Finally, field calibration experiments are carried out using
multiple flight blocks obtained over the Songshan remote
sensing comprehensive field and the Hegang area of Hei-
longjiang Province. By analyzing and comparing the calibra-
tion results, the calibration values of
GNSS
lever arms and
IMU
boresight misalignment are obtained. Reliable Leica ADS
camera files (
CAM
) for the forward, nadir, and backward
CCD
line arrays are generated after calibration. Using
GNSS
lever
arms and
IMU
boresight misalignment calibration values and
CAM
files, the uncontrolled
DG
precision of the
GFXJ
can be
greatly improved. Supported by several ground control points
(
GCPs
) for
AT
, the geopositioning accuracy of the
GFXJ
camera
can meet the 1:1000 scale topographic mapping requirements.
Empirical results validate the correctness and effectiveness
of the proposed
GNSS
lever arms and
IMU
boresight misalign-
ment calibration models, the piecewise self-calibration model
based on the
CCD
viewing angle and the iterative two-step
calibration scheme.
GNSS Lever Arms Calibration of the GFXJ Camera
In the
GNSS
/
IMU
system, the
GNSS
system dynamically mea-
sures the spatial position of the airborne
GNSS
antenna center
(phase center), whereas
AT
processing needs the spatial
coordinates of the camera lens center (perspective center).
In practice, to avoid signal occlusion of the
GNSS
, the
GNSS
antennas are generally placed at the top of the aircraft. The
offset between the
GNSS
antenna center (phase center) and
the perspective center is called the
GNSS
lever arms, whose
initial value can be measured before flight. However, due to
the influence of various factors, such as air flow and flight
movement, the actual value of the
GNSS
lever arms during
flight will deviate from the initial laboratory measurements.
Thus, it is necessary to establish a mathematical relationship
for accurately transforming the
GNSS
measurements into the
exterior orientation (
EO
) elements required for
AT
.
The geometric relationship between the
GNSS
antenna cen-
ter and the optical perspective center S is shown in Figure 3,
where A represents the
GNSS
antenna center and S represents
the perspective center.
O
-
XYZ
is the ground coordinate
system,
S
-
xyz
is the image spatial coordinate system, (
u,
v, w
) represent the
GNSS
lever arms to be calibrated. Accord-
ing to the imaging relationship, the geometric model of the
GNSS
lever arms is established as follows (Tempelmann 2000;
Hinsken 2002). In this paper, the omega, phi, kappa (
OPK
)
angle system is adopted. The meanings of the symbols are
summarized in Table 1.
Figure 3. Relationship between the
GNSS
antenna center and
the optical perspective center.
Table 1. Symbols and their meanings.
Symbol
Meaning
(
X
s
,
Y
s
,
Z
s
)
the coordinates of the camera’s perspective center in the ground coordinate system
O – XYZ
, also called as the linear EO elements
(
X
j
S
,
Y
j
S
,
Z
j
S
)
the linear EO elements of scanning line j
(
ω
,
φ
,
κ
)
the angular EO elements
(
Δ
X
s
,
Δ
Y
s
,
Δ
Z
s
,
Δ
ω
,
Δ
φ
,
Δ
κ
)
the changes in the unknowns of EO elements
(
a
i
,
b
i
,
c
i
),
i
= 1, 2, 3
the elements in the rotation matrix constructed by angular EO elements
(
ω
,
φ
,
κ
)
.
X
s
k
,
Y
s
k
, …,
κ
k
the EO elements for orientation fix (k)
X
s
k
+1
,
Y
s
k
+1
, …,
κ
k
+1
the EO elements for orientation fix (k + 1)
dX
s
k
,
dY
s
j
, …,
d
κ
j
the changes in
X
s
k
,
Y
s
j
, …,
κ
j
dX
s
k
+1
,
dY
s
k
+1
, …,
d
κ
k
+1
the changes in
X
s
k
+1
,
Y
s
k
+1
, …,
κ
k
+1
(
X
A
, Y
A
, Z
A
)
the coordinates of the GNSS antenna center in the ground coordinate system
O – XYZ
,
also called GNSS observations for the GNSS antenna center
(
X
A
, Y
A
, Z
A
)
0
the initial values of (
X
A
, Y
A
, Z
A
)
(
u, v, w
)
the coordinates of the GNSS phase center in the image spatial coordinate system S - xyz,
i.e., the GNSS lever arms to be calibrated
(
Δ
u,
Δ
v,
Δ
w
)
the changes in the unknowns of the GNSS lever arms
(
α
,
β
,
γ
)
the IMU observations
(
e
x
,
e
y
,
e
z
)
the IMU boresight misalignments
(
Δ
e
x
,
Δ
e
y
,
Δ
e
z
)
the unknowns of the IMU boresight misalignment
(
x, y
)
the image plane coordinates
(
x
′
, y
′
, z
′
)
the normalized image space coordinates
p
(
x
′
, y
′
, z
′
)
the image point
P
(
X
,
Y
,
Z
)
the ground point, (
X
,
Y
,
Z
) are the coordinates of the ground point
(
Ψ
x
,
Ψ
y
)
the viewing angles for the corresponding CCD element
(tan(
Ψ
x
), tan(
Ψ
y
))
the image point spatial coordinates
ax
i
0
,
ax
i
1
,
ax
i
2
,
ax
i
3
,
bx
i
0
,
bx
i
1
,
bx
i
2
,
bx
i
3
the additional parameters (APs) for CCD segment
i
ax
0
i
+1
,
ax
1
i
+1
,
ax
2
i
+1
,
ax
3
i
+1
,
bx
0
i
+1
,
bx
1
i
+1
,
bx
2
i
+1
,
bx
3
i
+1
the additional parameters (APs) for CCD segment
i
+ 1
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2019
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