整体最小二乘法及其在测量数据处理中的应用

【作者】 丁克良； 欧吉坤； 陈义；

【Author】 Ding Ke-liang,OU Ji-kun,Chen yi (1Beijing Institute of Civil Engineering And Architecture, School of Geomatics and urban information, 100044 2 Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, 430077 3. Department of Surveying and Geo-Informatics , Tongji University , Shanghai 200092 , China)

【机构】 北京建筑工程学院测绘与城市空间信息学院； 中国科学院测量与地球物理研究所； 同济大学测量与国土信息工程系；

【摘要】 在参数求解中,针对参数估计模型的观测向量和系数矩阵都可能存在误差情况,20世纪80年代提出了整体最小二乘方法。本文系统阐述了整体最小二乘基本原理、思想,基于奇异值分解原理详细阐述了整体最小二乘的解算方法。在对普通最小二乘和整体最小二乘深入比较的基础上提出要注意整体最小二乘应用条件问题。更多还原

【Abstract】 For parameter solution, the total least square (TLS) method was proposed in early 80’s of twenty century as to deal with some estimation models that both the observation and design matrix are subject to errors. The basic concept of TLS, principle of computational algorithms for TLS based on the singular value decomposition theory are described systematically in this paper. The applicability and limitation of TLS in surveying data process are proposed based on comparisons and analyses between the ordinary least squares and the total least squares.更多还原