorithm using total least squares (TLS) approach has shown better performance than classical least squares (LS) approach. However, the TLS approach which is based on minimizing the mean squared total error may be irrational in the presence of impulsive noise. To address this problem, a novel robust adaptive algorithm, named as the total least mean M-estimate (TLMM) algorithm, is proposed in this brief, which combines the advantages of TLS approach and M-estimate function. In addition, to further improve the performance of the TLMM algorithm, its variable step-size (VSS) version has been developed. Moreover, we carry out the local stability analysis and the computational complexity analysis. Simulation results show that the proposed algorithms outperform some well-known algorithms.

中文翻译：

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一种用于脉冲噪声抑制的鲁棒的总最小均值 M 估计自适应算法

变量误差 (EIV) 模型广泛用于输入和输出信号都受到噪声污染的线性系统。对于 EIV 模型中的参数估计，使用总最小二乘法 (TLS) 方法的自适应滤波算法表现出比经典最小二乘法 (LS) 方法更好的性能。然而，基于最小化均方总误差的 TLS 方法在存在脉冲噪声时可能是不合理的。为了解决这个问题，本文提出了一种新的鲁棒自适应算法，称为总最小均值 M 估计 (TLMM) 算法，它结合了 TLS 方法和 M 估计函数的优点。此外，为了进一步提高 TLMM 算法的性能，还开发了其可变步长 (VSS) 版本。而且，我们进行了局部稳定性分析和计算复杂度分析。仿真结果表明，所提出的算法优于一些众所周知的算法。