测绘学报 ›› 2014, Vol. 43 ›› Issue (11): 1139-1143.doi: 10.13485/j.cnki.11-2089.2014.0193

• 学术论文 • 上一篇    下一篇

三维坐标转换的通用整体最小二乘算法

方兴1,曾文宪1,刘经南2,3,姚宜斌1   

  1. 1. 武汉大学测绘学院
    2. 武汉大学卫星定位导航技术研究中心
    3. 武汉大学 测绘学院
  • 收稿日期:2014-01-08 修回日期:2014-04-07 出版日期:2014-11-20 发布日期:2014-12-02
  • 通讯作者: 曾文宪 E-mail:wxzeng@sgg.whu.edu.cn

A General Total Least Squares Algorithm for Three-dimensional Coordinate Transformations

FANG Xing1,ZENG Wenxian1,LIU Jingnan1,2,YAO Yinbin1   

  1. 1. School of Geodesy and Geomatics, Wuhan University
    2. Research Center of GNSS, Wuhan University
  • Received:2014-01-08 Revised:2014-04-07 Online:2014-11-20 Published:2014-12-02
  • Contact: ZENG Wenxian E-mail:wxzeng@sgg.whu.edu.cn

摘要:

三维坐标转换模型属于非线性EIV(errors-in-variables)模型,现有整体最小二乘算法均设定了某些特殊假设条件,如仅适用于小角度或者属于非统计意义上的数值解,并且不能用于结构性的系数矩阵等,算法适用性受到极大限制。本文提出了三维坐标转换模型的通用加权整体最小二乘算法,该算法适用于任意旋转角度以及一般性的权矩阵情况下的三维坐标转换模型,并且将结构性系数矩阵、同时包含随机和非随机元素的系数矩阵等情况纳入到了统一的坐标转换模型算法。实例计算表明,本文提出的算法具有通用性,适用于实际应用中的各类三维坐标转换模型。

关键词: 整体最小二乘估计, 三维坐标转换模, EIV模型, 非线性算法

Abstract:

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.

Key words: Total least-squares method, Three-dimensional coordinate transformations, errors-in-variables model, Nonlinear program

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