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 -