多变量系统的辅助模型辨识方法的收敛性分析*

Convergence Analysis of the Auxiliary Model Identification Algorithm for Multivariable Systems

中文关键词  多变量系统  参数估计  条件数  辅助模型方法  鞅收敛定理

英文关键词  Multivariable system  parameter estimation  conditional number  auxiliary model identification algorithm  martingale convergence theorem

中文摘要

      丁锋，谢新民[1]假设协方差阵P0-1（t）=的最大特征值与最小特征值之比（即条件数）有界，和系统噪声{w（t）}方差有界，证明了辅助模型辨识其法参数估计的一致收致性．本文将分别放松这两个条件，即ⅰ）条件数无界，ⅱ）系统噪声为非平稳噪声，且方差无界，探讨了辅助模型算法的收敛性．分析表明在这种较弱的假设下，辅助模型算法保持很强的鲁棒性，参数估计是一致收敛的．

英文摘要

      The convergence of the recursive auxiliary model (RAM)identification algorithm was proved provided that both ratio of the maximum to minimum eigenvalues of the covariance matrix （t）= [i. e. conditional number] and the variance of the observation noise {w(t)} are bounded in reference [1]. In this paper，the convergence rate of RAM algorithm is studied under either unbounded conditional number or unbounded noise variance. The results show that the parameter estimates given by RAM algorithm are consistently convergent and that this algorithm is robust.