Studia Geophysica et Geodaetica

, Volume 59, Issue 3, pp 366–379 | Cite as

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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Copyright information

© 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

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