This adjustment problem can be handled in several ways. The most suitable 
approach is found by combining the two into: 
2 
LL ~AX, 2 AX (3.2) 
Again, the known coordinates of the control points are not to be changed, which is 
achieved by assuming xl to be non-stochastic. Then (1 - A X.) has weight 
k 
matrix P and the adjustment leads to the solution: 
2 T -l,T i 
X = (A,P A,) A„P (1 - AX) (3.3) 
. . LJ . T -1 
with apparently the variance covariance matrix (AP A,) for. the 
coordinates X. . 
1 
But now one has to realize that the known coordinates X, are only assumed to be 
1 n 
non-stochastic in order to keep X unchanged. In reality X. is stochastic 
according to variance covariance matrix G and a realistic variance covariance 
matrix for X is then obtained by application of the error propagation law to (3.3), 
which leads to 
X I 0 X 
= 1T (3.4) 
1 
C 
2 T “1 T T - 
: (AGP A2) AGP A, (AP A) ARLE 
X 
\ 
It will now be shown that the solution obtained in (3.4) is completely indentical to 
the result of the adjustment in steps of (2.10), provided that a free adjustment is 
possible, This is always the case in a two-dimensional block adjustment and in 
three dimensions when the height connection between the strips is possible 
without using height control points. 
Then, using (2.2) - (2.4): 
X 
1 
Ciz 1 1 (3.5) 
2|£ 1 :9275:21 22^ loq ilg , 
C 
X -Q Q Q ALP 
Using from (2.5): 
- 33h -