变步长LMS自适应滤波算法的研究

发布时间：2018-03-26 09:04

本文选题：自适应滤波　切入点：LMS算法　出处：《湖南师范大学》2015年硕士论文

【摘要】：1967年Window和Hoff提出了自适应滤波理论,使得滤波器的参数能自动地调整到最佳值,实现最优滤波。自适应滤波器的性能良好且易于硬件实现。滤波算法的好坏决定着滤波器的性能,因此算法的设计在整个滤波器的设计过程中占有举足轻重的地位。追求收敛速度快、稳态误差小、计算复杂度低、易于硬件实现的算法已经成为信号处理领域中人们研究的目标。基于维纳滤波理论发展起来的最小均方(LMS)算法具有较好的收敛性能和稳态误差性能,加上LMS算法的结构简单、计算量少、便于硬件实现等特点,被广泛地运用于信道均衡、噪声处理、系统辨识、线性预测等领域。本论文在论述自适应滤波理论的基础上,通过介绍目前一些最主要的自适应滤波算法及其应用,分析和研究了传统固定步长LMS算法,总结了现有自适应LMS算法的特点。为了克服传统固定步长LMS算法在收敛速度与稳态误差性能之间存在的不足,提出了一种基于双曲正弦(Sinh)函数的新变步长LMS算法,分析了新算法中参数a、b、c的选取对算法性能的影响。通过实验认证该算法在收敛速度和稳态误差性能方面明显优于固定步长LMS算法和文献[57]所提出的SVS-LMS算法。由于在不同噪声环境中,自适应滤波算法的收敛速度和稳态失调系数会受到不同信噪比的影响。本文通过对双曲正切(Tanh)函数进行数学变化,提出了一种新的改进型的变步长LMS自适应滤波算法。新的改进算法跟改进前的算法比较,改进算法明显具有较快的收敛速度、时变跟踪速度及较小的稳态失调系数。更重要的是当环境中的信噪比比较低时,新的改进算法仍然能保持较好的性能。
[Abstract]:In 1967, Window and Hoff proposed the adaptive filtering theory, which allows the parameters of the filter to be adjusted to the optimum value automatically. The performance of adaptive filter is good and easy to implement in hardware. The filter algorithm determines the performance of filter. Therefore, the design of the algorithm plays an important role in the whole filter design process. The pursuit of fast convergence, small steady-state error, low computational complexity, The algorithm which is easy to implement in hardware has become the research target in the field of signal processing. The least mean square (LMS) algorithm developed based on Wiener filter theory has better convergence performance and steady error performance, and the structure of LMS algorithm is simple. It is widely used in the fields of channel equalization, noise processing, system identification, linear prediction and so on. By introducing some of the most important adaptive filtering algorithms and their applications, the traditional fixed-step LMS algorithm is analyzed and studied. The characteristics of the existing adaptive LMS algorithms are summarized. In order to overcome the shortcomings between the convergence speed and the steady-state error performance of the traditional fixed-step LMS algorithm, a new variable step size LMS algorithm based on the hyperbolic sinusoidal sinh function is proposed. In this paper, the influence of the selection of parameter abbc on the performance of the new algorithm is analyzed. It is verified by experiments that the algorithm is superior to the fixed step size LMS algorithm and the SVS-LMS algorithm proposed in reference [57] in terms of convergence speed and steady-state error performance. In different noise environments, The convergence rate and steady-state misalignment coefficient of adaptive filtering algorithm are affected by different signal-to-noise ratio (SNR). In this paper, the hyperbolic tangent Tanh function is changed mathematically. In this paper, a new modified variable step size LMS adaptive filtering algorithm is proposed. Compared with the previous algorithm, the improved algorithm has a faster convergence rate. More importantly, when the SNR in the environment is low, the improved algorithm can still maintain good performance.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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