On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model

2015 ◽  
Vol 89 (6) ◽  
pp. 573-576 ◽  
Author(s):  
Guobin Chang
Keyword(s):  
Least Squares ◽  
Similarity Transformation ◽  
Transformation Problem ◽  
Least Squares Solution ◽  
3D Similarity

scholarly journals PERFORMING 3D SIMILARITY TRANSFORMATION WITH LARGE ROTATION ANGLES USING CONSTRAINED MULTIVARIATE TOTAL LEAST SQUARES

2020 ◽  
Vol 26 (4) ◽  
Author(s):  
Wuyong Tao ◽  
Xianghong Hua ◽  
Shaoquan Feng
Keyword(s):  
Least Squares ◽  
Similarity Transformation ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Translation Vector ◽  
Large Rotation ◽  
Parameter Matrix ◽  
Transformation Parameters ◽  
Least Squares Algorithm ◽  
3D Similarity

Abstract: 3D similarity transformation is frequently encountered operation in the field of geodetic data processing, and there are many applications that involve large rotation angles. In previous studies, the errors of the coefficient matrix were usually neglected and a least squares algorithm was applied to calculate the transformation parameters. However, the coefficient matrix is composed of the point coordinates in source coordinate system, i.e., the coefficient matrix is also contaminated by errors. Therefore, a total least squares algorithm should be applied. In this paper, a new method is proposed to address the 3D similarity transformation problem with large rotation angles. Firstly, the scale factor and rotation matrix are put together as the parameter matrix to avoid the rank-defect problem. Then, the translation vector is removed and the multivariate model is constructed. Finally, the constraints are introduced according to the properties of the parameter matrix and the constrained multivariate total least squares algorithm is derived to obtain the transformation parameters. The experimental results show that the proposed method has a high computational efficiency.

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