关于鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析

鞅超收敛定理是研究随机时变系统辨识算法有界收敛性的一个有效数学工具，它是鞅收益是在随机时变系统中的推广。文「１」用它证明了遗忘因子最小二乘算法参数估计误差的有界收敛性，但是文「１」假设系统的理各态遍历的，且协方差阵是用它的数学期望代替的，所得到的结果是近似的。而本文精确地给出了协方差阵的上下界，改进了文「１」的结果。

Remarks on Martingale Hyperconvergence Theorem and the Convergence Analysis of the Forgetting Factor Least Squares Algorithms

The martingale hyperonvergence theorem (MHCT) is an effective mathematical tool of analyzing the boundedconvergence of identification algorithms and the extension of the martingale convergence theorem in stochastic time-varyin sys-tems. The upper boundedness of the parameter estimation error of forgetting factor least squares algorithms was given by usingMHCT in Ref. 1], but the upper boundedness of the covariance matrix was replacecd with its expectation. approximately.Inthe paper the upper and lower boundedness of the covariance matrix is given and the results of Ref. 1] are improved.