y- 
and 
ra- 
on 
3e 
ne 
on 
1] 
id 
le 
The suggested stochastic model shows several advantages. First 
of all, the treatment of the additional parameters as observa- 
tions is completely general, Free unknowns and constants are 
special cases of observations and can easily be implemented by 
the special weights 0 and = (102°). Furtheron the appropriate 
weights of the additional parameters guarantee optimal accuracy. 
The most important advantage however, is the avoidance of un- 
reliable results. 
Such results have to be feared if the additional parameters are 
treated as free unknowns and the available control points and 
tie points don't allow for an accurate determination of all the 
correction terms, put up. The normal equation matrix then be- 
comes ill conditioned and in extreme cases even singular. In the 
latter case the minimum equation of the adjustment is fulfilled 
by every arbitrary value of the corresponding parameters. 
This danger is avoided when the additional parameters are treated 
as observations. The residuals v, then directly influence the 
minimum condition, which leads to a definite solution for 
all correction terms used. The geometrically poorly determined 
parameters in this case show up in form of insignificant amounts 
of the corresponding correction terms. 
Last not least it shall be mentioned that self calibrating block 
adjustment with additional parameters can also be treated as a 
collocation problem. The appendix contains the derivation of the 
corresponding equation system and shows it's equivalence with 
the observation equations (1a), (1b). 
3.3 Operational Points of View 
Besides an efficient mathematical model for simultaneous self 
calibration the secure and comfortable execution of the extended 
block adjustment is the most important point, Therefore, the 
additional burden of the program user should be limited to an 
additional! input, determining, which group of additional para- 
meters has to be assigned to the occasional image or model. 
With the establishment of the parameter groups it is assumed, 
that the systematic deformations only change if a corresponding 
change of project parameters occurs (different cameras or camera 
installations, different films or film processing, different 
measuring instruments and so on). A dependency of the systematic 
deformations on the flight direction is avoided if the image or 
model coordinate system itself relates to flight direction. 
Consequently, a new group of additional parameters is only re- 
quired if at least one of the project parameters has changed, 
That means that the number of parameter groups usually will be 
small. 
When the self calibrating block adjustment is executed, the com- 
puted correction terms haye to be checked critically by statisti- 
cal means, For that the covariance matrix of the additional un- 
knowns y is needed, which can be obtained from a partial in- 
version of the normal equation matrix, The numerical effort of 
this operation is relatively small.