& Calibration, and 50 reserved
GCPs
are used as checkpoints.
The
AT
& Calibration results are displayed in Table 3.
Table 3 shows that after
AT
& Calibration, the geometric
accuracy of the
GFXJ
is greatly improved. The positioning
errors caused by the camera lens and
CCD
line deformation,
GNSS
lever arms and
IMU
boresight misalignment are effec-
tively eliminated after
AT
& Calibration.
GNSS Lever Arms and IMU Boresight Misalignment Calibration
Calibration values of
GNSS
lever arms and
IMU
boresight mis-
alignment obtained from Data A, Data B, Data C, and Data D
are listed in Table 4. The second, third, fourth, and fifth rows
in the table display calibration values from Data A, B, C, and
D, respectively. The sixth row calculates the average, and the
seventh, eighth, ninth, and tenth rows show the differences
between A, B, C, and D and the average, respectively. Since
the initial values of the
GNSS
lever arms have been measured
in the laboratory before flight and the measured values have
been adopted into the
GNSS
/
IMU
observations, the calibra-
tion values of the
GNSS
lever arms i
between the actual
GNSS
lever arms
arms due to various factors during f
surements are carried out beforehan
are the actual values of the
GNSS
lever arms. Because the axes
of the
IMU
are not visible and the
IMU
installed inside the
camera itself is not visible, the
IMU
boresight misalignment
cannot be measured directly. The initial values of the
IMU
boresight misalignment are zero, and the calibration values
are the actual values of
IMU
boresight misalignment. The unit
for the
GNSS
lever arms values is meters, and the unit for the
IMU
boresight misalignment values is degrees.
Table 4 shows that the calibration values of the
GNSS
lever
arms and
IMU
boresight misalignment remain basically con-
stant among the four blocks. To verify the applicability of the
GNSS
lever arms and
IMU
boresight misalignment calibration
values,
GNSS
/
IMU
observations of Data A, B, C, and D are up-
dated using the average of the calibration values according to
Equations 18 and 19.
DG
-based updated
GNSS
/
IMU
observations
are listed in Table 5.
Comparing Table 2 and Table 5, it can be seen that the
updated
GNSS
/
IMU
observations can significantly enhance
the planimetric accuracy, but they make little contribution
to the height accuracy enhancement. From this finding, we
can conclude that the
GNSS
lever arms and
IMU
boresight
misalignment are the main error sources that lower the plane
accuracy of the camera.
CAM Files Calibration
To make a more visual comparison between the nominal
viewing angles, the viewing angles (
Ψ
x
,
Ψ
y
) of each element
on the forward/nadir/backward
CCD
line arrays are calculated
from corresponding
CAM
files. For each
CCD
line array, the
viewing angles of 32 756
CCD
elements can form two viewing
angle curves in the flight direction and in the
CCD
line array
direction (vertical to the flight direction). The viewing angle
curves for the forward view
CCD
line array are shown in Fig-
ure 10, those for the nadir view are shown in Figure 11, and
those for the backward view are shown in Figure 12. In Fig-
ures 10–12, (a) shows the viewing angles for each
CCD
element
in the flight direction, and (b) shows the viewing angles in the
CCD
line array direction (vertical to the flight direction). Data
rom the same region, so Data A,
sen for display. In Figures 10–12,
element number, from 1 to 32 756,
are in radians.
Figures 10–12 show that, for the forward, nadir and
backward view
CCD
line arrays, the differences among the
three sets of viewing angle curves are all extremely small in
the
CCD
direction. The change trend is highly uniform. In the
flight direction, for the forward and nadir views, the viewing
angle curves are basically the same, and the differences are
small. For the nadir view, more obvious differences exist on
the left side of the
CCD
line array among the three viewing
angle curves. Taking the viewing angle curves of Data B as
a reference, the differences with respect to Data A and Data
D were calculated by subtraction. The statistical results are
shown in Table 6, which shows the differences in the viewing
angles of 32 756
CCD
elements in the flight direction and in
the
CCD
direction. The statistical values are converted into the
number of pixels by the pixel size.
Comparing Data B with Data A, in the flight direction, the
mean values of the viewing angle differences are 2.067, 0.756,
and 4.608 pixels for the forward, nadir, and backward views,
respectively. The RMSE values are 0.771, 0.538, and 0.598
Table 4. Calibration values of
GNSS
lever arms and IMU boresight misalignment.
Data Source
u
(meters)
v
(meters)
w
(meters)
e
x
(degrees)
ey (degree)
ez (degree)
Data A
0.0078561782
0.0061256785 −0.0197653245 −0.0763424541 −0.0677445456 −0.0171454645
Data B
0.0089344543
0.0072327323
−0.0286597794 −0.0800227018 −0.0530755474 −0.0164611998
Data C
0.0061857732
0.0046496046
−0.0298780489 −0.0722768518 −0.0618586180 −0.0187345429
Data D
0.0080588347
0.0072026730 −0.0265010496 −0.0762129931 −0.0612929418 −0.0172514684
Average
0.0077588101
0.0063026721 −0.0262010506 −0.0762137502 −0.0609929132 −0.0173981689
Diff A
0.0000973681 −0.0001769936 0.0064357261 −0.0001287039 −0.0067516324 0.0002527044
Diff B
0.0011756442
0.0009300602 −0.0024587288 −0.0038089516 0.0079173658
0.0009369691
Diff C
−0.0015730369 −0.0016530675 −0.0036769983 0.0039368984 −0.0008657048 −0.001336374
Diff D
0.0003000246
0.0009000009
−0.000299999
0.0000007571 −0.0003000286 0.0001467005
Table 5. Direct geopositioning based on updated
GNSS/IMU
observations.
Test
Data
Accuracy in X direction (meter)
Accuracy in Y direction (meter)
Accuracy in Z direction (meter)
Max
Min Mean Std
Max
Min Mean Std
Max
Min Mean Std
Data A 1.573 −0.736 0.048 1.286 0.591 −1.146 0.173 1.143 0.799 −6.811 −1.961 4.186
Data B 1.482 −1.052 −0.035 1.049 1.115 −1.271 0.026 1.136 0.608 −6.457 −1.433 4.275
Data C
1.633 −1.352 0.058 1.066 1.772 −1.523 −0.019 1.067 1.088 −5.625 −1.209 4.107
Data D
1.812 −1.143 0.071 1.175 1.756 −1.711 0.747 1.156 0.382 −7.790 −2.009 5.129
652
September 2019
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
