Improved second order design and the datum choice

It is shown that also in a rank deficient Gauss-Markov model higher weights of the observations automatically improve the precision of the estimated parameters as long as they are computed in thesame datum. However, the amount of improvement in terms of the trace of the dispersion matrix isminimum for the so-called “free datum” which corresponds to the pseudo-inverse normal equations matrix. This behaviour together with its consequences is discussed by an example with special emphasis on geodetic networks for deformation analysis.