On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

By Burkhard Schaffrin, Y. Felus. 2008

110 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/08de9439d6eb7e1bfc6375fba2cc0b8b59485570

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. X. Fang
2. Guobin Chang
3. Yi Chen
4. Yunzhong Shen
5. Bofeng Li
6. Alireza Amiri-Simkooei
7. S. Jazaeri
8. Peiliang Xu

In Artificial Intelligence

1. Guobin Chang
2. X. Fang
3. Yi Chen
4. Yunzhong Shen
5. Bofeng Li

In Environmental Engineering

1. X. Fang
2. Guobin Chang
3. Yi Chen
4. Yunzhong Shen
5. Bofeng Li
6. Alireza Amiri-Simkooei
7. S. Jazaeri

Citations in the corpus

• On non-combinatorial weighted total least squares with inequality constraints (2014, background): “(3), e is the random extended error vector, where eA = vec(EA) (‘vec’ denotes the operator that stacks one column of a matrix underneath the previous one; see Schaffrin and Felus 2008).”
• On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model (2015, methodology): “It is noted that more general weighting strategies, e.g., those by Schaffrin and Felus (2008), Schaffrin and Wieser (2008) and Teunissen (1985, 1988), may disturb the equivalence, maybe even the existence of closed-form solution.”
• A total least squares solution for geodetic datum transformations (2014, background): “…all uncertainties is arranged as D (l) = D ([ vec (A) vec (Y) ]) = D (v) = D ([ vec (VA) vec (VY) ]) = D ([ vA vY ]) = σ 20 [ QAA QAY QYA QYY ] = σ 20 Qll = σ 20 P−1, (6) where vec denotes the operator that stacks one column of a matrix underneath the previous one (Schaffrin and Wieser 2008).”
• An iterative solution of weighted total least-squares adjustment (2011, methodology): “This coincides with the model used by Schaffrin and Wieser (2008) for the same data set.”
• Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, methodology): “One frequently used TLS approach is based on the singular value decomposition (SVD) procedure (Felus 2004; Akyilmaz 2007; Schaffrin and Felus 2008), and another commonly explored option is to utilize auxiliary Lagrange multipliers to rearrange the specially weighted TLS problem as a constrained…”
• A structured and constrained Total Least-Squares solution with cross-covariances (2013, methodology): “A large number of varying methodologies to compute the transformation parameters have been surveyed on the basis of the TLS principle for affine transformations (e.g., Schaffrin and Felus, 2008) and as the STLS for Stud.”