## 3 Results
### Results and Analysis
#### 3.2.1 Satellite Position Inversion Accuracy Evaluation  
In the scope of this research, the satellite's position during imaging was determined utilizing the innovative autonomous LOS vector intersection method formulated specifically for this study. To assess the efficacy of this method, a detailed comparison was conducted between the satellite positions calculated using this technique and those documented in the ephemeris data. The ephemeris provides a meticulous description of the satellite's trajectory, capturing its precise position and velocity at sequential time intervals. For the purpose of accurate determination, the ephemeris data were subjected to both temporal and spatial interpolation to pinpoint the exact position of the satellite at designated moments. This study conducted a thorough evaluation of the inversion method's accuracy by comparing the satellite positions and radar incident angles derived from our autonomous LOS vector intersection approach with the positions provided by the ephemeris data and the true incident angle. The comparative analysis highlighted discrepancies in satellite  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Area1**} & \multicolumn{3}{c}{**Area2**} \\ \hline Radius & 116.06\({}^{\circ}\)–116.78\({}^{\circ}\) E, 38.92\({}^{\circ}\)–40.30\({}^{\circ}\) N & 116.06\({}^{\circ}\)–116.78\({}^{\circ}\) E, 38.92\({}^{\circ}\)–40.30\({}^{\circ}\) N \\ Group & A & B & C & D \\ Rail & descent & lift & descent & lift \\ Date & 8 September 2016 & 21 December 2016 & 27 December 2016 & 16 February 2017 \\ Image ID & gf1 & gf2 & gf3 & gf4 & gf5 & gf6 & gf7 & gf8 & gf9 & gf10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: GF-3 data.  
Figure 4: GF-3 data. (**a**) area1; (**b**) area2. The red box indicates the data of rail lift and the blue box indicates the data of rail descent.  
position \(\Delta S\), slant-range errors \(\Delta R\), and incident angle error \(\Delta\theta\), which were systematically documented and are detailed in Table 2 and visually represented in Figure 5.  
Table 2 shows that satellite position errors for the images range from 0.8041 m to 63.1564 m, with an average value of 20.4998 m. In contrast, slant-range errors vary from 0.0001 m to 0.4523 m, with an average of 0.0430 m, and the average error of the incident angle is only 0.0001\({}^{\circ}\). Figure 5a visually presents the distribution of satellite position errors, revealing significant fluctuations in satellite position errors across different images, though within a specific range. For instance, satellite position errors for the gf6, gf7, and gf10 images are relatively small, with the minimum error being less than 1 m. In contrast, errors for the gf5 and gf9 images are comparatively larger; however, the maximum error remains within several tens of meters. Figure 5b illustrates the distribution of slant-range errors, with all the errors confined to within 0.5 m. The slant-range error curves show that the gf-8 image exhibits a significant abrupt change in error, whereas the error curves for the other images, excluding gf-8, are relatively smooth. In conclusion, the satellite position inversion method employed in this study proves highly effective, yielding minimal satellite position errors and negligible slant-range errors.