ANALYZING ON PIXEL POSITIONING ACCURACY OF SAR IMAGES 
BASED ON R-D LOCATION MODEL 
H. B. Luo a , X. F. He a , M. He a 
a Institute of Satellite Navigation & Spatial Information System, Hohai University, Nanjing, Jiangsu, 210098, China. - 
( hbluo, xfhe, mhe)@hhu.edu.cn 
KEY WORDS: SAR, Image, Targets, Pixel, Error, Analysis 
ABSTRACT: 
The range-Doppler (R-D) model, which requires no reference points and is independent of satellite attitude knowledge and control, is 
used to determine the location of SAR images. However, its error has not been analyzed sufficiently. This paper investigates the 
effects of the pixel positioning accuracy of SAR images based on R-D model on uncertain measurement errors such as range 
measurements, Doppler center frequency measurement, orbit and the earth model. The test results indicate the earth model and zero- 
Doppler condition have severe effect on the pixel positioning accuracy, but they can be corrected accurately using the known DEM 
and Doppler parameters. Orbit errors are the critical errors and it must be corrected using the precise orbits to achieve a positioning 
accuracy of around 25 m. Compared with the errors given above the atmospheric delay error is less, but it may become remarkable 
in low latitude areas. Moreover, the pixel positioning errors of SAR images are nonlinear, and the errors decrease gradually with 
decreasing latitude as well as increasing longitude. 
1. INTRODUCTION 
2. DESCRIPTION OF THE R-D MODEL 
Effective utilization of synthetic-aperture radar (SAR) image 
often requires precise location of each image pixel. Historically, 
the absolute positioning of space-borne SAR image has relied 
on the use of reference points on the earth which are 
recognizable in SAR image. However, for many oceanic 
applications, such as registration of image to monitor ice 
motion, the image dose not contain any recognizable features, 
therefore, no reliable reference points are available for image 
positioning. In this conditions, the range-Doppler model was 
presented, which has an advantage over previous techniques in 
that it requires no reference points and is independent of 
satellite attitude knowledge and control. 
The R-D model was originally presented by Borwn (Brown, 
1981). It requires only the satellite ephemeris data and the 
characteristics of the SAR data collection system as input. The 
accuracy of the result depends primarily on the validity of the 
assumed earth model and the characterization of the target 
range, the satellite ephemeris data and the center Doppler 
information. Many methods were developed to solve R-D 
equations, however the error of it has not been analyzed 
sufficiently (Curlander, 1982; Chen, et al, 2000; Zhou, et al, 
2001; Zhang, et al, 2005; Zou, 2005; Yang, et al, 2006). In this 
paper, the three fundamental relationships of R-D model are 
introduced and analyzed firstly and then its error models are 
derived based on the law of error propagation by differentiating 
the equations with respect to the slant range from sensor to 
target, the satellite positions and velocities, the target positions, 
the Doppler center frequency and the normal height. At last, 
three scenes test data of the ERS-2 C-band SAR from Tibet 
Zhang autonomous region, Nanjing city and Taiwan province 
are used to investigate the effects of the pixel positioning 
accuracy of SAR images on uncertain measurement errors such 
as range measurement, Doppler center frequency measurement, 
satellite orbit and the earth model. 
The location of an arbitrary pixel in a SAR image is 
determined by the intersection of the centroid of the radar beam 
with the planet surface. This intersection is determined by three 
fundamental relationships: 1) the SAR range equation defining 
the distance from the sensor to the target; 2) the SAR Doppler 
equation defining the plane of the centroid; 3) a model 
describing the earth’s shape. Figure 1 illustrates the 
intersection of three equations. 
Earth Model 
ge Model 
Pterio of «»iter Beam 
Figure 1. Schematic diagram for pixel positioning using R-D 
model. R is the slant distance from sensor to target. 
2.1 Range equation 
The slant range from the sensor to the target on the earth is 
defined by the equation 
(1)