4, AN ARTIFICIAL VARIANCE COVARIANCE MATRIX FOR CONSTRAINED 
COORDINATES 
As indicated in section 2, formula (2.11) of the variance covariance matrix of 
constrained coordinates (in relation to (2.5) as the variance covariance matrix of 
free coordinates), is very suitable to construct an artificial matrix to describe the 
precision of constrained coordinates. 
Here two aspects, which are confusingly mixed up in case of a combined ad- 
justment, are now very nicely seperated: 
1. Propagation of covariances because of the combination of independant 
models into the free block, the first phase of the adjustment. 
2. Forcing the free block to the control points, in the second phase. 
The first aspect is thoroughly studied in terrestrial networks by, for instance, 
Alberda, Baarda, Borre, Grafahrend and Meisll. In a kind of "absolute" system the 
following artificial covariance matrix is constructed (/3/, /2/, /11/): 
  
  
Xi Xr : Xs ; Yi Ws Yr Ys 
2 2 42 2 2 2 2 
xj. 1d d^-d ij ddr d^- d^. 
2 2. 2 2.2. 2.2 . 
X; d^-d ji d d^-d jr d^-d js : 0 
2 2 2 12 2 2 2 
xe ] d^ d^ d^-d rj d d^-d^ i 
2 2 2 2 
X. d2-d d^ d sj d^-d^ d 
Yi 
yj same submatrix 
Yr 0 as left upper part 
Ys 
  
(4.1) 
  
  
By means of an S-transformation to the S-system of the free network the nuisance 
parameter d? disappears from the formulas and the matrix derived in this way has 
been shown to be almost equivalent to the real variance Sovariance matrix G ‚of 
the free coordinates. A simple covariance function like d. . = Cl T has 
J 
proven to be sufficient in practical applications. This is illustrated in figure 4.1. 
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