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

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