# 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  
In these experiments, we used different numbers of GCPs and CPs to validate the accuracy of the five models. In particular, zero, one (labeled G01/F01), three (G01/F01 to G03/F03), six (G01/F01 to G06/F06), twelve (G01/F01 to G12/F12), and twenty (G01/F01 to G20/F20) GCPs were selected, and the accuracies of the five types of refinement models are summarized in Tables 5 and 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**GCP/CP** & **Classical** & **One-Parameter** & **Three-Parameter** & **Four-Parameter** & **Six-Parameter** \\
**Number** & **Model** & **Parameter Model** & **Parameter Model** & **Parameter Model** \\ \hline
0/38 & 1.19 & 1.19 & 1.19 & 1.19 & 1.19 \\ \hline
1/37 & 0.61 & 0.53 & / & / & / \\ \hline
3/35 & 0.39 & 0.38 & 0.38 & / & / \\ \hline
6/32 & 0.32 & 0.38 & 0.33 & 0.34 & 0.38 \\ \hline
12/26 & 0.20 & 0.32 & 0.18 & 0.20 & 0.21 \\ \hline
20/18 & 0.20 & 0.31 & 0.20 & 0.18 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Geolocation accuracy in miniKu-2 for the five models with different GCPs (unit: meters). Figure 5: GCP distribution and parts of the two UAV miniSAR-Ku images: GCP distribution in the miniSAR-Ku-1 (**a**) and miniSAR-Ku-2 (**b**) images; parts of the miniSAR-Ku-1 (**c**) and miniSAR-Ku-2 (**d**) images. The numbers in Figure (**a,b**) are serial numbers of the GCPs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**GCP/CP** & **Classical** & **One-Parameter** & **Three-Parameter** & **Four-Parameter** & **Six-Parameter** \\
**Number** & **Model** & **Parameter Model** & **Parameter Model** & **Parameter Model** \\ \hline
0/28 & 1.36 & 1.36 & 1.36 & 1.36 & 1.36 \\ \hline
1/27 & 0.57 & 0.61 & / & / & / \\ \hline
3/25 & 0.38 & 0.47 & 0.39 & / & / \\ \hline
6/22 & 0.32 & 0.40 & 0.30 & 0.31 & 0.36 \\ \hline
12/16 & 0.17 & 0.33 & 0.17 & 0.16 & 0.17 \\ \hline
20/8 & 0.16 & 0.29 & 0.17 & 0.13 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Geolocation accuracy in miniKu-1 for the five models with different GCPs (unit: meters). In the absence of GCPs, the image orientation accuracies for the miniKu-1 image were 8.45/2.76 pixels in the distance/azimuth direction, and the mean absolute values for all CPs were 7.97/2.45 pixels. For the three-parameter model with 12 GCPs, the accuracies were 0.86/1.02 pixels for the GCPs and 0.95/0.91 pixels for the CPs. Similarly, in the absence of GCPs, the orientation accuracies for the miniKu-2 image were 7.29/1.81 pixels, with mean absolute values of 7.22/1.42 pixels. For the three-parameter model with 12 GCPs, the GCP accuracies were 0.89/0.77 pixels, and the CP accuracies were 1.01/0.89 pixels. For the miniKu-2 image, 12 GCPs were utilized to refine the three-parameter model and the classical model, and the refined parameters were subsequently employed to orthorectify the image. The Digital Orthophoto Map (DOM) obtained using the three-parameter model and DEM from AW3D30-V2.2 [42] is shown in Figure 6, and the stitched images in two local regions (indicated by the boxes in Figure 6) for both models are displayed in Figure 7. In the stitched images of the local areas, part A and part C (top-left and bottom-right) represent the corrected results achieved using the three-parameter model, while part B and part D (bottom-left and top-right) show the corrected results obtained using the classical model. In the airSAR-X image experiments, it was observed that the two uncalibrated images exhibited geolocation accuracies of 174.5 and 183.7 m, constituting a difference of nearly 10 m. When considering orientation accuracy, the two image orientation accuracies in the range/azimuth direction were 514.85/4.83 pixels and 514.14/4.42 pixels, respectively, with the difference being less than 1 pixel. Within the same scene imagery or among images acquired with the same sensor in close temporal proximity, the image orientation residual errors demonstrated greater consistency, compared to the errors for geolocation coordinates.