总体最小二乘方法在三维坐标转换中的应用  

APPLYING TOTAL LEAST SQUARES TO THREE-DIMENSIONAL DATUM TRANSFORMATION

作　　者：陆珏[1] 陈义[1] 郑波[1] 

机构地区：[1]同济大学测量与国土信息工程系,上海200092

出　　处：《大地测量与地球动力学》2008年第5期77-81,共5页Journal of Geodesy and Geodynamics

摘　　要：对比研究总体最小二乘方法与最小二乘方法在三维小角度空间直角坐标转换中的适用性及优越性,发现在三维坐标转换中,由于新旧两套坐标系下点坐标的量测值均存在误差,因此若用总体最小二乘方法对误差方程中的系数矩阵A以及观测向量b同时改正,能够建立更加合理的计算模型。算例证明相对于LS方法,利用总体最小二乘方法能够得到精度更高的坐标转换参数解。Through the comparative research on applicability and superiority of Total Least Squares（TLS） and least squares in the space rectangular coordinates tranformation with 3-D small angles, it is found that in this kind of 3-D coordinate transformation because there are observational errors of the point coordinate in both the previous and new coordinate systems, if the coefficient matrix A and observed vector b of the error equation are corrected simulaneously with the TLS, thus more reasonable computation model can built out. The calculated example has proved that the more accurate coordinate transformation parameter solution can be given with TLS as compared with the LS.

关 键 词：总体最小二乘 坐标转换 最小二乘 混合最小二乘与总体最小二乘 误差 

分 类 号：P207.1[天文地球—测绘科学与技术]