# An Image Compensation-Based Range-Doppler Model for SAR High-Precision Positioning
## 3 Experiments
### Experiments Conducted on UAV-Mounted miniSAR-Ku Strip Images
#### 3.3.2 Experimental Results
The tests for airborne miniSAR-Ku and spaceborne SAR images exhibited a similar trend. This consistency provides further experimental support for the application of compensation functions in imagery as an alternative approach to achieving high-precision SAR image positioning. The airSAR-X tests indicated that, even though internal and external geometric calibrations were not carried out for the sensors and the original parameters of the image revealed poor accuracy, satisfactory accuracy can still be achieved using the compensation model and sparse GCPs, suggesting that low-order polynomials can effectively absorb the significant image errors derived from coarse sensor parameters. The one-parameter model is capable of geometric positioning across various GCP configurations. Even for images whose original parameters are insufficiently accurate, such as airborne SAR data, a single GCP could significantly enhance the performance. The positioning results--both with sparse and sufficient GCPs--demonstrated that the one-parameter model enhances the accuracy of spaceborne SAR images more significantly than it does the airSAR-X and miniSAR-Ku images, enabling it to readily achieve near-pixel precision, meaning that the errors of satellite images exhibit more regularity compared to those of airborne images. The three-parameter model consistently yielded optimal performance for all tested SAR image types. Its accuracy was comparable to that of the classical refinement model, regardless of GCP density. Compared to those caused by image resolution, the differences in geolocation accuracy were negligible. Moreover, when there were enough GCPs, the three-parameter linear model was superior to the one-parameter model. Comparing the four- and six-parameter models with the three-parameter model, when there were enough GCPs, the four- and six-parameter models outperformed the three-parameter model. However, the distinction in accuracy between the four- and six-parameter models was minimal when compared to the image resolution. When there were sparse GCPs, the accuracy of both models with respect to CPs was lower than that of the three-parameter model, and the accuracy of the six-parameter model was lower than that of the four-parameter model. This means that sparse GCPs render muti-parameter models prone to overfitting. From the experimental results, it is evident that the three-parameter model reaches an accuracy comparable to that of the classical refinement model for satellite images. Under the condition of sufficient GCPs, the four-parameter model slightly outperforms the three-parameter model and the classical model, with regard to the positioning of large-width or long-strip images. Furthermore, in scenarios with sparse GCPs, the one-parameter model can achieve an accuracy approximately comparable to that of the classical model. The experimental results demonstrate that, through selecting the appropriate compensation model based on the number and distribution of control points, it is possible to achieve--or even slightly exceed--the precision of the classical model. The ICRD shares similarities with the RFM of satellite imagery in its processing approach, both of which employ low-order polynomial compensation in the image space to mitigate imaging errors. This paper took imagery from two spaceborne sensors as the research subjects and compares the results of the proposed ICRD model with those of the RFM. Based on the R-D model, we first fitted the RPC parameters for the corresponding images [21; 28], achieving fitting accuracy losses of less than \(10^{-4}\) and \(10^{-3}\) pixels, respectively, for TerraSAR-X and GF-3. We then utilized the RFM to incorporate one-parameter and three-parameter compensation models in the image space, and compared the results with those obtained under the same experimental conditions. The differences in accuracy under various conditions were all less than \(10^{-3}\) pixels.