993 
OPTICAL/SAR SENSORS STEREO POSITIONING 
Shuai Xing*, Qing Xu, Yan Zhang, Yu He, Guowang Jin 
Zhengzhou Institute of Surveying and Mapping, 450052 Zhengzhou, China - xing972403@163.com 
Commission I, ICWG I/V 
KEY WORDS: Accuracy, Mapping, Orientation, Optical, Photogrammetry, Stereoscopic, SAR 
ABSTRACT: 
Up till now it is still difficult to acquire stereoscopic space-bome image pairs of some area due to climate condition or atmosphere 
pollution. This paper describes the geometric aspects and the mathematical treatment for the stereoscopic image pair composed of 
optical and SAR space-bome images in positioning. First, the geometric equation for linear array push-broom imagery and F. Leberl 
model for SAR imagery as well as methods to simultaneously determine or refine individual parameters of these models are briefly 
reviewed. And a straight-forward single-step procedure has been developed which follows the philosophy of photogrammetric bundle 
adjustment techniques. Secondly, from these imaging models of one optical and SAR image, the composite stereoscopic pair is 
constructed. The stereo positioning is the process of determining the ground coordinate of a ground point from a pair of homologue 
points in the composite stereoscopic pair. Experimental results show that it is feasible to construct stereoscopic pair with one optical 
and SAR image, of which the average positioning RMS value is close to stereoscopic pair with optical/optical or SAR/SAR images. 
1. INTRODUCTION 
High resolution optical stereoscopic image pairs achieved by 
some commercial remote sensing satellites, such as IKONOS, 
SPOT5, Quickbird etc, have been widely used to produce 
medium and large scale cartography. But until now it is difficult 
to acquire satisfied optical space-bome image of some area, like 
basin or tableland, for complicated climate or serious 
atmosphere pollution. Radargrammetry is a good solution to 
this problem, but the stereoscopic observation and interpretation 
of SAR stereoscopic image pair are extremely rigorous. So this 
paper describes another solution as Figure 1, which constructs a 
stereoscopic pair with optical/SAR space-bome images for 
stereo positioning. 
Figure 1. Scheme of a multi-sensor stereo positioning 
After Moore first proposed the stereoplotting based on the 
stereoscopic pair with SAR and optical images in 1970, lots of 
works on theory have been done in the past twenty years. In 
1990 Johannes Raggam and Alexander Aimer (Raggam 
Johannes et al., 1990) of institute for image processing and 
computer graphics in Austria have analyzed the geometric 
aspects and the mathematical treatment of stereoscopic pair 
composed of optical and SAR space-bome images, and have 
chosen a Seasat SAR image, SPOT image and Landsat TM 
image to construct three stereoscopic pairs. Accuracies of stereo 
positioning are that planimetrie error is 28-45m and altimetric 
error is 14-30m. In the middle of 1990s, two satellites, ERS-1 
and Radarsat-1, have been launched successfully and high 
resolution SAR images could be acquired. And the high 
accuracy of composite positioning has been achieved too. In 
1993 Renouard and Perlant (Renouard L., 1993) combined 
SPOT and ERS image to achieve planimetrie error 15m and 
altimetric 10m. In 1994 Toutin chose Radarsat, RSO-C/X, ERS, 
SPOT and Landsat TM images, and stated planimetrie errors 
around 15m and altimetric around 20m. In 2004 Alain Giros of 
ESA tried to auto register and composite position SPOT and 
ERS-2 images to achieve planimetrie error 10-40m and 
altimetric 10-17m. (Jordi Inglada et al., 2004; Alain Giros, 
2005) In 2006 Fang Yong et al. (Fang Yong et al., 2006) tried 
to stereoplotting with Radarsat-1 and ERS-2 stereoscopic pair 
based on G. Konecny model and achieved planimetrie error 
34.24m and altimetric 14.08m. 
In this paper the stereoscopic pair composed of linear array 
push-broom and SAR space-bome images is discussed, its 
construction and procedure of stereo positioning are described 
in details. First the imaging models for linear array push-broom 
imagery and SAR imagery are introduced in section 2. Then the 
mathematical treatment of composite stereoscopic pair is 
constructed in section 3. Section 4 shows experimental results 
with six stereoscopic pairs and section 5 shows conclusions. 
2. TWO IMAGING MODELS 
2.1 The Scanning Model 
The linear array push-broom imagery is acquired with linear 
sensors by scanning the Earth surface. The relationship between 
ground and image is rigorous central projection. Each line of 
the image has different elements of exterior orientation. The 
collinearity equation of i line is expressed in the following 
way: (Qian Zengbo et al.,1992; Chang Benyi, 1989; Yan Qin et 
al., 2001)