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This paper starts from defining the relative equations between the ground space and the image space, based on two radargrammetric conditions when the image is formed by the side- looking airborne radar system, furthermore, analyzing and studying for the mathematical model. The experimental data are two SAR images with opposite side-looking in the Chao-chou area, Pintung County. These two images are digital complex images, and the digital number is obtained from the number of the scan lines in the azimuth direction and the sample number in the range direction. Since the exterior orientation and the flight speed of the radar antenna carrier is time-varying, one goal of this paper is to find a mathematical model in order to define the time-varying characteristic. On the single SAR image , we used different order polynomials to describe the changes of dynamic exterior orientation and squint angle of SAR carrier , and then the track of the airborne carrier is solved by the mixed adjustment, therefore the three-D spatial coordinates of the 16 conjugate check points on two SAS images can be set up according to these data. The root mean square error of the ground conjugate points can be at the level of 7-8 m horizontally and 9m vertically ,if the solution is solved by the intersection of two images. With such an considerable improvement compared to the earlier researches, the mathematical model set up by this research is stated clearly in the following text.
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