Studia Geophysica et Geodaetica

, Volume 59, Issue 3, pp 366–379

# On total least squares for quadratic form estimation

• Xing Fang
• Jin Wang
• Bofeng Li
• Wenxian Zeng
• Yibin Yao
Article

## Abstract

The mathematical approximation of scanned data by continuous functions like quadratic forms is a common task for monitoring the deformations of artificial and natural objects in geodesy. We model the quadratic form by using a high power structured errors-in-variables homogeneous equation. In terms of Euler-Lagrange theorem, a total least squares algorithm is designed for iteratively adjusting the quadratic form model. This algorithm is proven as a universal formula for the quadratic form determination in 2D and 3D space, in contrast to the existing methods. Finally, we show the applicability of the algorithm in a deformation monitoring.

### Keywords

total least squares quadratic forms high power structured errors-invariables homogeneous equation deformation monitoring

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© Institute of Geophysics of the ASCR, v.v.i 2015

## Authors and Affiliations

• Xing Fang
• 1
• Jin Wang
• 2
• Bofeng Li
• 3
• Wenxian Zeng
• 1
• Yibin Yao
• 1
1. 1.School of Geodesy & GeomaticsWuhan UniversityWuhanChina
2. 2.Beijing Key Laboratory of Traffic EngineeringBeijing University of TechnologyBeijingChina
3. 3.College of Surveying and Geo-InformaticsTongji UniversityShanghaiChina