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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均方算法 (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 :i)对于确定性时不变系统 ,LMS算法是指数速度收敛的 ;ii)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 ;iii)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 .
Under the conditions of non-stationary data assumptions and ergodic traits, the stochastic process theory is used to study the bounded convergence of the Least Mean Square (LMS) algorithm. The upper bound of the estimation error is given. The LMS convergence factor or Step selection method to minimize the upper bound of parameter estimation error.This is of great significance for improving the practical application effect of LMS algorithm. The convergence analysis of LMS algorithm shows that: i) the LMS algorithm exponentially converges for deterministic time-invariant systems; ii) for deterministic time-varying systems, the convergence factor equals 1, and the LMS algorithm has the smallest upper bound on the estimated error; iii) For time-varying or invariant stochastic systems, the LMS algorithm’s parameter estimation error is uniformly upper bound.