ngle 
o 1 
| the 
o] 
| the 
tion 
is 
le to 
ents 
‘the 
can 
=1) 
"(2j 
d of 
OT 
ults 
and 
r to 
for 
nter 
y of 
The 
a in 
the 
vector corresponding to vector v. 
  
  
u] 
I, I, I; I, Is Is u”, 
0 0: 0.0.0.6 uj 
= aru. 
Bo 0.20: 29:94l,, Crd 
0 0 90 P, 0 0 Us 
Ug 
Where  submatrices I are coefficients of error 
equations for image observations. I,, I4 and L,, I, 
correspond to vector u,, u5, and u,, u4, which 
represent the corrections for sensor position, 
attitude and their linear rate respectively. I5 and Ig 
correspond to vector ug and ug which express the 
corrections for scene distortion and calculated coordinates of 
ground points. Submatrices P, and P, are the 
coefficients of constraint equations for sensor 
position and linear rate. 
For a single point, 
ZÍí-Xx Yx -Y f 
I,= dy (3-2--1) 
ts = Y a 
-Yx St Xf 
Z 
f 0x 
L,= = 3-22 
0 £4 4Y 
Z 
= = 
L=) © z 3--2--4) 
5 Y 23 ( 
== -X f= 
7 Z 
l2 7 tj 14 I4 = li Ig Ig 7 - Ig 
Z 0 
Aw 9 32-5 
| ; 1 3-2-5) 
The coordinates of ground control points should be 
considered as weighted observations. Submatrix G, 
corresponding to the control points, is a unit matrix. 
69 
In the submatrices P, and P, are same form as G : 
100 
P,=P,=G=|0 10 (3--2--6) 
001 
Through solving equations (3) using the weighted 
least square method, 26 unknown parameters for a 
stereopair are obtained. The weights for several 
equations can be valuated according to the variances 
of residuals of the equations. 
2.3 The correction for the error caused by earth 
rotation 
  
Firstly, we discuss the displacement in the scanning 
direction. As shown in figure 1 , while the SPOT 
sensor scans the surface of the earth from point P, 
to point Py, the displacement D, is caused due to 
the earth rotation. This error is symmetric 
obviously and must be removed before adjustment. 
In figure 1, We represents the angular velocity 
of earth rotation, r is the radius of the parallel 
through Py, B represents the latitude of point Pp, 
N expresses the radius of the prime vertical 
through point Pg. The displacement D, can be 
given as: 
D, = r Weth 
r=Ncos B 
N= 2 
Y1- e sin^B 
where a represents the long radius of earth, e is the 
eccentricity of earth, ty represents time interval 
from point Pg to point Py. 
  
the displacement 
in the scanning direction 
Figure 1