LMS算法的二次稳定性及鲁棒LMS算法

摘要

The stability property of LMS algorithm (least mean square algorithm) and the design of robust LMS algorithm are discussed in this paper. The standard LMS algorithm is transferred into a standard state equation form of diserete-time system. Then its quadratic stability property is analyzed by linear matrix inequality technique. Owning to the noise often emerging in input and measure of filter, a robust LMS algorithm, in which convergence, robust stability and robust property are all considered, is developed. In the end, simulafon results are presented to support the analysis and to compare the performance of the robust algorithm with the usual LMS algorithm. They show that the algorithm is feasible.%本文在时域内研究LMS算法(least mean square algorithm)的稳定性及鲁棒LMS算法的构造。首先将LMS算法表达式转化为标准的离散时间系统状态方程形式，之后运用线性矩阵不等式(LMI)技术对其二次稳定性进行了分析。针对滤波过程中会出现的输入和测量噪声干扰，本文提出了一种兼顾收敛性、鲁棒稳定性以及鲁棒性能的鲁棒LMS算法，最后给出了仿真算例，通过和一般的LMS算法的比较，体现了这种鲁棒LMS算法的优越性。