自适应最小均方算法及其能量函数研究

Study of Adaptive LMS Algo rithm and Its Energy Function

根据递推随机理论，用李雅普诺夫法研究最小均方算法的微分方程，结论是，不管信号是平稳过程还是非平稳过程，该算法大范围渐近稳定。在均方意义下定义自适应时间常数为李雅普诺夫函数与其导数之比，由此建立时间常数、步长。

Differential equation of the least mean squares algorithm is studied by method of Lyapunov based upon the recurisive stochastic algorithm. A conclusion comes that LMS algorithm converges asymptotically in the large area whether input signal is a stationary process or a nonstationary one. Adaptation time constants is defined, in the mean square sense, as the absolute of the ratio of the Lyapunov function to its differentiation. The paper establishes a new relationship among the time constants, the step size,the eigenvalue and the bandwidth of signal.