The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part BI. Beijing 2008
rising quality, but it is still affected by systematic errors, which
is called drift error. Here, GPS measurement is applied as actual
measurement in order to aid IMU by correcting this huge drift
error. Through Kalman filter operation, an optimal estimate of
the sensor position and attitude is determined from GPS and
IMU.
Figure 8 shows Kalman filter circulation diagram for GPS/IMU
integration (Kumagai, et al., 2000). Individual measurement
equations and transition equation are selected and the
initialization of each covariance is necessary to continue the
Kalman filter circulation in response to the GPS validation.
Accuracy of GPS/IMU integration depends on accuracy of
referenced GPS. In this case, it is approximately 30 cm.
Figure 8. Kalman filter circulation diagram
In addition, boresight offset must be estimated between GPS
and IMU, and also the other sensors. In the Kalman filter
circulation, differences of position and velocity between IMU
and GPS are used to estimate amount of errors in IMU. If the
UAV just goes straight, amount of errors is not affected because
the relative movement is constant. However, if the UAV makes
a turn, amount of errors is not constant. Position and velocity of
near axis of gyration is small, though its far axis of gyration is
large. In this research, boresight offset from GPS to IMU in the
UAV is obtained by direct measurement.
3.4 Bundle block adjustment of CCD images
Meanwhile, orientation of digital camera is determined by
bundle block adjustment. Bundle block adjustment is a non
linear least squares optimization method using tie-points of
inside block. Bundle block adjustment is used for the
determination of the orientation parameters of all CCD images
(Takagi and Shimoda, 2004). Bundle block configuration
increases both the reliability and the accuracy of object
reconstruction. An object point is determined by intersection
from more than two images, which provides local redundancy
for gross error detection and which makes a better intersection
geometry as a result (Chen, et al., 2003). So, in this research,
CCD images are taken for more than 60% overlapping in
forward direction, and more than 40% overlapping in side.
GPS/IMU allows automatic setting of tie-points and it reduces
searching time of tie-points by the limitation of searching area
based on epipolar line. The epipolar line is the straight line of
intersection of the epipolar plane with the image plane which is
estimated by GPS/IMU. It connects the image point in one
image through the image point in the next image.
Figure 9 shows a series of image orientation with tie points
which overlapped each other. Resolution of those images is
approximately 1.5cm. This is super high resolution image. So it
is not difficult to detect small gaps or cracks.
Figure 9. Image processing
Table 2 shows the result of bundle block adjustment, “cp” is the
control points which is measured by total station as true values,
“ba” is the computation result by bundle block adjustment.
Accuracy is estimated by comparing 20 control points and the
result of bundle adjustment. Average of residual of its plane (X,
Y) is approximately 3cm to 6cm. Average of residual of its
height (Z) is approximately 10cm. That is, this result is very
accurate as compared with differential GPS or GPS/IMU
integration. Therefore, the result of bundle block adjustment
aids the Kalman filter by initialization of position and attitude.
Num
X(cp:m)
Y(cp:m)
Z(cp:m)
X(ba-m)
Y(bam)
Z(ba:m)
residuai: X
residual: Y
resdual:Z
1
0
0
-12.584
0.094
-0.059
-12.311
0.094
0.059
0.273
2
11.3105
0
-12.3825
11.293
-0.062
-12.48
0.0175
0.062
0.0975
3
20.8395
0.168
-12.4065
20.79
0.111
-12.515
0.0495
0.057
0.1085
4
32.588
0.2885
-12.441
32.527
0.229
-12.564
0.061
0.0595
0.123
5
46.196
0.5035
-12.5105
46.103
0.447
-12.518
0.093
0.0565
0.0075
6
0.074
-8.1735
-12.515
0.173
-8.145
-12.336
0.099
0.0285
0.179
7
11.3245
-7.905
-12.428
11.346
-7.891
-12.458
0.0215
0.014
0.03
s
20.5425
-7.703
-12.4345
20.525
-7.72
-12.499
0.0175
0.017
0.0645
9
30.677
-7.315
-12.406
30.622
-7.341
-12.575
0.055
0.026
0.169
10
46.7025
-7.81
-12.566
46.608
-7.849
-12.459
0.0945
0.039
0.107
11
0.4485
-14.9755
-12.473
0.551
-14.917
-12.376
0.1025
0.0585
0.097
12
11.6895
-15.058
-12.4075
11.734
-15.019
-12.483
0.0445
0.039
0.0755
13
20.3605
-14.902
-12.419
20.361
-14.891
-12.518
0.0005
0.011
0.099
14
30.447
-15.3555
-12.47
30.424
-15.347
-12.503
0.023
0.0085
0.033
15
46.3735
-15.455
-12.5715
46.289
-15.456
-12.401
0.0845
0.001
0.1705
16
0.3535
-24.139
-12.443
0.453
-24.072
-12.522
0.0995
0.067
0.079
17
11.911
-23.7855
-12.455
11.987
-23.721
-12.466
0.076
0.0645
0.011
18
20.594
-23.461
-12.453
20.623
-23.421
-12.507
0.029
0.04
0.054
19
30.176
-23.1665
-12.4505
30.165
-23.13
-12.491
0.011
0.0365
0.0405
20
46.258
-22.5005
-12.5545
46.2
-22.493
-12.39
0.058
0.0075
0.1645
ave
0.05655
0.0376
0.09915
Table 2. Result of bundle block adjustment
3.5 Positioning by multi-sensor integration
The positioning and attitude of sensors are decided by
integration of GPS/IMU, as well as CCD images. One of the
main objectives of this research is to integrate sensors for
developing the high precision positioning system by using
inexpensive equipments. Integration of GPS, 1Hz, and IMU,
200Hz, has to be made with Kalman filter for geo-referencing
of laser range data with the frequency of 18Hz. Positioning
accuracy of GPS/IMU is approximately 30cm, because it is
limited by the accuracy of GPS. On the other hand, position and
attitude can be estimated for very high accurately with bundle
block adjustment of CCD images, though the images are taken
in every 10 seconds.
Therefore, the combination of bundle block adjustment and
GPS/IMU by the Kalman filter is conducted to achieve higher
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