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B. Schaffrin, A. Wieser:
"Total least-squares adjustment of condition equations";
Studia geophysica et geodaetica, 55 (2011), 529 - 536.

The usual least-squares adjustment within an Errors-in-Variables (EIV) model is often
described as Total Least-Squares Solution (TLSS), just as the usual least-squares
adjustment within a Random Effects Model (REM) has become popular under the name of
Least-Squares Collocation (without trend). In comparison to the standard Gauss-Markov
Model (GMM), the EIV-Model is less informative whereas the REM is more informative.
It is known under which conditions exactly the GMM or the REM can be equivalently
replaced by a model of condition equations or, more generally, by a Gauss-Helmert
Model. Similar equivalency conditions are, however, still unknown for the EIV-Model
once it is transformed into such a model of condition equations. In a first step, it is shown
in this contribution how the respective residual vector and residual matrix look like if the
TLSS is applied to condition equations with a random coefficient matrix to describe the
transformation of the random error vector. The results are demonstrated using a numeric
example which shows that this approach may be valuable in its own right.

total least-squares, condition equations, Errors-In-Variables Model