General Total Least Squares Theory for Geodetic Coordinate Transformations

Applied Sciences

Bin Wang¹  Wenxian Zeng²  Yuxin Qin²  Xing Fang² 

[1] College of Geomatics Science and Technology, Nanjing Tech University, Nanjing 211816, China;School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;

关键词: total least squares;    Gauss–Newton algorithm;    errors-in-variables;    affine/orthogonal/similarity/rigid transformations;    constraints;    general algorithm;   

DOI  :  10.3390/app10072598

来源: DOAJ

【 摘 要 】

Datum transformations are a fundamental issue in geodesy, Global Positioning System (GPS) science and technology, geographical information science (GIS), and other research fields. In this study, we establish a general total least squares (TLS) theory which allows the errors-in-variables model with different constraints to formulate all transformation models, including affine, orthogonal, similarity, and rigid transformations. Through the adaptation of the transformation models to the constrained TLS problem, the nonlinear constrained normal equation is analytically derived, and the transformation parameters can be iteratively estimated by fixed-point formulas. We also provide the statistical characteristics of the parameter estimator and the unit of precision of the control points. Two examples are given, as well as an analysis of the results on how the estimated quantities vary when the number of constraints becomes larger.

【 授权许可】

Unknown