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| 整体最小二乘法直线拟合 | |
| 引用本文： | 丁克良,沈云中,欧吉坤. 整体最小二乘法直线拟合[J]. 辽宁工程技术大学学报(自然科学版), 2010, 29(1) |
| 作者姓名： | 丁克良 沈云中 欧吉坤 |
| 作者单位： | 1. 北京建筑工程学院,测绘与城市空间信息学院,北京,100044;现代工程测量国家测绘局,重点实验室,上海,200092 2. 现代工程测量国家测绘局,重点实验室,上海,200092 3. 中国科学院测量与地球物理研究所,湖北,武汉,430077 |
| 基金项目： | 现代工程测量国家测绘局重点实验基金资助项目(ES-SBSM-(07)-05);;国家自然科学基金资助项目(40771178) |
| 摘 要： | 针对在直线拟合中,因变量选取不同拟合的结果有差异现象,提出采用整体最小二乘法进行直线拟合。文章在分析直线方程特点的基础上,采用EIV模型描述直线方程,在解算中根据系数矩阵的特点应用QR分解分为将方程两部分,采用了混合最小二乘法求解。理论分析和实际计算结果表明,整体最小二乘法顾及了因变量和自变量的误差。拟合精度高于普通最小二乘法,采用整体最小二乘拟合直线,整体上优于普通最小二乘法。 |
| 关 键 词： | 直线拟合 普通最小二乘法 整体最小二乘法 EIV模型 |
Methods of line-fitting based on total least-squares |
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| DING Keliang,SHENG Yunzhong,OU Jikun. Methods of line-fitting based on total least-squares[J]. Journal of Liaoning Technical University (Natural Science Edition), 2010, 29(1) | |
| Authors: | DING Keliang SHENG Yunzhong OU Jikun |
| Affiliation: | 1.Beijing university Civil Engineering And Architecture;School of Geomatics and Urban Information;Beijing 100044;China;2. Key Laboratory of Advanced Engineering Surveying of SBSM;Shanghai 200092 China;3. Institute of Geodesy and Geophysics;Chinese Academy of Sciences;Wuhan;430077;China |
| Abstract: | Line fitting obtained by ordingary least square is often different if the independent variable is defferent,the reason that result in the defference is analysised in the paper. Then the method of line fitting by total least squares is proposed. We describle the line equation with errors-in-variables model,and in the parameter solution the coefficient matrix is divided into two parts by using the QR decomposition. And then the Related parameter can be achieved by the ordianary least squares and total least s... |
| Keywords: | line fitting ordinary least squares total least squares errors-in-variable model |
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