Acta Geodaetica et Cartographica Sinica ›› 2014, Vol. 43 ›› Issue (11): 1139-1143.doi: 10.13485/j.cnki.11-2089.2014.0193

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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

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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