On total least squares for quadratic form estimation

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.