Total Least Squares Solution of Coordinate Transformation

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Iterative algorithm for weighted total least squares adjustment (2014, methodology): “Specific TLS solutions for coordinate transformation have been presented earlier in geodetic literature for example by Felus and Schaffrin ([5]), Akyilmaz ([1]), Schaffrin ([18]) and Schaffrin and Felus ([19]) and Schaffrin et al.”
Deformation analysis with Total Least Squares (2006, methodology): “(12)–(16) are as follows (Akyilmaz, 2005): diag(D) = [∑ X1X1 ∑ Y1Y1 ∑ Z1Z1 · · · ∑ XnXn ∑ YnYn ∑ ZnZn ] (24) C = tr( ∑ xyz) tr(D) 0 0 0 0 tr( ∑ yz) tr(D) 0 0 0 tr( ∑ xz) tr(D) 0 0 tr( ∑ xy ) tr(D) 0 1 (25) where tr(·) is the trace operator of the argument matrix, the elements of the matrix D are…”
Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation (2010, methodology): “In order to solve this adjustment problem, Akyilmaz (2007) elaborates on a so-called “generalized TLS procedure” (GTLS) which is known to not necessarily furnish the weighted TLS solution according to Schaffrin and Wieser (2008).”