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Michael Cramer 
  
applications, like the supervision of long, straight and narrow surface objects like power lines or traffic routes, in case 
of so-called pin-point photogrammetry, where only a few images are required to cover a very small surface area, or for 
orthoimage production, where in general no overlapping image recording is necessary. In such applications the 
geometric boundary conditions on block design are very uneconomical for the evaluation process. Additionally, for 
digital line sensor technology (e.g. airborne line scanners, laser scanners) direct georeferencing provides the only 
solution for the operational and economical data processing. Since the exterior orientations are required with very high 
frequency for each scan line, the indirect sensor orientation is almost impossible due to the very large number of 
required ground control points. 
If directly measured orientation elements are utilized for sensor orientation, the mathematical model has to be adopted 
for this application. Since the orientation sensors are physically displaced from the sensor to be oriented, additional 
correction terms are introduced (e.g. Skaloud et.al. (1996)). Assuming an integrated GPS/inertial system in combination 
with an imaging sensor the physical shifts between inertial system and GPS-antenna on the one hand and the 
perspective centre of the camera on the other hand are corrected by lever arms defined in the local aircraft body frame. 
For each system installation these specific lever arms have to be determined using conventional terrestrial survey 
methods. The attitudes provided by the integrated GPS/inertial system are related on the inertial body frame coordinate 
axes. Thus an additional misalignment matrix has to be taken into account to transfer the measured attitudes to the 
imaging sensor frame. Since the misalignment angles between IMU and camera frame are not directly observable via 
conventional techniques they have to be determined indirectly in an appropriate calibration procedure. This attitude 
transfer is a quite demanding task because reference orientations of superior accuracy are necessary for precise 
alignment. Although traditional AT provides independent attitude information with high theoretical accuracy, the 
estimated values are affected by remaining systematic and do not agree with the true physical orientation as it was 
demonstrated in the section before. Nevertheless, photogrammetry provides the only method for determining the 
misalignment angles in a kinematic airborne environment and the attitude differences between the exterior orientations 
estimated from AT and GPS/inertial at - preferable - several camera stations have to be used for the misorientation 
calibration. The quality of the misalignment calibration is strongly dependent on the budget of non modeled systematic 
errors in the bundle adjustment. The calibrated misalignment angles should remain constant as far as there are no 
relative movements between the two sensor components. After correcting the GPS/inertial exterior orientations by the 
translational offsets and the misalignment angles, the reduced orientations are interpolated on the exposure times of the 
imaging sensor to overcome the time offset between the different sensors. 
3 EMPIRICAL ACCURACY TEST 
3.1 Test flight design 
In order to evaluate the performance of the tested GPS/inertial system POS/DG310 from Applanix for the direct 
measurement of exterior orientation, a photo flight was carried out over a well surveyed test field (extension 7km x 
5km) close to Stuttgart in December 1998. During the test flight several GPS receivers with different baseline lengths 
from 0-380km were used as reference stations to check the influence of varying baselines on the performance of the 
GPS/inertial orientation parameters. Aerial imagery was captured at a flying height of 1000m and 2000m above ground, 
resulting in two different image scales of 1:6000 and 1:13000. The large scale imagery is located in the eastern part of 
the test site. Two strips, each consisting of eight images, were acquired. The 1:13000 block covered the whole test area 
by three long image strips and three cross strips. Both blocks were captured twice in order to enlarge the flying time. 
Overall, 72 (scale 1:13000) and 32 (scale 1:6000) images were captured in a time period of 1.5h. Altogether, 142 
control points with theoretical standard deviations better than five centimetres were available for the accuracy checks. 
Additionally, AT provides independent values for the exterior orientations directly measured. Although the orientations 
from AT are affected with remaining systematic errors as pointed out before, they are suitable for first estimations on 
the expected accuracy potential of the GPS/inertial system (Section 3.3). To estimate the order of accuracy of the 
complete sensor system object points are directly georeferenced from GPS/inertial orientations and compared to their 
pre-surveyed coordinates (Section 3.4). 
3.2 GPS/inertial data processing 
The integration of the GPS/inertial raw data was done using the Applanix POSPac software (Scherzinger (1997)). 
Within the data evaluation, the GPS phase solution trajectory (position, velocity) is determined using a standard GPS 
software package first. In a second step the results from GPS data processing are used as update information to perform 
an optimal integration with the IMU measurements using a Kalman filter approach. Afterwards a smoothing computes a 
blended solution from the data obtained in the previous step. The initial alignment of the IMU is obtained from the in- 
air alignment capability of the system. After processing, position, velocity and attitude data from GPS/inertial are 
continuously available for the complete trajectory with a data rate at 50Hz. Utilizing the recorded trigger times the 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 201