The variable step size least mean square algorithm has been suggested since a number of years as a potential solution for improving the performance of least mean square algorithm. In this article, the variable step size least mean square algorithm is classified by the techniques which are used to update step size. Unfortunately, for variable step size least mean square algorithms with forgetting factor, a constant forgetting factor may slow down its convergence speed. For this reason, a variable forgetting factor method for variable step size least mean square is proposed in this article. First, the convergence analysis of a new variable step size least mean square algorithm with the variable forgetting factor is provided. Then, simulations expose the characteristics of this variable forgetting factor method. Last, a micro-vibration control experimental system is established. Four typical variable step size least mean square algorithms and their variable forgetting factor modified version are verified through experiments. The results show that the proposed variable forgetting factor method can effectively improve convergence speed while maintaining the steady-state performance of the variable step size least mean square algorithm with the constant forgetting factor.

多年来，人们一直建议将可变步长最小均方算法作为提高最小均方算法性能的潜在解决方案。在本文中，可变步长最小均方算法根据用于更新步长的技术进行分类。不幸的是，对于具有遗忘因子的可变步长最小均方算法，恒定的遗忘因子可能会减慢其收敛速度。为此，本文提出了一种可变步长最小均方的可变遗忘因子方法。首先，提供了一种具有变量遗忘因子的新型变步长最小均方算法的收敛性分析。然后，仿真揭示了该变量遗忘因子方法的特征。最后的，建立了微振动控制实验系统。通过实验验证了四种典型的变步长最小均方算法及其变遗忘因子修正版本。结果表明，所提出的变遗忘因子方法在保持遗忘因子不变的变步长最小均方算法的稳态性能的同时，可以有效提高收敛速度。