A note on Constrained Total Least-Squares estimation

By Burkhard Schaffrin. 2006

104 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/6150a3e5a84201bc2b8536c0703851dbe5d21a41

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In Applied Mathematics

In Environmental Engineering

In Management Science and Operations Research

Citations in the corpus

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms (2008, background): “To circumvent convergence to a local minimum, which is different from the global minimum, one should begin with the iteration scheme of Algorithm 2 until the convergence slows down, and then continue with Newton’s type iteration of Algorithm 3. A similar strategy has been proposed by Bjorck et al. (”
A structured and constrained Total Least-Squares solution with cross-covariances (2013, methodology): “e is the extended error vector, which is expressed by the vectorized augmented matrix   vec A y     E e , where ‘vec‘ denotes the operator that stacks one column of a matrix underneath the previous one, see Schaffrin and Felus (2008).   T 1 , n n n n u          B ξ I I is a matrix d”
An iterative solution of weighted total least-squares adjustment (2011, background): “…have been developed to solve the homoscedastic (Schaffrin et al. 2006; Schaffrin and Felus 2008), weighted (Van Huffel and Vandewalle 1989; Markovsky et al. 2006; Schaffrin and Wieser 2008), constrained (Schaffrin and Felus 2005; Schaffrin 2006) and regularized (Golub et al. 1999) TLS problems.”
Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis (2012, methodology): “…systems and control and signal processing (see e.g. van Huffel and Vandewalle 1991; Markovsky and van Huffel 2007) and geodesy (see e.g. Felus 2004; Schaffrin 2006; Akyilmaz 2007; Schaffrin and Wieser 2008; Felus and Burtch 2009; Schaffrin and Felus 2009; Neitzel 2010; Shen et al. 2011), only to…”
An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation (2011, methodology): “Later, in a constrained TLS estimation (CTLSE) (Schaffrin 2006), the RHS vector in the constraint equations is assumed to be affected by random errors, whereas the constraining matrix is error-free.”
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.”