三维坐标转换的通用整体最小二乘算法
收稿日期: 2014-01-08
修回日期: 2014-04-07
网络出版日期: 2014-12-02
A General Total Least Squares Algorithm for Three-dimensional Coordinate Transformations
Received date: 2014-01-08
Revised date: 2014-04-07
Online published: 2014-12-02
方兴 曾文宪 刘经南 姚宜斌 . 三维坐标转换的通用整体最小二乘算法[J]. 测绘学报, 2014 , 43(11) : 1139 -1143 . DOI: 10.13485/j.cnki.11-2089.2014.0193
The model of three-dimensional coordinate transformation is a nonlinear EIV (errors-in-variables) model. The methods proposed in published literatures are always restricted in practice for their special assumptions, such as size of rotation angles, structured design matrix and special weight matrix. In this paper, a general weighted TLS algorithm of a three-dimensional coordinate transformation is investigated. The new algorithm can be applied in transformations with an arbitrary rotation angles and any applicable weights of the observations, as well as the structured design matrix or the design matrix with both random and fixed elements. The example given in this paper illustrates that this algorithm is general and suits to all kinds of three-dimensional coordinate transformations in practice.
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