Full text: Proceedings of the Symposium "From Analytical to Digital" (Part 3)

  
resulting system is represented by equation (4), in which 
only one unknown per condition is added to the border 
(Brown /3/, Ebner /6/). 
If the existing system (2) is singular, because of defects 
in the definition of the datum, the system (4) is formally 
similar to a so-called free adjustment. This given datum 
deficiency has to be considered in an appropriate algo- 
rithm or concept for the solution of the normal equation 
system. 
If the existing system (2) shows geometric defects or 
geometric weakness, however, the application of method c) 
is not recommended, because in that case the solution 
algorithm would have to include also certain pivot strate- 
gies for numerical reasons. 
Both methods a) and c) leave the main part of the 
structure of the original system unchanged and do not 
introduce restrictions concerning the kind of the addi- 
tional observations, also mentioned by Brown /3/. À:possi- 
ble criterion, which of the two methods is appropriate, is 
given by the resulting borderwidth. Whereas for method a) 
the resulting borderwidth is equal to the number of 
unknowns involved, for method c) only one unknown per 
condition equation is added to the border. Therefore in 
those cases where the method can be applied without numer- 
ical difficulties, as mentioned above, it results in a 
more favourable borderwidth, when the unknowns are deter- 
mined by a relatively small number of non-photogrammetric 
observations. 
Another topic that has been considered in the field of 
combined adjustment is a new arrangement of the unknowns 
so that additional information could be included more 
easily. 
Therefore some concepts give up the strict separation of 
the unknown parameters into groups and the elimination of 
the point unknowns, but try to get favourable structures 
by general ordering algorithms for all unknowns or by 
certain ordering strategies. For example Kruck /8/ pro- 
poses especially for close range applications that the 
orientation parameters are numbered across the larger side 
of the block and the point unknowns are arranged before 
the parameters of the image, in which they are measured 
first. 
Whether these concepts with complete normal equation sys- 
tems including all unknowns are better suited for photo- 
grammetric aerotriangulation with classical or general 
non-photogrammetric information depends on a number of 
factors. Not only the structure of the non-photogrammetric 
data, but also the actual connection structure of the 
photogrammetric observations, depending on project parame- 
ters, and the mathematical modelling of the photogram- 
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