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.
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Fang, X., Wang, J., Li, B. et al. On total least squares for quadratic form estimation. Stud Geophys Geod 59, 366–379 (2015). https://doi.org/10.1007/s11200-014-0267-x
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DOI: https://doi.org/10.1007/s11200-014-0267-x