摘要使用输入输出来测量系统模型的方法就是系统辨识。随着现代控制理论的迅速发展，系统辨识得到了迅速而蓬勃发展，并已经成功运用于多种工程应用领域。

系统辨识分为经典辨识方法和逐渐发展的现代辨识方法，其中最小二乘法(Least Squares，LS)是一种经典的和最基本的，也是应用最广泛的方法，一般最小二乘法只能有效辨识白噪声系统，而实际系统中大多为有色噪声，所以，就有了增广最小二乘法(Extended Least Squares，ELS)和广义最小二乘法(Generalized Least Squares，GLS)这两种针对有色噪声模型的辨识方法，通过分析增广最小二乘法和广义最小二乘法可以使最小二乘法在实际应用中起到更大的作用。63908

本文的主要目的就是分析研究最小二乘法及其扩展得到的增广最小二乘法和广义最小二乘法的辨识原理及数据仿真。同时，设计一个友好的GUI界面也是本次设计的目的之一。

毕业论文关键词 系统辨识 最小二乘法 增广最小二乘法 广义最小二乘法 有色噪声

毕业设计说明书（论文）外文摘要

Title  System identification related algorithms program and  interface design 

Abstract The method of using input and output model to measure the model of system is system identification. With the rapid development of modern control theory, system identification has been rapidly and vigorously developed, and has been successfully used in a variety of engineering applications.

System identification is pided into classical identification methods and the developing modern identification method, Least Squares(LS) method is a classic method and of the most basic, and it is the most widely used method, Least Squares method can only effectively identify white noise system, however ,in actual system ,there is mostly colored noise, so there are the Extended Least Squares(ELS) method and the Generalized Least Squares(GLS) method，these two kinds of methods are for the identification of colored noise model , by analyzing the Extended Least Squares method and Generalized Least Squares method, Least Squares method can play a greater role in practical applications.

The main purpose of this paper is to analyze and study the identification theory and data simulation of Least Square method and its extension of Extended Least Squares method and the Generalized Least Squares method. While the design of a friendly GUI interface is also one of the purposes of this design.

Keywords  system  identification  LS  ELS  GLS  colored noise

1 引言 1

1.1  系统辨识综述 1

1.2  系统辨识研究现状 2

1.3  最小二乘的发展 2

2 系统辨识 5

2.1  辨识的定义 5

2.2  辨识问题的表达形式 5

2.3  辨识算法的基本原理 6

2.4  辨识的内容和步骤 8

3 最小二乘法 11

3.1  最小二乘法原理 11

3.2  加权的最小二乘 12

3.3  最小二乘一次算法 13

3.4  递推最小二乘法 14

3.5  增广最小二乘法 16

3.6  广义最小二乘法