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