# High-Resolution Spaceborne SAR Geolocation Accuracy Analysis and Error Correction
## 3 Results  
### Geolocation Accuracy  
We chose the image acquired on 17 January 2019, as the reference image for the TerraSAR-X. First, we visually selected the measurement points in the TerraSAR-X reference image and then coregistered it to other TerraSAR-X images to control the quality of the point selection. For each measurement point (Figure 7a), we selected a 65 m \(\times\) 65 m area surrounding it, subdividing it into 1 m \(\times\) 1 m grids, and transferring the image onto this area based on the GNSS elevation. Given that the elevation-related geolocation error, \(\Delta s_{ele}\), is at the centimeter level, the range geolocation error, \(\Delta s_{rg}\), is approximately equivalent to the atmospheric delay, \(\Delta s_{tro}+\Delta s_{ion}\). The geolocation results without atmospheric correction have smaller range coordinates (Figure 7b), consistent with the model in Equation (9). Wechecked the geolocation results with the atmospheric correction for all 164 measurement points and found that every point was accurately geolocated to the expected coordinate (Figure 7c), indicating that the geolocation residuals, \(\Delta s_{rg}\) and \(\Delta s_{aze}\), were less than 1 m. The results substantiate the completeness of the geolocation error decomposition in Equations (1) and (2) and the effectiveness of the atmospheric correction. Through the geolocation procedure proposed in Section 2.4, the TerraSAR-X images can achieve an accuracy better than 1 m.  
We coregistered the TerraSAR-X images using version 2.6.3 of the Interferometric Synthetic Aperture Radar Scientific Computing Environment (ISCE) software. The ISCE resampled the secondary image to the coordinate system of the reference image before coregistration to mitigate terrain effects, which is equivalent to geolocation without atmospheric correction (Figure 7b) but in the radar center coordinate system. The ISCE uses a constant offset in each direction to describe the coregistration result (Figure 8). In azimuth, the offsets are all less than 0.1 pixels, indicating virtually no geolocation error. In range, the offsets are less than 0.2 pixels, except for the image acquired on 5 August 2018, for which the tropospheric delay is about 0.3 pixels larger than those of the reference image. Therefore, we infer that the main cause of the offset is the difference in the tropospheric delay. The offsets affected by other factors, including the difference in ionospheric delays, are usually less than 0.2 pixels.  
By contrast, the Tianhui-2 image geolocation results exhibit noticeable residuals. The geolocation error of the reference image is approximately \(-1\) m in azimuth and \(-1.5\) m in range (Figure 9a). For the secondary image, the azimuth geolocation error is \(-1\) m, too, while the range error is estimated to be \(-2.5\) m (Figure 9c). Because the geolocation error aligns with those of other studies [40], we infer that the primary source of the geolocation residual is the orbit error of the Tianhui-2 satellites. The secondary image's lower geolocation accuracy may be attributable to deficiencies in time synchronization between the two satellites. We shifted the reference image by \(-1\) m in azimuth and \(-1.5\) m in range to correct the results and performed a similar correction for the secondary image (Figure 9b,d). We found that both images could geolocate all of the measured points accurately, indicating that the residual is independent of the imaging time, range, and  
Figure 7: Geolocation results for two representative measurement points: (**a**) measurement points depicted in a Google Earth image; (**b**) TerraSAR-X image results without atmospheric correction; (**c**) TerraSAR-X image results with atmospheric correction. The red boxes indicate the measurement points, and the arrows denote the range direction.  
Doppler frequency. The results also substantiate the effectiveness of the geolocation model for the secondary satellite described in Section 2.4.