Rigorous Sensor Modeling and Triangulation for OrbView-3 - asprs

where
where
δ δ
ω , ϕ , and κ
δ
δ δ δ
δ 2
⎡ω
⎤ ⎡ω
⎤ ⎡ ⎤ ⎡ ⎤
0 ω1
TC
ω2TC
⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ 2 ⎥
⎢ϕ
⎥ = ⎢ϕ0
⎥ + ⎢ϕ1
TC
⎥ + ⎢ϕ2
TC
⎥
⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ 2 ⎥
⎣κ
⎦ ⎣κ0
⎦ ⎣κ1
TC
⎦ ⎣κ
2TC
⎦
are the corrections to the image-to-ground Euler orientation angles, omega, phi, and
kappa, respectively, whose initial values are assumed zeros
δ δ δ
ω0 , ϕ0
, and κ0
are the triangulated offset correction values for omega, phi, and kappa, respectively
δ δ δ
ω1 , ϕ1
, and κ1
are the triangulated linear (velocity) correction values for omega, phi, and kappa,
respectively
δ δ δ
ω2 , ϕ2
, and κ2
are the triangulated non-linear (acceleration) correction values for omega, phi, and
kappa, respectively
TC is the time at the given input line coordinate with origin at image center.
The exterior orientation positional corrections are
A
δ
⎡X
⎢
= ⎢Y
⎢
⎣ Z
δ
δ
δ
δ δ
δ 2
⎤ ⎡X
⎤ ⎡ ⎤ ⎡ ⎤
0 X1
Tc
X 2Tc
⎥ ⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ 2 ⎥
⎥ = ⎢Y0
⎥ + ⎢Y1
Tc
⎥ + ⎢Y2
Tc
⎥
⎥ ⎢ δ ⎥ ⎢ δ ⎥ ⎢ δ 2 ⎥
⎦ ⎣ Z0
⎦ ⎣ Z1
Tc
⎦ ⎣ Z2
Tc
⎦
δ
A is the correction for the sensor position vector in ECEF WGS84 meters
δ δ
δ
X , Y , and Z
are corrections to the sensor position in ECEF WGS84 meters, respectively
δ δ
δ
X 0 , Y0
, and Z0
are the triangulated offset correction values for the sensor position
δ δ
δ
X1
, Y1
, and Z1
are the triangulated linear (velocity) correction values for the sensor position
δ δ
δ
X 2 , Y2
, and Z2
are the triangulated non-linear (acceleration) correction values for the sensor position
T C is the time at the given input line coordinate with origin at image center.
Equation 1 can be updated based on the triangulation components outlined in equations 2-4. The new image-toground
function is
G O δ 1
A = A + A + k
M
δ ( a + a )
δ
where M is the 3x3 correction rotation matrix defined by image-to-ground Euler angle corrections
δ δ δ
ω , ϕ , and κ from equation 3. The M rotation matrix is formed from the quaternion values interpolated based
on time (T ) from the attitude metadata. All other parameters are defined in equations 1-4 above.
ASPRS 2006 Annual Conference
Reno, Nevada ♦ May 1-5, 2006
δ
M
(3)
(4)
(5)