The characteristics of the network solution are as follows: 
(1) ifthere are multiple baselines of similar length, the 
different reference stations have the effect of 
repeated measurements. 
(2) ifthe baselines are different in length, and thus the 
quality of the GPS/IMU observations differs, the 
network solution yields an average result, which is 
obviously not as accurate as the one for the shortest 
baseline, but better than the one for the longest 
baseline. 
—. 
2 
— 
if there are short term errors in any of the baselines, 
the network solution is able to reduce, and perhaps 
to eliminate, the effect of these errors. 
In any case, multiple baselines lead to a larger redundancy of 
the adjustment system, and thus to an increased possibility 
for detecting gross errors, and to a more reliable solution for 
the parameters of exterior orientation. Of course, any 
problems connected to the GPS receiver in the aircraft cannot 
be detected, neither can the standard deviation of computed 
object space coordinates be improved, if the limiting factor is 
the measurement accuracy of the corresponding ima 
coordinates, and not the exterior orientation. 
ge 
& 
e 
3 Test data 
In order to analyse our model we used the data of the OEEPE 
test “Integrated sensor orientation” (see Heipke et al. 2002a; 
b and Nilsen 2002). For this paper we used only a subset of 
the test data. 
The test was flown over the test field Fredrikstad in Southern 
Norway. The test field has a size of approximately 4,5*6 km“ 
and contains about 50 signalised GCP with object space 
coordinates known to sub-centimetre accuracy. 
The aircraft was flown at an altitude of 1.600 meters above 
ground resulting in an image scale of approximately 
1:10.000. Two flights were selected: the calibration flight 
included four strips, two strips in west-east and east-west 
direction and two further strips in north-south and south- 
north direction; and a project flight with five strips in north- 
south and south-north direction. In order to achieve a good 
initial alignment for the IMU axes with the gravity field, the 
aircraft made an S-like turn before the first flight strip. Image 
coordinates of a sufficient number of tie points and of all 
GCP were measured manually on an analytical plotter. 
The selected GPS/IMU aircraft equipment was a POS/AV 
510-DG from Applanix, consisting of a high quality off-the- 
shelf navigation grade IMU as typically used in precise 
airborne position and attitude determination. The POS/DG 
equipment was tightly coupled to a wide angle Leica RC30, 
the latter mounted on the gyro-stabilised platform PAV30. 
The PAV30 data and thus rotations of the camera and the 
IMU relative to the plane body were recorded at 200 Hz and 
introduced into further processing. The claimed accuracy is 
better than 0.1 m for the IMU position, and better than 0.005 
degree in roll and pitch, and better than 0.008 degree in yaw 
(Applanix 1999). 
During data acquisition several GPS reference stations were 
used and the GPS equipment in the aircraft and on the 
reference stations consisted of dual frequency receivers 
performing differential carrier phase measurements at 2 Hz. 
The following reference stations were used for the results 
reported in this paper: 
- Raade (baseline 8 — 30 km), 
Moss (baseline 15 — 38 km), 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
- Torp (20-50 km baseline), 
- Soer (25-60 km baseline), 
- Stavanger (baseline approx. 307 km). 
The different values for the baselines arc caused by the flight 
pattern, for Stavanger this effect amounts to only 10 % of the 
length and is negligible. Figure 1 shows the accuracy of the 
GPS-position for the reference station Raade for the various 
strips of the project flight. In the upper part of the figure, the 
PDOP (position dilution of precision), a common descriptor 
for GPS position accuracy (Seeber 2003) can be seen as the 
straight line, the baseline length is the more undulated line. It 
is clearly visible that the PDOP increases sharply during the 
first strip indicating some problem in the GPS signal, and 
only decreases after the fourth strip. In the lower part, the 
resulting GPS accuracies in X, Y, and Z derived from 
processing different satellites (but no IMU data) are shown. 
The correlation between the large PDOP value and the large 
c 
standard deviations for the GPS position can clearly be seen. 
Ref Sation Raad 
  
  
   
Tirae (sec ) 
  
  
  
        
Figure 1: Accuracy of GPS position, reference station 
Raade 
The small peaks in the X,Y and Z accuracies in the lower part 
of figure 1 can be smoothed when introducing IMU data 
during Kalman filtering. It is not possible, however, to 
compensate the weaker accuracy over the longer time period 
in the same way. Only a network solution or additional GCP 
can overcome this problem. 
4 Sensor calibration 
Based on the model explained in section 2 and the calibration 
flight data described in section 3 we performed a calibration 
of the equipment used in the test. The displacement vector 
between the GPS antenna and the IMU centre of mass was 
determined before the flight mission using conventional 
surveying techniques and was used as a constant lever arm 
correction. 
Since we only had one flying height, we selected the six 
standard parameters (boresight misalignment and GPS offset 
parameters). In addition, we solved for a time 
synchronisation offset. In the adjustment, we introduced 
twelve GCP, together with sufficient, well distributed image 
coordinates of tie points together with the pre-processed 
position and attitude data. Initial values for all unknowns 
could also be made available. 
   
   
        
  
   
   
   
   
    
    
    
  
    
    
   
    
   
  
  
   
   
  
  
  
  
  
  
  
   
    
    
   
    
   
  
  
   
     
    
   
   
    
   
    
    
    
     
   
  
  
  
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