# An Image Compensation-Based Range-Doppler Model for SAR High-Precision Positioning
## 5 Conclusions  
Due to the complexity and the empirical nature of precision assignment in SAR rigorous model refinement, among other shortcomings, the number of commercial remote sensing software packages capable of supporting SAR image high-precision positioning with rigorous models is significantly fewer compared to those for optical images. In this study, we presented an image compensation-based R-D (ICRD) model that can achieve high-precision geometric positioning and be used for the geometric correction of spaceborne and airborne SAR images. The experimental results demonstrate that the proposed model can achieve the same accuracy as the classical R-D refinement model, and can also be applied to the same range of scenarios as the classical model. However, when compared to the classical refinement models, the proposed ICRD model is much simpler and easier to implement. As the number of parameters to be solved is small, the solution of our model is more robust under the condition of sparse GCPs. Furthermore, our model can be applied not only to spaceborne SAR images but also to airborne SAR images, whereas the RFM-based approach is usually applied to spaceborne SAR images. The method presented in this paper not only significantly simplifies the positioning process of the classical R-D model but also provides a foundation for ensuring consistency in the positioning and geometric correction of imagery from various aerospace SAR sensors. As the precision information of the original auxiliary parameters of the imagery is not required when modeling, we can deviate from the conventional technical approach of tailored modeling for specific sensors to achieve high-precision positioning with the R-D model. In the preprocessing stage, we merely extract the image parameters from various sensors and incorporate them into standardized structural data. During the intermediate positioning calculations, the software provides a unified algorithm and program for the mutual conversion between image space and object space coordinates. In the parameter optimization phase, the four image compensation models exhibit distinct characteristics under varying GCP conditions, and the construction and selection can be made based on requirements. Depending on the image type and characteristics, as well as the number, accuracy, and distribution information of GCPs, a program can be designed to automatically select the most suitable compensation model. Alternatively, following the method outlined in [38], the program can utilize the four-parameter model and treat the refined model parameters as weighted virtual observations within the adjustment model, thus enabling the image compensation model to cater to the requirements of various scenarios and conditions. SAR image types mainly include ground-based SAR, airborne SAR, and spaceborne SAR. However, whether the proposed method is suitable for ground-based SAR applications has not been studied. In addition, our model and approach, similarly to the classical R-D model, need to provide imaging, sensors, and orbital parameters. Without this information, the implementation of our method would not be feasible. The methods in this paper are mainly applied to SAR data obtained from R-D imaging. Images imaged by other methods, such as back projection imaging data, have not been verified using the methods in this paper. Although the image refinement model proposed in this article has the advantages of simple computation, high accuracy, robust solutions, and broad applicability, this study mainly focused on the application of single-scene SAR images, confirmation of the feasibility of the models, and the provision of a basis for further applications. Stereo positioning and block adjustment of multi-view SAR images are important aspects in SAR geometric processing.