are: 
px, py are image coordinates(IMC). they are 
expressed in image center coordinate system. The 
origin of the system is the scene center. In which px 
is expressed as the pixel number in a scanline and py 
is expressed as the line number of scanlines. 
t is the time interval with respect to the scene center 
. The interval can be calculated from the py- 
coordinate, 
ti = (PYi - PYo) ts (1) 
Where py; and py, are the coordinates of an image 
point and scene center respectively; t, is the time 
interval needed to made a scanline. 
X, YZ are local tangent plane coordinates (LTC). The 
origin is the satellite position corresponding to a 
scene center. LTC are employed during bundle 
adjustment. The geographic or Gauss -Krueger or 
UTM coordinates should be translated into the 
system. 
2.2 Error equations for SPOT imagery 
Considering some errors due to the movement of 
satellite and sensor as well as the change of inner 
orientation parameters, Collinearity equations for 
SPOT imagery can be expressed as: 
px dxe X- Xs dx; dx, 
0+] 0 |=kR|Y-Yg|+ldys|+]dy,]| (2) 
= 0 22.11 9 0 
i.e. 
xs X ax 
Z 
0-11 -dy 
Z 
X = pX + dx, 
dx = dx; + dx, 
dy = dy; + dy, 
Where, k represents the scale factor between image 
and ground points, R = R, R,, R, is a rotation matrix 
corresponding to the rotation of SPOT sensor, 
68 
R, is a constant matrix corresponding to the angle 
of sensor incidence. The vector [ dx; dy; 0 It 
represents the correction for the error due to the 
change of focal length, the vector [dx, dy, opt 
expresses the correction for the error due to the 
distortion of scene, dx, represents the correction 
of radial distortion in scanning direction, dy, is 
introduced to compensate for the distortion due to 
the possible misalignment of scene, dx, represents 
the correction for the error due to rotation of the 
earth, the correction will be discussed below. 
The extra orientation elements in formula (2) can 
be expressed as: 
@;|=|0,|+ti| @, (2——1) 
K; Ko Kr 
Xsi Xo Xr 
Ysi|=] Yo|+ti] Yr (2-2) 
Zei Zo Zr 
The number of unknown parameters in formula (2) 
is 26 for a stereopair. The fact that the view field of 
the sensor is very narrow (4.139), and the SPOT 
orbit reaches into the height 820 kilometers results 
in intensive correlation between the angular and 
linear elements in the same direction. In order to 
reduce the correlation, the constraint conditions for 
the position of sensor corresponding to the center 
scanline and the components of average velocity of 
the satellite movement are employed. The 
constraints can be driven from the ephemeris data in 
SPOT CCT. 
The standard condition equations based on the 
discussion above are expressed as: 
Av = Bu+l (3) 
v-[v, vg vg] (3:4) 
Vm [v ae Man (3-1-1) 
Vo = [ Vx1 Vy4 Vz1------ VXk VYk VZk It (3-1 -2) 
Va =[Vxs Vvs Vzs Vx Vy vz I! (8 -1-3) 
Where n is the number of observations, k is the 
number of control points, and 1 is the residual 
vector 
Bu- 
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