E 
: 
© 
5 
2 
-3 
4 
284000 285000 286000 287000 288000 [sec] 
Figure S a: Trajectory differences Stuttgart - Area 
(Antenna 1, Gauss-Krüger coordinates) 
3 
2 
51 
£ 
$0 
s 
51 
= 
-2 
3 
-4 
284000 285000 286000 287000 288000 [sec] 
Figure 5 b: Trajectory differences Darmstadt - Area 
(Antenna 1, Gauss-Kriiger coordinates) 
3 
H-A wax dy 
2 °C 
E 
o 
o 
o 
= | 
2 = — em 
o 
= 
a 
2 
3 
-4 | L i 1 À 
284000 285000 286000 287000 288000 [sec] 
Figure 5 c: Trajectory differences Hannover - Area 
(Antenna 1, Gauss-Krüger coordinates) 
It can be concluded that successful ambiguity solutions are likely to 
provide consistent and accurate GPS trajectories. But there are 
exceptions, the conditions for which must be flagged out by the 
software, being dependent on the details of the satellite geometry. 
The internal evaluation of the restored GPS trajectories is here not 
pushed any further, at this time. It remains to be seen whether the 
results of different software packages and of the other test flights 
show the same effects. 
4 
3. ABSOLUTE CHECKS 
3.1 Camera air stations for comparison 
The results of Chapter 2 referred to GPS data directly, no other 
information having been brought in. Now, we make use of the aerial 
photographs taken during the flights over the test area. By 
photogrammetric aerial triangulation the coordinates of the camera 
air stations are obtained. They serve as check points for the GPS 
station coordinates, after offset-reduction to the GPS antennae. 
The photogrammetric block, consisting of 67 aerial photographs of 
scale 1 : 13000, had multiple overlaps (see Fig. 3). The analytical 
aerial triangulation, based on 40 GPS determined ground control 
points, included selfcalibration with 12 parameters. The theoretical 
accuracy of the resulting coordinates of the perspective photo- 
centres is about 12 cm horizontally and 8 cm vertically. It should be 
kept in mind, however, that systematic errors are to be expected in 
the same order of magnitude, at least. The block-adjustment referred 
directly to the national Gauss-Krüger coordinate system. 
The coordinate differences between the photogrammetrically 
determined camera air stations and their GPS equivalents were 
calculated for each of the 67 camera air stations. The further 
comparisons were all based on the arithmetic means of the 
differences per strip, composed of 7 resp. 5 air stations, the accuracy 
of the individual GPS positions being not the goal of the 
investigation. The photogrammetric error part in the mean 
differences therefore is expected to be in the order of 5 cm for the 
random components. The systematic photogrammetric errors, 
however, may still be in the order of 10 to 20 cm. This is to be kept 
in mind, as we deal here with differences of absolute errors. 
3.2. Comparison 
The mean differences per strip between photogrammetric and GPS 
positioning of the camera air stations (reduced to the respective GPS 
antenna positions) are collected in Table 1. The figures all concern 
GPS antenna 1 and refer to the national Gauss-Krüger coordinate 
system: y = R = E; x = H = N; z = h. The table also summarizes the 
overall arithmetic means for all strips (mean values taken over all 
ground stations) and the arithmetic means for all ground stations 
(mean values taken over all strips). 
It is somewhat difficult to directly assess and interpret the detailed 
contents of Table 1 as the coordinate differences refer to different 
flight directions. It is obvious, however, that there are clear 
systematic error effects which alternate with the flight direction, 
whilst error effects related to the GPS ground stations seem not to be 
predominant. Also, a constant difference in z of considerable 
magnitude (40 cm) is evident. In order to separate potential error 
effects, for further evaluation, the values of Table 1 have been re- 
classified with regard to a reference system fixed to the airplane: L 
(in flight direction), C (perpendicular to the flight direction, + to the 
right), V (vertical = z). 
Now, the results look considerably more consistent. Especially the 
mean differences in L and C (in flight direction and perpendicular to 
it), taken of all photo-strips per ground station, show practically no 
dependency on the distance to the ground stations at all. Those mean 
differences are listed in Table 2 and plotted in Fig. 6. It can be seen 
that the coordinate differences between photogrammetrically and 
GPS-determined air stations have in first instance constant shifts 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B6. Vienna 1996 
  
  
  
Differences [cm] 
F