International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
range of 110km corresponding to a local scale in the UTM
system of 1 : 0.99975, causing a shift of the projection centres
fog the image scale 1:5000 of 20cm and for the image scale
1:10000 of 40cm. If the boresight misalignment is determined
with images of the same scale in the project area, the shift in the
projection centre is compensated by the Z-shift. This is different
if the determination of the misalignment will be done in a
location with a different distance from the reference meridian or
with a different image scale (see figure 3).
A /\e /N3
distance
v » from center
meridian
Figure 4. compensation of the scale difference between Z
and X, Y by modified focal length
The affine model deformation can be compensated with a
modified focal length (fc = {/local scale). This will compensate
the scale difference between the horizontal and vertical scale in
a sufficient manner for close to vertical view directions (see
figure 4). The transfer of the so determined orientations to
analytical or digital photogrammetric work stations has to
respect the used geometric configuration.
Distance | local scale focal length (mm)
from in UTM
centre UTM with | UTM with | Tangential
meridian earth local scale
curvature | correction
4'| 0.999 60 153.421 153.360 153.359
56'| 0.999 64 153.416 153.360 153.359
1°56’| 0.999 75 153.398 153.360 153.359
2?56'| 0.999 96 153.368 153.360 153.359
Table 2. Focal length determined in shifted reference blocks in
3 different locations (1° 56’ = original)
With the data set of the OEEPE test "Integrated Sensor
Orientation" (Heipke et al., 2000) a system calibration using the
UTM and the tangential coordinate system has been made. For
showing the influence of the reference block location, the
ground coordinate system has been shifted by -2?, -1? and +1°
longitude. In the UTM coordinate system a computation with
just the earth curvature correction and a computation with
additional local correction of the focal length has been made.
Table 2 shows the result — if the local net scale will not be
respected, the achieved focal length is linear depending upon
the local scale of the UTM coordinate system. If this local scale
will be respected, the focal length is independent upon the
location of the reference block and it is with the exception of a
negligible rounding error identical to the result achieved in the
tangential coordinate system.
5. INFLUENCE OF GEOID AND DEVIATION OF
NORMAL
The national height values are related to the geoid. GPS and the
combination of GPS and IMU are originally geocentric values,
which have to be transformed to geographic values. At first the
height values are related to the earth ellipse (e.g. WGS 84).
These height values have to be improved by the geoid
832
undulation. As visible in figure 5, the European quasigeoid
EGG97 in the OEEPE-test area is mainly a tilted plane (Denker
1998). The geoid undulation in the shown area goes from
37.20m up to 38.66m. The mean square differences against a
tilted plane are just +/-2.2cm.
Corresponding to the surface of the geoid, the normal has a
deviation in east-west-direction from 8” up to 12” and in the
north-south-direction from —0.7" up to 4.6". The deviation of
the normal is directly influencing the roll and pitch values. This
is causing a shift of the location of the determined ground
points in the OEEPE test area for the used image scale 1 : 5000
with a flying height of 750m above ground of 4cm up to 4.4cm
in east-west direction and 0.7cm up to 1.0cm in the north-south-
direction. Such a size should be respected, but it can be
compensated by the shift values of the misalignment if the
calibration site is not far away. After such a shift the final effect
to the determined ground points is just in the range of few mm.
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Figure 5. contour lines of the Geoid undulation in the OEEPE-
test area
The geoid should be respected by the GPS-processing in the
reference and the project area. Only the difference between the
geoid in the GPS reference stations to the flight areas is
influencing the result. The distance from the flight area to the
local GPS reference station should not exceed 30km if the
highest possible accuracy is required. In the above shown
example (figure 5), the geoid undulation is changing over 30km
up to Im — this cannot be neglected. Datum problems are
compensated by the GPS reference station.
6. STABILITY OF CALIBRATION
The stability of the geometric relation of the IMU to the
imaging system and the stability of the inner orientation are
important for the decision if a system calibration is required for
any project or not or even if a calibration is required before and
after any flight. Some investigations have been published by
Hansa Luftbild (Dreesen 2001, Schroth 2003), the Institut
Cartografic de Catalunya (Baron et al 2003), the University
Stuttgart (Cramer et al 2002), the Finnish Geodetic Institute
In
