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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