基于正态分布曲线的分段式变步长LMS算法

针对传统最小均方误差(Least Mean Square, LMS)自适应滤波算法由于步长固定,在解决稳态误差与收敛性之间的关系时,始终处于矛盾状态的问题,在对传统的固定步长LMS自适应滤波算法分析的基础上,根据变步长LMS自适应滤波算法的步长调整原则,通过构造步长因子与误差信号的非线性函数,提出了一种基于正态分布曲线的分段式变步长LMS自适应滤波算法,并分析了参数取值对算法性能的影响。针对实际信号处理过程中参考信号难以选取的问题,提出了一种基于分裂阵的参考信号选取方法。理论和海试数据分析结果表明:该算法的收敛速度和稳态误差明显优于固定步长的LMS自适应滤波算法和基于Sigmoid函数的变步长LMS自适应滤波算法。

Segmented variable-step-size LMS algorithm based on normal distribution curve

The Traditional LMS(least mean square) adaptive filtering algorithm is always in a contradiction state because it has a fixed step size and resolves the relationship between steady-state error and convergence. Based on the analysis of the filtering algorithm, according to the step-size adjustment principle of the variable-step LMS adaptive filter algorithm, a segmented variable step size LMS adaptive filtering algorithm based on the normal distribution curve was proposed by constructing the nonlinear function of the step-size factor and the error signal, and the influence of the parameter value on the performance of the algorithm was analyzed. Aiming at the problem of difficult selection of reference signal in actual signal processing, a method of reference signal selection based on the splitting array was proposed. The theoretical and sea trial data analysis results show that the convergence speed and steady-state error of the proposed algorithm are obviously better than the fixed-step LMS adaptive filtering algorithm and the variable step size LMS adaptive filtering algorithm based on the Sigmoid function.