鞅超收敛定理与遗忘因子最小二乘算法的收敛法分析

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

中文关键词  时变系统  鞅收敛定理  鞅超收敛定理  参数估计  遗忘因子最小二乘法

英文关键词  time-varying system  martingale convergence theorem  martingale hypervonvergence theorem  parameter estimation  forgetting factor least squares algorithm

中文摘要

      本文扩展了用于分析时不变系统辨识算法收敛性的鞅收敛定理（MCT），建立了鞅（martingale）超收敛定理 （MHCT）。它可以作为工具来分析时变系统的各种辨识算法的收敛性，为解决时变系统收敛性和稳定性分析这一困难课题提供了新方法，开辟了新路。本文以遗忘因子最小二乘算法为例，成功地用MHCT分析了它的参数估计的收敛性。

英文摘要

      In this paper, the martingale convergence therorem used to analyze the convergence of identify-cation algorithms of time-invariant systems is extended. The martingale hyperconvergence theorem((MHCT) is established, which may analyze the convergence of various algorithms for time-varying systems and give a new method for analysis of covengence and stability of time-varying systems. Taking the forgetting factor least squares algorithm (FFLS) as an example, we prove the convergence of the FFLS algorithm by means of MHCT.