The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
358 
There is linear relation between image coordinate and time, and 
(U x ,U y ,U z ) is the function of time(Xiao G.C. Zhu C.Y., 
2001; Fan H.D., 2007). As follows: 
X = image coordinate of SAR image in along-track 
Function (3) is carried in Function (1) and Function (2), and F. 
Leberl imaging equations are obtained. Function (4) is about it. 
T = m x -x 
X s = Qq + a x T + q 2 T 2 + a 3 T 3 
Y s = b 0 +b x T + b 2 T 2 +b 3 T 3 
Z s =c 0 + c x T + c 2 T 2 + c 3 T 3 (3) 
u x = a x + la 2 T + 3 a 3 T 2 
u y =b x + lb 2 T + 3 b 3 T 2 
u z =c x + 2 c 2 T + 3 c 3 T 2 
where 
f = (D s +m y -y)~ [{X ~(a 0 +a x T + a 2 T 2 + a 3 T 3 )) 2 
+ (Y- (b 0 + b x T + b 2 T 2 + b 3 T 3 )) 2 
+ (Z-(c 0 +c x T + c 2 T 2 + c 3 r 3 )) 2 f 
g = (a x + 2a 2 T + 3 a 3 T 2 )-(X ~(a 0 +a x T+ a 2 T 2 + a 3 T 3 )) 
+ {b x + 2b 2 T + 3b 3 T 2 ) • {Y - (b 0 + b x T + b 2 T 2 + b 3 T 3 )) 
+ (c, +2 c 2 T + 3 c 3 T 2 )-(Z ~(c 0 +c x T + c 2 T 2 +c 3 T 3 )) 
(4) 
Function (5) is differential and linearized equation about 
Function (4). It is error equation of multi-photo combined 
adjustment model. 
T = time 
m x = resolution of SAR image in along-track 
da 0 
. 
K 
K 
K 
& 
M- 
dA 
d>A 
d>A 
da 0 
da 3 
db 0 
db 3 
dc 0 
dc 3 
dX x 
8Y X 
dX k 
dY k 
VA' 
Wn. . 
ÈL 
V» 
dfn 
df n 
df n 
vf n 
da 0 
da 3 
db 0 
db 3 
dc 0 
dc 3 
dX x 
dY x 
dX k 
dY k 
Vg t 
dgi 
fjgf 
%> 
d gi 
d 8i 
dg x 
da 0 
da 3 
db 0 
db 3 
dc 0 
dc 3 
8X x 
3Y X 
dx k 
dY k 
Vgn. 
d g n 
d g n 
dg n 
dg n 
bg„ 
d gn 
d g» 
dg n 
dg„ 
_da 0 
da 3 
db, 
db 3 
dc 0 
dc 3 
8X x 
dY x 
dX k 
dY k 
da 3 
db 0 
db 3 
dc 0 
dc 3 
dX x 
dY\ 
dX k 
ß\ 
~f n ° 
0 
(5) 
where k = number of Pass Points 
Because of low base-height ratio and low intersection angle of 
corresponding points, observation data in same side can be 
resulted in poor elevation accuracy. But multi-photo combined 
adjustment of observation data in different side can lead to 
geminate expense of data acquisition. The elevation value is 
obtained from 1:50,000 scale DEM, considered pass points as 
elevation points(Huang G.M. et al, 2008). There is no 
dx .,dY. about GCP. 
2.2 Conditions of Multi-photo Combined Adjustment 
Model 
nP photos are given, the number of GCPs is TlGCP, the 
number of Pass Points is YlJM . The total number of GCPs 
participated in calculation is TlCalGCP , and the total 
number of Pass Points participated in calculation is nCalJM. 
nCalGCP > nGCP (6) 
nCalJM > nJM (7) 
n- 2 x (nCalGCP + nCalJM) (8) 
t = \2xnP + 2x nJM (9) 
where YlP = number of photos given 
nGCP = number of GCPs 
nJM = number of Pass Points 
nCalGCP = total number of GCPs participated in 
calculation 
nCaUM = total number of Pass Points 
participated in calculation 
n = number of condition equations 
t = number of necessary observation