ISPRS Commission III, Vol.34, Part 3A ,Photogrammetric Computer Vision“, Graz, 2002 
  
  
  
  
  
  
  
system installation is used for direct georeferencing. The 
question is, whether the estimated boresight misalignment 
remains constant for a longer time period? This open task 
should be answered from flight data material presented here. 
Table 4 shows the distinct estimated boresight alignment angles 
from the 8 normal-angle system installations, where in Figure 7 
the variations from the mean estimated boresight angle are 
depicted for normal-angle flight days. 
  
  
  
  
  
  
  
  
Day | #Ftighe | STP AXo STD AY, | STD AZ, 
[m] [m] [m] 
Jan 29 1:2 0.183 0.233 0.148 
Jan 31 546 0.151 0.357 0.077 
Feb05 | 849 0.274 0.252 0.103 
Feb 18 | 10+11 | 0.197 0.156 0.118 
Feb 19 | 12+13 | 0.090 0.130 0.050 
Feb 21. | 14+15.0. 0.226 0.199 0.135 
Feb24 | 164317] 0.223 0.123 0.184 
Mar 12 | 18+19 | 0.136 0.183 0.122 
Mean | 0.185 0.204 0.117 
  
Table 2. Variation of GPS/inertial positions. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Day #Flight STD Ao | STD A@ STD Ar 
[gon] [gon] [gon] 
Jan 29 1+2 0.0079 0.0053 0.0086 
Jan 31 5+6 0.0066 0.0079 0.0053 
Feb 05 849 0.0021 0.0066 0.0109 
Feb 18 10-11 0.0058 0.0034 0.0226 
Fcb19 | 12+]13 0.0052 0.0051 0.0439 
Feb 21 14+15 0.0029 0.0061 0.0052 
Feb 24 | 16+17 0.0029 0.0059 0.0069 
Mar 12 | 18+19 0.0051 0.0051 0.0076 
Mean 0.0048 0.0057 0.0139 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
# | Day | #Flight | A0 [gon] | Ag [gon] |_Ax [gon] 
1 Jan 29. |. Lt2 0.4851 0.0702 -0.1349 
21. Jan 3L-| +310 0.4805 0.0656 -0.1278 
3 |Feb05| 8+9 0.4882 0.0607 -0.1124 
4 | Feb 18 | 10+11 | 0.4880 0.0617 -0.1431 
5 | Feb 19 | 12+13 | 0.4782 0.0689 -0.1207 
6 | Feb 21 | 14+15 | 0.4901 0.0563 -0.1289 
7 | Feb 24 | 16+17 | 0.4870 0.0629 -0.1328 
8 | Mar 12 | 18+19 | 0.4900 0.0557 -0.1348 
Mean | 0.4859 0.0628 -0.1294 
STD 0.0041 0.0049 0.0088 
Table 4. Estimated boresight alignment angles. 
0.020 T 
0.015 
  
  
  
Table 3. Variation of GPS/inertial attitudes. 
4.2 Stability of boresight alignment 
Within the following subsection the results from long term 
stability analysis of estimated system calibration parameters are 
presented. As already mentioned the parameters are derived 
from an GPS/inertial-AT where constant position and boresight 
angle offsets are estimated together with self-calibration terms 
based on Ebner polynomial coefficients. 
For all investigated flights the influence of self-calibration 
shows similar behaviour with a slight cushion effect in flight 
direction, potentially caused by film transportation or film 
shrinking. For some mission days an additional shear 
component is present indicating the variation of influences of 
additional self-calibration. As it is known from the beginning of 
self-calibrating bundle adjustment the a priori estimation of 
image distortion parameters is difficult. Hence, uncorrected 
effects have to be taken into account in direct georeferencing. 
According to the estimated positioning offsets, vertical shifts 
are present for almost all flight days, where the amount of 
vertical offset correction (if significantly present) is not 
constant but shows day-to-day variations between 12-40cm for 
the different calibration flight days. For horizontal components 
smaller offset corrections between 10-20cm are estimated for 
approximately 50% of the flights. Although such offsets should 
not be expected for high quality GPS positioning, they are well- 
known from GPS-assisted AT, where in especially in height 
component conflicts are present mainly due to inconsistencies 
between physical reality and mathematical model. In general, it 
seems to be reasonable to correct for mean vertical offset. 
Anyway, day-to-day variations have to be taken into account 
and will deteriorate the quality of direct georeferencing in case 
position offset calibration is not refined for each mission flight. 
Nonetheless, during system calibration the main focus is laid on 
the quality and stability of boresight alignment estimation, since 
this effect cannot be pre-surveyed manually and therefore has to 
be estimated from an additional calibration process before the 
  
0.010 
0.005 — 
  
  
  
0.000 4 
-0.005 4 
Boresight variation [gon] 
-0.010 
  
  
  
  
-0.015 4 
mOmega Phi 0 Kappa 
  
  
  
-0.020 
# Calibration flight day 
Figure 7. Variation of estimated boresight angles. 
At a glance the results from analysis of the stability of boresight 
alignment seems to be worse especially in x. The variation of 
the mean k—boresight angle about 0.009gon (30") cannot be 
accepted for high performance requirements. The question is, 
whether these estimated variations truly represent the physical 
misorientation changes between the inertial measurement unit 
and the camera coordinate frame over the 2 months time 
period? Fortunately the answer is no, since the results given in 
Table 4 and Figure 7 are strongly influenced from remaining 
errors in the GPS/inertial attitude determination. This can be 
seen clearly from the 3*1.5* calibration flight day, where the 
large variations in x-angle coincide with the high RMS values 
from Table 3. As far as such errors are present, the results from 
boresight angle stability are less meaningful since the optimal 
performance from GPS/inertial attitude is not fully exploited 
during system calibration. Excluding these three data sets from 
boresight calibration, the variations (STD) of mean estimated 
boresight angles are well within the noise level of GPS/inertial 
attitude determination: 04470.0035gon (117), o4,70.0055gon 
(18”), on=0.0029gon (9"). This variation values indicate a