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B. Schaffrin, A. Wieser:
"Empirical Affine Reference Frame Transformations by Weighted Multivariate TLS Adjustment";
in: "Geodetic Reference Frames", H. Drewes (ed.); issued by: IAG; Springer Verlag, 2009, ISBN: 978-3-642-00859-7, 213 - 218.

In order to determine the transformation parameters between two reference frames empiri-cally, a sufficient number of point coordinates (or possibly higher dimensional features such as, e.g., straight lines or conics) need to be observed in both systems. A proper adjustment of the observed data must take the different variances and covariances into account.
The resulting adjustment model is of type Errors-in-Variables rather than of type Gauss-Markov because both sets of coordinates are associated with errors. In the homoscedastic case, the least-squares principle thus leads to the Total Least-Squares Solution (TLSS) rather than the standard Least-Squares Solution (LESS).
Here, we generalize the TLSS by allowing the individual variances to be different and the cova-riances to be non-zero, while still maintaining a certain reasonable variance-covariance structure. This leads to the Weighted TLSS. We show expe-rimentally that the Weighted TLSS yields slightly better estimates (in terms of precision) than LESS or TLSS, but significantly more accurate dispersion measures.

Total Least-Squares adjustment, weights, reference frames, empirical coordinate transformations