Toshiaki Hashimoto
where (X,,Y,,Z,) :any vectorin ECR
(X,, Y, Z, ) :any vector in orbital coordinate s
m -nxu - (x, y, .Z,)F directiona l vector for Y, axis (in ECR)
k =mxn =(x,,y,,Z,)F directiona | vector for X, axis (in ECR)
The satellite movement can be also expressed using the distance between the Earth center and the satellite center (R),
the longitude of ascending node(U), the inclination(), the latitude argument from ascending node on the orbital
plane(u) as follows (Hashimoto, T., 1998).
X. X. cos sinQ O1 0 0 —sinu O0 cosu Y X,
Y. |zP,. Y, |s| sin OQ —-cosG O[O sini -cos! 0 1 0 Y:
7 Ze 0 0 1|O0 cosi sini cosu 0 sinu Z7. 3)
— cos @ sin u — sin Q cos icosw sin Qsini cos cosu—sin Qcosisinu | X,
-|-sin Qsinu -- cosQ cosicosu —cosQsini sin Qcosu + cos Q cos isin u | Y.
sin icosu cos i sin i sin u Z
e
Both (P. , V.) and (R, U, i, u) are time dependent. The variation ratios of the former are bigger than those of the latter,
especially at the equator or the polar regions. So the latter is suitable for the expression of satellite movement. In this
work, the parameters for satellite movement and attitude are expressed by the polynomials of line number (L) as ;
P=P,+P -L+P, L’+--, P=(R,Q, ju,w, £, k). (4)
The coefficients of polynomials for (R, U, i, u) and attitude are determined by the regression analysis using the satellite
movement(position, velocity) and attitude in a standard product, respectively
The view vector and the observed ground point (X, Y, Z) satisfies the collinearity equations as follows (Hashimoto, T.,
1992), (Hashimoto, T., 1997).
F _ Bx, "c A Xara Y Yora uz 7»
S Bz, a; (X - Xo) c a,(Y - Yo) t a, (Z- Zo)
poSB XX) +a (Y-Yo ra Z-Zy _ 6
y Bz, a; (X - Ko) + as (Y - Yo) + A, (Z - Zo)
a, a, a,
where là; a, a, |= (P, P, yz P, JP c : assumed focal length.
a, ag a,
Xa cos © cos u — sin £2 cos isin u
Yo |=|sin @2 cos # + cos Q cos /sin & |- R
Zo sin isin u
In the equation (5), the parameters (R, U, i, u) and (à, ó, é) are treated as exterior orientation parameters. If the
observed satellite position is accurate and the unknown parameters are only satellite attitude, the equation (5) can be
approximated by Taylor development around the unknown parameters as;
F% + fo AES da = SE: ut _ JF: dé =0
qü qf Je
ES. Fs ae IF (6)
F^ eti: di ~ 2d - dé = 0
qü qf Je
0
where the notation * ' * means the approximation and (v,, v,) is residuals.
3.2 GCP collection
144 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
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