基于改进双曲正切函数的变步长最小平均p范数算法

在信号处理领域,传统的自适应滤波算法采用的固定步长会导致稳态误差和收敛速度无法同时兼顾。针对这个问题,对最小平均p范数(Least Mean p-norm,LMP)算法进行改进,提出了一种基于改进双曲正切(tanh)函数的变步长最小平均p范数算法。该算法利用改进的tanh函数来调节步长,采用移动加权平均法构造变步长函数;同时引入了一个调节函数以进一步提升算法的性能。通过在海洋脉冲噪声干扰下进行仿真,实验表明,与已有的固定步长和变步长算法相比,改进的变步长LMP算法较好地兼顾系统的收敛速度和稳态误差;引入调节函数后的新算法在保证原有算法收敛速度的同时进一步降低了算法的稳态误差,从而兼顾了算法的收敛性和稳定性,具有较好的可行性。

A variable step size least mean p-norm algorithm based on improved hyperbolic tangent function

IIn the field of signal processing, the traditional adaptive filtering algorithm with fixed step size cannot take the steady-state error and the convergence speed into account at the same time. To solve this problem, the least mean p-norm (LMP) algorithm needs to be improved, and an improved variable step size least mean p-norm (IVSLMP) algorithm based on the improved hyperbolic tangent function is proposed. The algorithm uses an improved hyperbolic tangent function to adjust the step size, and uses a moving weighted average method to construct a variable step function; at the same time, an adjustment function is introduced to further improve the performance of the algorithm. Through the simulation experiment under the interference of ocean impulse noise, it is shown that compared with the existing fixed step size and variable step size algorithms, the improved variable step size LMP algorithm can well take the convergence speed and steady state error of the system into account; and for the new algorithm after introducing the adjustment function, the steady state error is further reduced while ensuring the convergence speed of the original algorithm, so that the convergence and stability of the algorithm are better considered, and it has better feasibility.