系统辨识(5):迭代搜索原理与辨识方法  

System identification.Part E:Iterative search principle and identification methods

作　　者：丁锋[1,2,3] 

机构地区：[1]江南大学物联网工程学院,无锡214122 [2]江南大学控制科学与工程研究中心,无锡214122 [3]江南大学教育部轻工过程先进控制重点实验室,无锡214122

出　　处：《南京信息工程大学学报（自然科学版）》2011年第6期481-510,共30页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：国家自然科学基金(60973043)

摘　　要：递推辨识与迭代辨识构成了两类重要的参数估计方法.递推辨识的递推变量与时间有关,因而可以用于在线估计系统参数;迭代辨识的迭代变量是自然数,与客观世界的时间无关,通常用于离线估计系统参数.基于辅助模型辨识思想、多新息辨识理论、递阶辨识原理、耦合辨识概念等辨识方法都可以用递推算法和迭代算法实现.迭代方法渊源很早,如求解矩阵方程Ax=b的雅可比迭代、高斯-赛德尔迭代等.迭代辨识方法主要使用梯度搜索、最小二乘搜索、牛顿搜索原理来实现.为此主要研究了CARMA系统和Box-Jenkins系统的最小二乘迭代辨识方法与梯度迭代辨识方法.这些方法也可推广到其他所有方程误差类系统和输出误差类系统,以及非线性系统.迭代辨识方法通常用于有限量测数据的系统辨识,其收敛性证明是辨识领域极具挑战性的研究课题.Recursive identification and iterative identification are two important parameter estimation methods.The recursive index in the recursive identification is a time variable and the recursive identification can be used for online estimating system parameters;the iterative index in the iterative identification is a natural number and independent of time and the iterative identification is generally used for off-line estimating system parameters.The auxiliary model identification idea,multi-innovation identification theory,hierarchical identification principle and coupling identification concept based methods can be realized through recursive algorithms and iterative algorithms.Iterative methods can be traced to hundreds of years ago Jacobi iteration and Guass-Seidel iteration for solving the matrix equations Ax=b.Iterative identification methods are based on the gradient search,least-squares search and Newton search principle.This paper studies the least squares based and gradient based iterative identification methods for CARMA systems and Box-Jenkins systems.The propsed methods can also be extended to other equation error type systems,output error type systems and nonlinear systems.Iterative methods usually apply system identification with finite data and their convergence analysis is very difficult and is a challenging research topic.

关 键 词：迭代辨识 递推辨识 参数估计 FIR模型 CAR模型 CARMA模型 CARAR模型 CARARMA模型 输出误差模型 OEMA模型 OEAR模型 辅助模型辨识 多新息辨识 递阶辨识 耦合辨识 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]