时变系统有限数据窗最小二乘辨识的有界收敛性

利用随机过程理论证明了有限数据窗最小二乘法的有界收敛性,给出了参数估计误差 上界的计算公式,阐述了获得最小均方参数估计误差上界时数据窗长度的选择方法.分析表明, 对于时不变随机系统,数据窗长度越大,均方参数估计误差上界越小;对于确定性时变系统,数 据窗长度越小,均方参数估计误差上界越小.因此,对于时变随机系统,一个折中方案是寻求一 个最佳数据窗长度,以使均方参数估计误差最小.该文的研究成果对于提高辨识算法的实际应 用效果有重要意义.

BOUNDED CONVERGENCE OF FINITE DATA WINDOW LEAST SQUARES IDENTIFICATION FOR TIME-VARYING SYSTEMS

In this paper the bounded convergence of finite data window least squares algorithm is proved by using stochastic process theory, and the formulae of computing the parameter estimation error are given. The way of choosing the data window length is stated so that the upper bound of the minimum mean square parameter estimation error is obtained. The analyses indicate that for time invariant stochastic systems, the smaller the data window length, the smaller the estimation error upper bound is, and that for deterministic time varying systems, the larger the data window length, the smaller the estimation error upper bound is. So a compromise is to choose a best data window length for a minimum mean square parameter estimation error.