The X-Z plane and the Xst-Zst plane are the same and the 
satellite flies on the plane towards the Xst axis direction. R 
is the earth's radius. h is the satellite altitude. Point C 
(Cx, Cy, Cz) is the earth's center in the ground co-ordinates. 
Point P on the earth's surface is directly below the satellite 
and the nadir looking sensor faces here. Point Q on the 
earth's surface is where the forward looking sensor is 
directed. Angle y can be determined from the base-to-height 
ratio of this stereoscopic imaging system. Angle B can be 
determined from the angle y. Length 1 is the length along the 
earth's surface between the origin O and the point Q. Angle a 
can be determined from the length 1. The satellite always 
faces the earth because the satellite rotates once when it 
flies around the earth. From these conditions mentioned above, 
the»; satellite ./positionc $2 (X95255Y$gy2 %g) 1ain 5uthesr ground 
co-ordinates and the satellite attitude, that is, the rotation 
angle’ w, 4, « around the axes X, Y, 2, can be expressed as 
follows. 
Satellite position 
Xyim Cx: (Rotsn) cosnm(S eipdkogy io, . od. Loue . an ius 
Yo = Cy Tfoijsismio ‚Lei dde... S53 a32) 
Zo = Cz + (R + h) sin (3 +580 3 BIEQLLILNLTH » Sid. HAGE) 
Satellite Attitude 
0) K= 0 000000600046 00000 0 0 0e (4) 
¢ -(o + B) 0.0.0.0 0.9. 0.0. 0.0.00 002000020005) 
The  co-ordinates transformation equation between ground 
co-ordinates (X, Y, 2) and satellite co-ordinates (Xst, Yst, 
Zst) can be expressed as follows. 
X a1] 812 ais Xst XQ 
Y = a9 1 8.29 a23 . Yst T YO 00e. {0) 
Z a3ı a32 8393 Zst vA) 
ayy Cosk * COSÓ 
a2] = sink * cos¢ * cosw + sinu * sin$ 
az] = Sino * sink * cos$ - sin$4 * coso 
aı2 = -sink 
a22 7 COSU * COSK 
agp 7 COSK * Sinu 
aj3 7 COSK * sing 
à23 7 COSU * Sink * sin$ - sinu * cos$ 
a33 7 Sinu * sink * sin¢ -* cosuo * cosó 
Using this transformation equation we can express the position 
of the linear array sensor and the center of projection in the 
ground co-ordinates. 
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