基于反余切函数的变步长LMS谐波检测算法

Variable step size LMS harmonic detection algorithm based on anti-cotangent function

分析定步长算法无法兼顾收敛速度和稳态误差性能方面的缺点和传统变步长最小均方(LMS)算法中存在的不足,针对以上问题,提出了一种基于反余切函数的变步长LMS算法。该算法利用误差信号的自相关平均估计获得期望误差估计均值,进而通过反余切作为核心函数来调节步长更新;消除了误差信号对步长更新的干扰,具有较小的稳态误差。并利用推导出来的三阶权值迭代公式来代替传统的权值迭代公式,以获得更快地收敛速度。仿真实验分析并验证了该算法在谐波检测中的有效性。

Analysis of the fixed-step algorithm can not take into account the shortcomings of convergence speed and steady-state error performance and the shortcomings in the traditional variable-step least mean square(LMS)algorithm, aiming at the above problems, a variable step size LMS algorithm based on anti-cotangent function is proposed.The algorithm uses the autocorrelation average estimate of the error signal to obtain the mean of the expected error estimate, then adjust the step size update by using anti-cotangent function as a core function;eliminates the interference of the error signal to the step update, with a small steady-state error.And use the derived third-order weight iteration formula to replace the traditional weight iteration formula to get faster convergence speed.The simulation experiment analyzes and verifies the effectiveness of the algorithm in harmonic detection.