Convergence Analysis of Parameter Estimation in System Identification
作者单位：Natural Science Research Center Harbin Institute of Technology
会议名称：《第25届中国控制与决策会议》
会议届次：25th
主办单位：IEEE;NE Univ;IEEE Ind Elect Chapter;IEEE Harbin Sect Control Syst Soc Chapter;Guizhou Univ;IEEE Control Syst Soc;Syst Engn Soc China;Chinese Assoc Artificial Intelligence;Chinese Assoc Automat;Tech Comm Control Theory;Chinese Assoc Aeronaut;Automat Control Soc;Chinese Assoc Syst Simulat;Simulat Methods & Modeling Soc;Intelligent Control & Management Soc
会议日期：2013年
学科分类：0711[理学-系统科学] 02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 071102[理学-系统分析与集成]
关 键 词：system identification parameter estimate prediction error method Hausdorff metric
摘 要：For linear time-invariant system model, this paper analyzes the convergence of parameter estimations as the length of the input-output data tends to infinity through prediction error method. It is known that the sequence of the prediction errors, called criterion functions, converges uniformly in the parameter with probability one as the data length tends to infinity. Given an input-output data of fixed length, the parameter estimation is represented by a set in general, instead of by a single point, on which the criterion function takes its minimum. Thus a mathematical feature of the convergence problem of parameter estimation is in that we are needed, from the convergence of a sequence of functions, to infer the convergence of the sequence of their sets of minimizing arguments. The Hausdorff metric, as a rational due tool, is suggested to measure the distance between sets and then is used to discuss the convergence problem here. We show that, according to Hausdorff metric, the convergence of parameter estimation can not be guaranteed in general, and give some conditions to guarantee.