基于双曲正切函数框架的最小均方算法

Least Mean Square Algorithm Based on Hyperbolic Tangent Function Framework

自适应滤波器在自适应控制、噪声消除、信道均衡、系统辨识以及生物医学等领域的应用中发挥着重要作用。由于其简单性、低计算量和易于实现等特点,其中最流行的自适应滤波算法是最小均方(Least Mean Square,LMS)算法。传统的LMS算法在处理高斯信号时具有良好的收敛性能,然而,针对非高斯信号的处理,自适应LMS算法的收敛性较差,甚至无法收敛。为了改进LMS算法在非高斯噪声干扰下的收敛性,本文通过将传统的LMS算法的代价函数嵌入到双曲正切(Hyperbolic Tangent)函数框架中设计了一种新的代价函数,从而提出了一种鲁棒的双曲正切最小均方(Hyperbolic Tangent Least Mean Square,HTLMS)算法。此外,针对HTLMS算法存在收敛速度与稳态误差相矛盾的问题,本文设计了一种可变λ参数的双曲正切最小均方(Variableλ-parameter Hyperbolic Tangent Least Mean Square,VHTLMS)算法。仿真结果表明,在系统辨识应用场景中,与LMS算法、最大相关熵准则(Generalized Maximum Correntropy Criterion,GMCC)自适应滤波算法和对数双曲余弦自适应滤波器(Logarithmic Hyperbolic Cosine Adaptive Filter,LHCAF)算法相比较,本文提出的HTLMS算法和VHTLMS算法在冲击噪声干扰下具有良好的鲁棒性、更快的收敛速度和较小的稳态误差。

Adaptive filters play an important role in applications such as adaptive control,noise cancellation,channel equalization,system identification,and biomedical fields.Due to its simplicity,low computational complexity,and ease of implementation,the most popular adaptive filtering algorithm is the least mean square(LMS)algorithm.The traditional LMS algorithm has good convergence performance when processing Gaussian signals.However,for the processing of non-Gaussian signals,the adaptive LMS algorithm has poor convergence or even cannot converge.In order to improve the convergence of the LMS algorithm under non-Gaussian noise interference,this paper defines a new cost function by embedding the cost function of the traditional LMS algorithm into the framework of hyperbolic tangent function,and thus proposes a robust hyperbolic tangent least mean square(HTLMS)algorithm.In addition,in response to the contradiction between convergence speed and steady-state error in the HTLMS algorithm,this paper designs a variableλ-parameter hyperbolic tangent least mean square(VHTLMS)algorithm.The simulation results show that in system identification application scenarios,compared with the LMS algorithm,generalized maximum correntropy criterion(GMCC)adaptive filtering algorithm,and logarithmic hyperbolic cosine adaptive filter(LHCAF)algorithm,the proposed HTLMS algorithm and VHTLMS algorithm in this paper have good robustness,faster convergence speed and smaller steady-state error under impulsive noise interference.