# High-Resolution Spaceborne SAR Geolocation Accuracy Analysis and Error Correction
## 3 Results
### Characteristics of the Elevation-Related Error  
We calculated the elevation-related error by subtracting the GNSS-based result from the DEM-based result. When geolocation was implemented on the WorldDEM and the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Satellite**} & \multirow{2}{*}{**Band**} & \multirow{2}{*}{**Frequency**} & \multicolumn{2}{c}{**Ionospheric Delay**} & \multirow{2}{*}{**VTEC Leads to 1 m of the Delay**} \\  & & & & **Corresponding to 25 TECU** & \\ \hline TerraSAR-X & X & 9.65 GHz & 0.19 m & 134.6 TECU \\ Sentinel-1 & C & 5.41 GHz & 0.59 m & 42.3 TECU \\ ALOS-2 & L & 1.26 GHz & 10.89 m & 2.3 TECU \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters associated with ionospheric delay in the three bands.  
Figure 14: (**a**) Variation in the VTEC at 12 PM and 6 PM local time in the study area during 2019; (**b**) average VTEC at 6 PM local time in the study area in 2019. The red dot indicates the location of the study area.  
SRTM, the elevation-related error, \(\Delta s_{ele}\), corresponding to the peak probability density, is negative in both cases (Figure 15a), indicating a tendency for the DEM elevation to be larger than the GNSS elevation at the measurement points. Specifically, the peak-density error is \(-1.5\) m for the SRTM, and the absolute error is less than \(4.0\) m for 83% of the measured points. For the WorldDEM, the peak-density error is \(-0.6\) m, and the absolute error is less than \(2.0\) m for 86% of the points (Figure 15b). Considering that the atmospheric correction residual is typically less than \(1\) m and often around \(0.1\) m, we conclude that the range geolocation error, \(\Delta s_{gg}\), can generally be controlled to within \(5\) m when using the SRTM and to within \(3\) m when using the WorldDEM. There is no relatively effective method for correcting the elevation-related error, so the influence of this error can be considered the most severe among all contributing factors.  
We analyzed the distribution of \(\Delta s_{ele}\) and found that it exhibits a significant correlation with the slope of the measurement points (Figure 16). As the slope increases, the distribution of \(\Delta s_{ele}\) becomes less focused, and the average gradually drifts away from the origin point. For the points with the same slope intervals, \(\Delta s_{ele}\) is smaller overall for the WorldDEM than the SRTM. By comparing the optical images at the time the SAR images were acquired and when the DEMs were obtained, we discover that the terrain around the points with the largest \(\Delta s_{ele}\) has undergone significant changes, indicating that utilizing the DEM close to the time the image is obtained can help prevent extreme conditions.  
Figure 16: (**a**) KDE curves of the geolocation error, \(\Delta s_{ele}\), based on the WorldDEM. Measurement points were divided into four groups based on the slope, using threshold values of \(0\), \(25\%\), \(50\%\), and \(75\%\); (**b**) KDE curves of \(\Delta s_{ele}\) based on the SRTM.  
Figure 15: (**a**) KDE curves of the geolocation error, \(\Delta s_{ele}\), based on the WorldDEM and SRTM; (**b**) cumulative percentage curves of the geolocation error, \(|\Delta s_{ele}|\), when based on the two DEMs.