加权总体最小二乘在三维基准转换中的应用

测绘学报

加权总体最小二乘在三维基准转换中的应用

袁庆¹,楼立志²,陈玮娴¹

1. 同济大学
2. 同济大学测量与国土信息工程系，现代工程测量国家测绘局重点实验室

收稿日期:2011-03-23 修回日期:1900-01-01 出版日期:2011-05-05 发布日期:2015-06-24
通讯作者: 袁庆

The Application of the Weighted Total Least-Squares on Three Dimensional-Datum Transformation

Received:2011-03-23 Revised:1900-01-01 Online:2011-05-05 Published:2015-06-24

摘要/Abstract

摘要： GPS中的WGS-84坐标系和地球椭球坐标系转换，属于三维空间小角度直角坐标系之间的转换。对比研究加权总体最小二乘(weighted total least-squares，WTLS)方法和混合最小二乘(LS-TLS)方法、最小二乘(least-squares，LS)方法在三维空间小角度直角坐标转换中的适用性。在两套坐标系下坐标测量值均存在误差时，用WTLS方法不但可以对观测向量y和系数矩阵A同时修改、将坐标先验精度引入平差计算，同时引入的权阵PA对系数阵起到固定常数元素而只修改必要数据元素的作用，使得模型更加精确合理，得到更合适的参数解。

Abstract: The coordinate system transformation between the WGS-84 coordinate system and geodetic coordinate system in GPS is the three dimensional small angular region rectangular coordinates transformation. We researched on the serviceability of weighted total least-squares method, the LS-TLS method and the least-squares method in the three dimensional small angular region rectangular coordinates transformation. We found that when the coordinate observed value was influenced by the error in both of the coordinate systems, using WTLS method could revise the observation vector y and the coefficient matrix A, introduce the coordinate prior precision to the adjustment computation, and fix the constant element and adjust the data element through with the weighted matrix PA.This would make the model to be more precise and more reasonable and obtain the high accuracy parameter solution.

袁庆,楼立志,陈玮娴. 加权总体最小二乘在三维基准转换中的应用[J]. 测绘学报.