ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision‘, Graz, 2002 
  
  
  
c) This example shows a spacing that corresponds to the short 
base. This leads to a geometrically very stable solution. Each 
observation falls into a separate pair of orientation fixes. This 
corresponds to a true three ray point. 
  
  
d) This example shows a dense spacing of the orientation fixes, 
shorter than the short base, which can result from the time limit 
of the gyro quality. The math model handles this configuration 
as long as sufficient tie points are measured. 
Figures 9(a-d): Impact of spacing of orientation fixes. 
3.3 Tie Points 
The distribution of the tie points depends on the interval of the 
orientation fixes. The interval should not exceed the short base 
length. Furthermore the interval depends on the quality of the 
gyros used. For the ADS40 the specifications define gyros that 
deliver a very high precision over an interval of at least 8 
seconds. The typical number of tie points is very similar to 
traditional triangulation. 
  
  
Figure 10: Minimum number of tie points for a photogram- 
metric determination of orientation fixes. 
To find the minimum number of tie points one can count the 
number of observations and unknowns. Assuming the scenario 
where the orientation fix spacing equals the short base the 
following calculation holds true. 
e 4 orientation fixes times 6 parameters = 24 unknowns 
e  8tie points times 3 co-ordinates = 24 unknowns 
e 8 tie points in 3 scenes times 2 co-ordinates = 48 
observations 
This simple calculation does not account for the GPS/IMU 
observations and the necessary datum definition, but it shows 
fairly well that the demands are similar to frame photography. 
3.4 Control Points 
Ground control can be limited to a minimum to define the 
datum. Each strip is geometrically very stable owing to the 
GPS/IMU information used. Control points should be placed in 
the corners of the block similar to traditional airborne GPS- 
supported triangulation projects. The coordinate transformation 
functions of ORIMA transform the given control points from 
the mapping system to the local Cartesian system. 
3.5 Calibration by Bundle Adjustment 
3.5.1 Misalignment 
To utilize the orientation values which are derived from 
GPS/IMU directly without triangulation, the coordinate 
transformation between the GPS/IMU system and the 
photogrammetric system must be known. The axes of the gyro 
system which represent the axes of the IMU cannot be perfectly 
aligned with the axes of the photogrammetric system. The 
remaining misalignment is determined by the bundle 
adjustment. 
The misalignment is modelled by the following equation: 
  
Misalign R OriFix, ( 9) 
Every rotation matrix can be described by 4 algebraic 
parameters: 
wih: d'-a 4b .czl (10) 
S me S. 
Two orthogonal 4x4 matrices are used: 
d 4 b e 
—a d C -b 
P= (11) 
-b -c d a 
-C b -a d 
d —-a -b -c 
Qs OQ d c —b 12) 
5 + d a ( 
€ b —a dud 
P'P,=Q,'Q,=1 (13) 
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