A STUDY OF THE RPC MODEL OF TERRASAR-X AND COSMO-SKYMED SAR 
IMAGERY 
Guo Zhang a ’ *, Xiaoyong Zhu b 
a State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, 
Wuhan University, Wuhan, China, 430079- guozhang@lmars.whu.edu.cn 
b School of Information Engineering and Remote Sensing, Wuhan University, Wuhan, China, 430079- 
zhuxytop@ 163 .com 
KEY WORDS: RPC model, TerraSAR-X SAR imagery, COSMO-SkyMed SAR Imagery 
ABSTRACT: 
The rational polynomial coefficient (RPC) model has recently raised considerable interest in the photogrammetry and remote 
sensing community. This model is a generalized sensor model that is capable of achieving high approximation accuracy. 
Unfortunately, in all previous literature, the computation of the parameters of the RPC model depends on initial values for the 
parameters. In this paper, an algorithm for the computation of the parameters without these initial values is presented. Finally, the 
algorithm is tested on TerraS AR-X and COSMO-SkyMed SAR imagery. Based on numerous tests, the following conclusion can be 
drawn. This study found that the RPC model is suitable for high resolution SAR imagery. 
1. INTRODUCTION 
The rational polynomial camera (RPC) model is a generalized 
sensor model that is capable of achieving high approximation 
accuracy. It can be solved with or without knowledge of the 
rigorous physical sensor model. If this model is available, a 
terrain-independent solution can be developed. Otherwise, the 
RPC solution will be highly dependent on the input of control 
points from the terrain surface (Tao et al., 2001; Chen et al., 
2006). 
When the RPC model is solved using the terrain-independent 
solution, the important question is whether the over 
parameterization of the RPC has led to the design matrix 
becoming ill conditioned and the normal matrix being singular 
in a row (Dolloff, 2004). This happens often when there are 
high order polynomials in the RPC model. In order to improve 
the condition number of the normal matrix, Tao applied the 
ridge estimate in which a small multiplication of the identity 
matrix is added (Tao et al., 2001). Tao determines the ridge 
parameter by the ridge mark method; other researchers all cite 
this paper (Gong et al., 2003; Zhang, 2005; Chen et al., 2006). 
But the ridge estimate raises two problems: the first is that the 
ridge estimate changes the isometric relation in the normal 
matrix leading to the estimated result being a biased estimator. 
The second is that the determination of the ridge parameter is 
difficult and can be selected over a wide range. So if the RPC is 
solved using a terrain-independent solution, an algorithm must 
be found that can improve the status of the normal matrix and 
does not change the isometric relation of the normal matrix. To 
overcome the two problems of the ridge estimate, we can use 
3D-grid control points to obtain an unbiased RPC estimator that 
is the base of the geometric processing of satellite imagery. 
The numerical properties and accuracy assessment of the use of 
RPC to replace the rigorous sensor model are reported. But only 
studies of push-broom imagery and aerial photographs have 
been undertaken!, with no one yet studying TerraS AR-X SAR 
and COSMO-SkyMed SAR SAR imagery. 
TerraSAR-X is a new German radar satellite that has been 
launched in 2007. The scheduled lifetime is 5 years. It’s high 
frequency X-band SAR sensor can be operated in different 
modes and polarisation. The SpotLight- (1.3 m), StripMap- (3.3 
m) and ScanSAR-modes (14.8 m) provide high resolution SAR 
images for detailed analysis as well as wide swath data 
whenever a larger coverage is required. Imaging will be 
possible in single, dual and quad-polarisation. Beam steering 
enables observation in different incidence angles and double 
side access can be realized by satellite roll maneuvers. The 
satellite will be positioned in an 11 days repeat orbit. The solar 
panel is mounted on top of the satellite bus. The SAR antenna is 
visible on the bottom side. The X-band downlink antenna is 
mounted on a small boom in order to avoid interference with 
the SAR-antenna. 
COSMO-SkyMed is an Earth observation satellite system 
funded by the Italian Ministry of Research and Ministry of 
Defence and conducted by the Italian Space Agency (ASI), 
intended for both military and civilian use. The space segment 
of the system will include four medium-sized satellites 
equipped with synthetic aperture radar (SAR) sensors with 
global coverage of the planet. Observations of an area of 
interest will be repeated several times a day in all-weather 
conditions. The four satellites are planned for sun-synchronous 
polar orbits, phased at 90° and at an altitude of 619 km with an 
orbit of 97 minutes. The expected operating life of each satellite 
is estimate in 5 years. COSMO SkyMed is equipped with a 
polarimetric X-band SAR. COSMO SAR is a multi-mode 
sensor, a programmable system which is able to operate 
providing different performance in terms of swath dimension, 
spatial resolution and polarization. The COSMO-SkyMed SAR 
instrument can be operated in different beam which include: 
Spotlight, Stripmap (himage and pingpong), Scansar 
* Corresponding author. 
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