International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
calibration including the inner orientation of the imaging
sensor. In addition it is important how often the system has to
be calibrated. On one side we do have the economic aspects, on
the other side we do have the required accuracy and reliability,
so a compromise between both is required which may be
dependent upon the product specifications.
For the correct estimation of the pros and cons, the possibilities
and requirements of the preparations have to be analysed
because of their strong effect to the economie situation and the
required additional handling time.
2. BORESIGHT MISALIGNMENT
The direct sensor orientation is based on a combination of an
inertial measurement unit and relative kinematic GPS-
positioning. Instead of the sometimes uses expression inertial
navigation system (INS), the expression IMU is used because in
this case the identical hardware for both applications will not be
used for navigation, but only for the registration of the attitude
and position data. The IMU attitude information and the
position, which is based on a double integration of the
acceleration, do have only good short time accuracy. By this
reason the IMU has to be combined with the GPS-positioning
which has an absolute accuracy. On the other hand GPS cycle
slips can be determined by the IMU, so the combination of both
lead to an optimal solution.
The orientation of the imaging sensor is requested, so the IMU
has to be fixed to the sensor. The mounting can only be done
approximately parallel to the system of sensor axis requiring a
calibration of the relation IMU — sensor.
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The offset of the GPS-antenna can be measured and respected.
More difficult is the relation of the IMU to the camera. This
boresight misalignment has to be determined by comparison of
the IMU-attitude and position data with the exterior orientation
of a controlled block adjustment. As reference at least a block
containing 2 flight strips, flown in opposite direction, should be
used to enable the separation of shift values in the ground
coordinate system from shift values depending upon the flight
direction. The GPS shifts cannot be separated from the position
of the principal point if we do have only one flight direction.
If the reference block will be flown with the same altitude
above ground like the project area, the determination of the
boresight misalignment is sufficient. Discrepancies of the focal
length will be compensated by the same flying height, but if the
height is different, a system calibration is required.
830
3. SYSTEM CALIBRATION
The interior orientation is determined in laboratories
under constant and homogenous temperature conditions.
Under actual flight conditions, the temperature is
different and we do have a not neglect able vertical
temperature gradient in the optics causing a lens
deformation. Meier (1978) has made a theoretical
investigation of the resulting change of the focal length (table
1).
In general the values have been confirmed by empirical tests,
but the values are just rough estimations which have to be
checked under operational conditions. The same problem exists
with the principal point location.
lens in free atmosphere
flying height 6km 14km
wide angle camera -47 um -80 um
f=152mm
normal angle camera
f=305mm
-110 um -172 um
Table 1. Change of the focal length depending upon the flying
altitude (Meier 1978)
An error of 47um for a focal length of 153mm is changing a
flying height of 1530m above ground (image scale 1 : 10 000)
by 0.47m. This is important for the direct georeferencing but
not so much for a usual image orientation by block adjustment
with control points as reference. In the case of a flat area such a
deviation of the focal length has no influence to the ground
points and for an undulating terrain with 100m difference in
height against the control points, the influence is limited to 3cm
in Z. Or reverse, the influence to Z is only exceeding the usual
vertical accuracy of 0.01% of the flying height above ground if
the height difference against the control points is larger than
30% of the flying height. Such relative height differences only
will be reached under extreme cases of steep mountains.
Based on projection centres determined by relative kinematic
GPS-positioning, a correction for the focal length can be
computed as well as the location of the principal point. But we
have to expect also constant errors of the GPS-values and
caused by the extreme correlation, it is not possible to separate
the influence of the inner orientation from constant errors of the
GPS-values if we do have only one flying altitude. For a
complete calibration under flight conditions it is necessary to
have at least 2 quite different flying altitudes with GPS-values
for both. The constant GPS-errors are the same for both flying
altitudes, but the inner orientation has an effect linear
depending upon it. So indirectly the inner orientation will be
determined based on the difference in the flying altitudes of
both flight levels.
Corresponding to the investigation of Meier (1978), the focal
length will not be the same for both flying heights. So by theory
a third flying altitude would be required for the determination
of a linear change of the focal length as a function of the flying
height. But this is not necessary for operational projects. The
common adjustment of GPS-shift* values and the inner
orientation corresponds to a three-dimensional interpolation
which is sufficient for different flying altitudes.
Empirical investigations have been made with the data of the
OEEPE-test “Integrated Sensor Orientation” (Heipke et al
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