The model based on range and Doppler equations (RD model) is the most precise model for SAR geolocation, and therefore SAR geolocation based on this RD model has become more and more popular. Unfortunately, the RD method requires iterative solution, in most case, which is time-consuming and prone to poor optimization due to observation errors of parameters. In face of the huge mass of measured data from global SAR measurements, how to improve processing speed while maintaining geolocation accuracy is an important problem. This paper examines how to solve the RD geolocation equations for single, interferometric, and stereo SAR. First, the RD geolocation equations for the three kinds of systems are abstracted into a unified equation form. Second, it is determined that the RD geolocation equation can be approximated as a mapping relationship using polynomials. Then a fast solution method for the unified geolocation equation is proposed based on the Range Doppler Polynomial Coefficient Model (RDPC). Third, the accuracy loss of the RDPC model is analyzed, and the precision differences among the three kinds of system are compared. Finally, several groups of TerraSAR-X measured data for the three modes are processed using the fast algorithm. The results show that the fast algorithm greatly reduces the amount of calculation while the geolocation accuracy loss is small. Performance evaluation demonstrates that the proposed method is efficient and correct.
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