The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bi. Beijing 2008 
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(wideregion or hugeregion), SPOTLIGHT, allowing SAR 
images with spot extension of 10x10 km 2 and spatial resolution 
equal to lxl m 2 single look; STRIPMAP (HIMAGE achieving 
medium resolution, wide swath imaging, with swath extension 
340 km and spatial resolution of 3x3 m 2 single look; 
STRIPMAP (PINGPONG), achieving medium resolution, 
medium swath imaging with two radar polarization’s selectable 
among HH, HV, VH and VV, a spatial resolution of 15 meters 
on a swath 330 km; SCANSAR (WIDE and HUGE region), 
achieving radar imaging with swath extension selectable from 
lOOx 100 km 2 (WIDE REGION) to 200x 200 km 2 (HUGE 
REGION), and a spatial resolution selectable from 30x30 m 2 to 
100x100 m 2 . 
0F X 
dF, 
dF x - 
da i 
db 
dc. 
dd, 
B = 
dFy 
dFy 
dFy 
dFy 
_ da, 
dbj 
dc, 
ddj _ 
/ = 
-К' 
~Fy\ 
*= 
_ a i b j c i 
•U T 
(/ = 1,20, j = 2,20) 
Based on the least squares method, the RPC are 
This paper aims to generate a RPC with an unbiased estimator ( T \ Tj 
for TerraSAR-X and COSMO-SkyMed SAR imagery. yB BjX = B l (4) 
2, RPC MODEL 
In the RPC model, image pixel coordinates d(line, sample) are 
expressed as the ratios of polynomials of ground coordinates 
D(Latitude, Longitude, Height). In order to improve the 
numerical stability of equations, the 2D image coordinates and 
3D ground coordinates are each offset and scaled to fit the 
range from -1.0 to 1.0. The RPC model between the image 
coordinates d and the ground coordinates D for an image can be 
presented as below (OGC, 1999), 
Y _ Num L (P,L,H) 
Den L (P,L,H) 
Y ... Num s (P,L,H) 
Den s (P ,L,H) 
Where Num f p > L >H) Den L (P,L,H) NumfP,L,H) Den s (P,L,H) 
are the terms of the third order polynomial of (P,L,H), Y and X 
are the normalized row and column index of pixels in the image, 
and P, L and H are normalized coordinate values of object 
points in the ground. 
Wang presents a new iteration for normal equation. The 
iteration is suitable for common normal equation, morbidity 
normal equations and rank-defect normal equations and its 
unbiased and convergent properties have been proved (Wang et 
al., 2001). 
We solve the Equ(4), based on Wang’s method, as follows: 
Add the x onto Equ(4): 
B + E^x = B T l + x (5) 
The x can be estimated: 
x (k) = (B T B + E)' (B T l + * lt_l) ) 
According to Wang et al., (2001), the estimator is unbiased. 
3. TEST DATA 
In order to fit the RPC using the rigorous sensor model, we can 
rewrite Equ. (1) as (Zhang, 2005), 
In this study, the TerraS AR-X and COSMO-SkyMed SAR 
image are used for the test. 
F x = Num s (P,L,H)-X* Den s (P,L,H) = 0 
F Y = Num L (P, L,H)-Y* Den L (P, L,H) = 0 
The observation error equations can then be formed as, 
V = Bx-1 (3) 
Where, 
TerraS AR-X Data 
The test image of TerraS AR-X is a full scene of Beijing; basic 
information about the scene is listed below. 
Image Size 
8104* 9042pixels 
Resolution 
1.6 m 
Topography 
Flat 
imaging mode 
SL 
Time of Acquisition 
2008/03/29/22:17:23.9 
Product Type 
ssc 
Table 1. Basic information on the Beijing TerraS AR-X 
imagery. 
COSMO-SkyMed Data 
The test image of COSMO-SkyMed is a full scene of Shang 
hai ; basic information about the scene is listed below.