This first advantage is nowadays generally acknowledged and in most adjustment 
software, both for surveying and for photogrammetry, data-snooping procedures in 
the free network/the free block adjustment are included, 
A second advantage of the adjustment in two phases is found in the quality 
analysis and quality description, For instance, as shown in /11/, the free network 
contains all information to predict the precision and reliability of the constrained 
network. 
In the context of this paper we will restrict ourself to precision. 
For the examination and description of precision an artificial variance covariance 
matrix can be of great help. On the one hand, such an artificial matrix can serve 
as a criterion matrix with the possibility to verify whether te demands described 
by such a criterion matrix are met via the general eigen value problem. On the 
other hand an artificial variance covariance matrix can be used to indicate and 
replace the precision of the coordinates given by the real variance covariance 
matrix, i.e. as a substitute matrix. 
Artificial matrices to replace the variance convariance matrix for free networks 
are now widely applied. In section 4 of this paper the more complicated case of an 
artificial matrix for constrained networks is elaborated. The approach is based on 
an adjustment in two steps, which is there fore summarized in section 2. 
However, usually constraint of the free network to known coordinates is not 
carried out seperately via a second phase (as in section 2), but one performs an ad- 
justment in one combined step. Then interpretation and understanding of the 
formulae is rather difficult, although the results are of course the same. There 
fore it is shown in section 3 that the coordinates and the variance covariance 
matrix resulting from the adjustment in one combined step can be transformed 
into the results of the adjustment in two steps of section 2. 
2. ADJUSTMENT IN TWO STEPS 
In the first phase, the adjustment of the free network or the free block, the usual 
adjustment procedure is followed. The known coordinates of the control points are 
not yet involved. Only the observations | (terrestrial directions, distances or 
photogrammetric model coordinates) are expressed in the unknowns Xe of the free 
adjustment, which are separated in: 
- 330 =