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Toshiaki Hashimoto
3 METHODOLOGY OF GEOMETRIC CORRECTION
31 Collinearity equation
First of all, the coordinates systems used here are defined as follows ;
e (X, Y,Z): ECR(Earth Center Rotation) coordinates where the origin is the gravity center of the Earth, X axis is
Greenwich Meridian at the equator, Z axis is North along the spin axis, Y is defined by right-handed rotation,
e (x, y, Z): Orbital Coordinates where the origin is the gravity center of the satellite, z axis is nadir, y axis is defined
by the outer product of z axis and velocity vector, x is defined by right-handed rotation.
assumed
focal plane
/
/ P(X.Y.Z)
Od.
ascending node
Figure 2. Collinearity condition
The view vector at the aperture (corresponding to the satellite coordinates) can be defined by the optical-mechanical
system of GLI as (Bx,, By,, Bz,) . The view vector in the coordinates are transformed into the orbital coordinates
using the attitude, (roll, pitch, yaw) = (ù, à, ê), as follows.
Bx, Bx, cosE -sinfE OY cosfö O sinfô\(1 0 0 Bx,
By, |- B. By, |=|sinf£ cosfE 0 0 1 0 0 cosfö —sinfô | By,
Bz, Bz 0 0 l|-sinfó O cosfOp0 sinfO0 cosfô | Bz,
where (Bx s» By, Bz,) : view vector in satellite coordinates (1)
(Bx ,, By,, Bz,): view vector in orbital coordinates.
The level 1B1 products contain the satellite position P, 2 (X,, Y,, Z,) and velocity V, 2 (V,,, V.,, V.) in ECR. The
transformation between orbital coordinates and ECR coordinates is expressed as follows (NOAA/NESDIS), (Patt, F.S.,
etal, 1994), (Rosborough,G.W., et al, 1994).
yr?
let n = (X > Y.>Z,) F Unit vector of P, u = (u,,u,,u,)F unit vectorof V ,
X, X. Xy Xm Xn X. (2)
then, Y. = P, 9 Y. IV. Vm Ya Y.
Z. Z, Zy Zn Za Ze
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 143
