最小二乘曲线拟合及MATLAB实现测绘专业.doc

内蒙古科技大学 本科生毕业设计说明书（毕业论文） 题 目：最小二乘曲线拟合及MATLAB实现 学生姓名：李亚 学 号：0972143230 专 业：测绘工程 班 级：2009测绘2班 指导教师：孙同贺 讲师最小二乘曲线拟合及MATLAB实现 摘 要 关键词：Square Methodand Its Realization with Matlab Abstract To introduce the basic theory of curve fitting and discuss the least squares principle in this paper, what’s more, we also discuss the basic principle of curve fitting and the establishment of polynomial curve fitting model. Meanwhile, we also introduce the least-square method of curve fitting in detail and part of the theory of orthogonal least square method. We mainly discuss the specific steps of polynomial fitting, and also introduces the nonlinear equation of the least squares fitting at the same time, which established on the theory of least squares curve fitting in MATLAB in order to realize the method to do research. Using MATLAB2012b platform to achieve the goal of measuring data and introducing the special structure of MATLAB and curve fitting tool. We can use ployfit function in MATLAB to polynomial curve fitting of experimental data, and get the MATLAB source program about curve fitting and the fitting curve. Finally, we need to prove the method of assessing the precision of the fitting is effective. Key words: least square method; curve fitting; MATLAB, metrical data 最小二乘曲线拟合及MATLAB实现 I 摘 要 I Curve Fitting in Least-Square Method and Its Realization with Matlab II Abstract II 第一章 引 言 1 1.1研究背景 1 1.1.1 历史理论原理 1 1.1.2 现代研究 1 1.2 问题定义 2 1.2.1 曲线拟合的思想 2 1.2.2 多项式拟合 3 1.2.3 利用Matlab的polyfit函数进行多项式拟合 3 1.3 论文结构 3 第二章 数据曲线拟合 4 2.1测量数据 4 2.2拟合模型 4 2.3最小二乘原理 5 2.3.1最小二乘法 5 2.3.2最小二乘估计与极大似然估计 7 2.4数据拟合 9 2.4.1曲线拟合理论 9 2.4.2最小二乘法线性拟合原理 10 2.4.3最小二乘非线性拟合 12 2.4.4正交多项式 13 2.4.5正交最小二乘曲线拟合 15 2.5曲线拟合精度评定 17 第三章MATLAB 19 3.1MATLAB概述 19 3.1.1MATLAB简介 19 3.1.2MATLAB的主要组成部分 21 3.2MATLAB2012b的运行简介 23 3.2.1启动和退出MATLAB2012b 23 3.2.2MATLAB2012b桌面系统 24 3.2.3MATLAB函数调用系统 26 3.2.4MATLAB2012b的帮助系统 27 3.2.5附件管理系统 28 3.2.6数据交换系统 28 3.2.7MATLAB 中的其他系统 29 3.3最小二乘曲线拟合法的MATLAB实现 30 第四章