Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation

By Frank Neitzel. 2010

178 citations recorded by the source corpus.

Subfields: Applied Mathematics, Plant Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/39ecdb6862001d8eaa447cba68e762f4fac7fcfe

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In Applied Mathematics

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Citations in the corpus

Iterative algorithm for weighted total least squares adjustment (2014, methodology): “in [15] Neitzel showed that the TLS solution within an errors-in-variables (EIV) model can also be identified as a special case of the method of least-squares within an iteratively linearised Gauss–Helmert model (GHM) where weight matrices can then be introduced without any limitations.”
Weighted total least squares formulated by standard least squares theory (2012, methodology): “TLS adjustment may not be regarded as a new adjustment method, but rather as an additional possibility to formulate a new algorithm in the frame of the general method of least-squares (Neitzel, 2010). We aim to have an impartial evaluation of both methods. The solution of the nonlinear GHM is somewh”
Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, methodology): “The nonlinear GHM has also been applied to the TLS field (Neitzel and Petrovic 2008; Neitzel 2010; Schaffrin and Snow 2010).”
A total least squares solution for geodetic datum transformations (2014, methodology): “This adjustment has been named TLS in the field of mathematics, although it is also known as the standard LS, as it is applied in the EIV model (see Neitzel 2010; Amiri-Simkooei and Jazaeri 2012).”
On non-combinatorial weighted total least squares with inequality constraints (2014, methodology): “From the point of view of model formulations, quite a few algorithms have been developed to adjust the univariate EIV model (see e.g., Markovsky et al. 2006; Schuermans et al. 2007; Schaffrin and Wieser 2008; Neitzel 2010; Fang 2011, 2013a; Shen et al. 2011; Amiri-Simkooei and Jazaeri 2012; Grafaren”
On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model (2015, methodology): “From the study by Teunissen (1985), it is apparent that TLS solution is essentially not a new adjustment method but only the traditional (nonlinear) LS solution to GHM, and this viewpoint was also emphasized recently by Neitzel (2010) and Schaffrin (2006).”
Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis (2012, methodology): “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 name a few areas.”
Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations (2015, result): “coincidewith the iterativeGHMsolution presented inNeitzel (2010). The results of the affine and rigid transformation are not much different from the results of the similarity transformation since the noises of the data set are small.”