introduced into the BINGO-F adjustment. This 
unknown stands in the BINGO-F adjustment until a 
new (resolved or unresolved) ambiguity occurs for 
this satellite. 
This yields to one additional unknown to be 
estimated in BINGO-F for every ambiguity that was 
left unresolved from GEONAP. In the worst case 
GEONAP cannot solve any ambiguity. In this case 
the maximum number of unknowns is one unknown 
per satellite and one additional unknown for each 
cycle slip occurred. In the best case, when 
GEONAP has solved all ambiguities, no additional 
unknown has to be carried along in BINGO. 
  
  
  
Fig. 2 Eccentricity e’ 
from the projection center to the antenna 
  
  
  
The last step after the computation of the aircraft's 
GPS antenna position is the interpolation of the 
camera exposure events between the GPS 
exposure events. The reduction from the GPS 
antenna position to the camera’s projection center is 
also done in this step. BINGO-F enables the 
estimation of the vector e’ from the projection 
center to the antenna (see Fig. 2) as additional 
unknown in the adjustment process. 
In most cases it suffices to derive the current 
orientation of the aircraft platform from the GPS 
trajectory. Sometimes it may be useful to take 
additional information into account for this purpose, 
e.g. from aircraft sensors. The interpolation should 
consider changes in the satellite configuration and 
unresolved cycle slips during the interpolation 
interval. 
398 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
6. Example 
Let us assume a configuration of 7 satellites, a 
smooth flight with no cycle slips, and a flight of 4 
strips. Let us assume additionally that all the 
ambiguities are left unresolved. With the usual 
approach there are 6 additional unknowns to be 
estimated per strip: 3 shift and 3 drift parameters. 
This yields to 24 additional unknowns for the flight. 
With the new approach, only 6 additional ambiguity 
parameters for the 7 satellites (one is linear 
dependent on the 6 others) have to be estimated for 
the whole flight. 
7T. Conclusions 
Advantages of the new approach: 
e only a minimum of required parameters have to 
be estimated. 
e noinformation in the GPS adjustment is lost. 
e the mathematical model is functionally correct, 
— no problems with possible non linear 
configurations. 
e the ambiguity resolution is possible in iterative 
steps, first in GEONAP and second in BINGO-F, 
and it is possible to use the additional 
information from the photo measurements for 
the sophisticated ambiguity search algorithms. 
It can already be said today that this method will 
gain acceptance due to economical reasons as 
costs can be saved for each photogrammetric block 
adjustment leading to a short pay-back period for 
the software development. 
8. Literature 
Kruck, E. Lósung grof$er Gleichungssysteme für 
photogrammetrische — Blockausgleichungen mit 
erweitertem funktionalen Modell. Wissenschaftliche 
Arbeiten der Fachrichtung Vermessungswesen der 
Universität Hannover Nr. 128. Dissertation 1983. 
Kruck, E. and Trippler, S.: Automatic Compu- 
tation of Initial Approximations for Bundle Block 
Adjustment with Program RELAX Optical 3-D 
Measurement Techniques Ill, Vienna, October 1995 
Wübbena, G.: Zur Modellierung von GPS-Beob- 
achtungen für die hochgenaue Positionsbestim- 
mung. Wissenschaftliche Arbeiten der Fachrichtung 
Vermessungswesen der Universitát Hannover Nr. 
168. Dissertation 1991. 
       
     
   
   
   
   
   
   
   
   
   
   
    
    
   
   
    
   
    
     
   
   
  
  
  
   
   
   
    
   
   
    
   
    
   
   
      
   
    
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