In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
cos^cos v(Y-Jfo) + sinK(Y-Ys) - sin (p cos k(Z-Zs) ^ 
sin cp( X - Xs) + (Z- Zs) cos <p 
y = [J(X-Xs) 2 +(Y- Ys) 2 + (Z -Zs) 2 -R,)pJM y 
(16) 
( Where b ^ y + , Rj is the slant range of the object 
point, j is the column coordinate//is geodetic altitude) 
According to the least squares method, the coordinate (X\ Y 
Z) of the ground point can be solved iteratively. 
Similarly, the range-coplanarity equation of explicit function 
of coordinates of image point in the geocentric coordinate 
system can also be obtained. 
It is concluded from the above equation that the mature 
method based on the collinearity equation model of optical 
images can be easily applied in the processing of 
photogrammetric data of SAR images. 
4.3 Refinement of Orientation parameters [4] 
The range-coplanarity equation of formula (16) is linearized, 
therefore the error equation can be obtained: 
f V x ~ f\Xs d Xs f\Ys d Ys f\Zs d Zs + f\K d K + f\q, d (p ~ h ^Q) 
\ V y ~ f2Xs d Xs + flYs d Ys + flZs d Zs + fl K d K + flip^cp ~h 
4. THE CORRECTION AND GEOCODING OF RADAR 
IMAGERY 
4.1 The preprocessing of attitude angles 
The cp-K-co system is adopted in the R-Cp model this paper, 
while generally oxp-K system is adopted in the original attitude 
measurements. Before three values of attitude angles in oxp-K 
system are used, they should be converted into the values in cp- 
K-co system. 
Since different attitude systems have the same translation 
matrix, that is: 
Where /. represents linear coefficient and /. represents 
constant. 
Correction model of observation data of exterior orientation 
elements expressed by low order polynomial of time parameter 
t: 
| d Pi = b m + V + b i2* 2 ( d Pi = dXs > dYs > dZs ) (21) 
da i = c m + c n { + C i2^ 2 ( da i = d( P. dk) 
R(co,cp,K)=R(cp,K,co) 
(17) 
Set R(co,(p,K)=[<3,y], (y=0,l,2) , and is matrix element 
which is obtained from formula(l). 
Thus, cp,K,co value of cp-K-co system can be calculated by a*j. 
(p = -arctan(a 30 / a 00 ) 
j k = -arcsin(<z 10 ) 
cy = arctan(a 12 /a u ) 
(18) 
In order to overcome the singularity of normal equation and 
satisfy adjustment with sparse control points, combined 
adjustment error equations can be formed using EO observing 
data along with virtual observing values of R-Cp: 
y y = B Rb b 
~l r - 
- p y 
K = B a b+ 
B Cc c — L c ... 
p x 
(22) 
<5 
Ctf 
II 
-k 
-P b 
K = 
E c c-L c 
■Pc 
4.2 Calculation of coordinates of ground point using image 
point 
The coordinates of ground point can be obtained using the 
corresponding coordinates of the image point in combination 
with distance condition, coplanarity condition and earth 
ellipsoid equation. The coordinate (X Y Z) can be acquired 
by the following three equations: 
'r. {X-Xsf + iY-Ysf + tZ-Zsf , A 
F '= W 1 = 0 09) 
< F 2 = i x (X - Xs) + iy(Y - Ys) + J Z (Z - Zs) = 0 
Fj= £l±Ii + _zl__i =0 
3 (a + H) 2 (b + H) 2 
Where V y , V b , V c are corrections of range equation, 
coplanarity equation, polynomial model parameters of EO lines 
and attitudes, respectively; b,c are polynomial coefficients for 
exterior orientation model. 
The above formula can be incorporated as: 
V=BX-L P (23) 
The solutions of orientations are: 
X=(B T PB) T (B T PL) 
(24) 
5. EXPERIMENT 
The experimental material was an ALOS/PALSAR image 
(70Kmx60Km, with pixel resolution of 3.189m in velocity 
direction and 9.368m in range direction), covering the 
mountainous areas in Shanxi province in the west of China.