衰减激励条件下最小均方算法的收敛性

Convergence of least mean squares algorithm under attenuating excitation conditions

给出了衰减激励信号的定义 ,并在衰减激励条件下 ,利用随机过程理论 ,研究了随机系统最小均方算法的收敛速率 ,阐述了参数估计误差收敛时 ,衰减指数和算法中设计参变量 (收敛因子或步长 )的选择方法 .分析表明 :在衰减激励条件下 ,最小均方算法也具有良好的性能 :当衰减指数和设计参变量满足一定条件时 。

The definition of attenuating excitation signal is given, and the convergence rate of the least mean square \{algorithm\}, using stochastic process theory, is studied for stochastic systems under attenuating excitation. The way to choose the attenuating index and design variable (convergent factor or stepsize) is stated for guaranteeing the convergence of the parameter estimates, and the analysis indicates that under attenting excitation the least mean square algorithm also has a good performance:i.e., the parameter estimation error given by the least mean square algorithm uniformly converges to zero when the attenuating index and design variable satisfy some proper conditions.