Geoscience Reference
In-Depth Information
Table 1 Calibration
parameters and their standard
deviation
Values (mm/
00
)
Calibration parameters
a
0
r
a
0
9.3
±
0.2
b
0
r
b
0
-1.1
±
2.1
b
1
r
b
1
2.9 ± 8.0
c
0
r
c
0
9.4 ± 2.8
Table 2 RMS of residuals
from the adjustments without
and with calibration
parameters
Observable
RMS (without)
RMS (with)
Range (mm)
5.6
4.0
Horizontal direction (
00
)
41.0
37.1
Vertical angle (
00
)
24.0
22.4
Table 3 Significant test for calibration parameters
Number of scanner stations
7
Degree of freedom
1925
Critical value for 't' (95 %)
1.645
Calibration parameters
Calculated 't'
Significant test
Constant rangefinder offset error (a
0
)
46.5
Significant
Collimation axis error (b
0
)
0.524
Not significant
Trunnion axis error (b
1
)
0.363
Not significant
Vertical circle index error (c
0
)
3.357
Significant
Further analysis has been carried out by running the bundle adjustment again
with calibration parameters. Table
2
presents the RMS of residuals for each
observable group for the cases without and with the self-calibration. The results
obtained have indicated the improvement in precision up to 29 %.
In order to have a concrete solution regarding the significance of the estimated
systematic error model, statistical tests were performed. All calibration parameters
were tested to investigate their significant. Using 95 % confidence level, the results
of the test are shown in Table
3
.
Results in Table
3
shows that null hypothesis was rejected for parameter of
constant rangefinder offset (a
0
), and vertical circle index (c
0
) errors. This indicates
that those parameters are significant. For the collimation axis (b
0
) and trunnion
axis (b
1
) errors, the null hypothesis has been accepted. In this study, only the
significant errors were applied to the raw data to ensure the improvement in
accuracy for the calibrated data.
By applying significant systematic errors to the raw data (test points), values of
new 14 vectors were calculated from raw and calibrated data. These values then
were subtracted from the true values (obtained from photogrammetry measure-
ment technique). Presented graphically in Fig.
16
, the results show an accuracy
