时变系统最小均方算法的性能分析

在无过程数据平稳性假设和各态遍历等条件下，运用随机过程理论研究了最小方算法（LMS）的有界收敛性，给出了估计误差的上界，论述了LMS算法收敛因子或步长的选择方法，以使参数估计误差上界最小。这对于提高LMS算法的实际应用效果有着重要意义。LMS算法的收敛性分析表明：（1）对于确定性时不变系统，LMS算法是指数速度收敛的；（2）对于确定性时变系统，收敛因子等于1，LMS算法的参数估计误差上界最小；（3）对于时变或不变随机系统，LMS算法的参数估计误差一致有上界。

Performance Analysis of Least Mean Square Algorithm for Time-Varying Systems

By means of stochastic process theory, the bounded convergence of least mean square algorithm (LMS) is studied without data stationary assumption and ergodicity condition. The upper bound of the estimation error is given, and the way of choosing the convergence factor or stepsize is stated so that the upper bound of the parameter estimation error is minimized. The convergence analyses indicate that i) for deterministic time invariant systems, LMS algorithm is convergent exponentially, ii) for deterministic time varying systems, the estimation error upper bound is minimal as the stepsize goes to unity, and iii) for time varying or time invariant stochastic systems, the estimation error is uniformly bounded.