# High-Resolution Spaceborne SAR Geolocation Accuracy Analysis and Error Correction
## 2 Materials and Methods
### Materials and Experiments  
Our study area is located within the Changping District of Beijing, China, spanning latitudes 40.15\({}^{\circ}\)N to 40.27\({}^{\circ}\)N and longitudes 116.20\({}^{\circ}\)E to 116.35\({}^{\circ}\)E, covering an area of 10 km \(\times\) 10 km. The geomorphological types from northeast to southwest are a mountainous region, a piedmont alluvial fan, and a plain. The measurement points were obtained by GNSS differential measurement with centimeter-level 3D positioning accuracy. A total of 164 points were utilized (Figure 6), of which 135 are situated in flat locations within the plain or piedmont alluvial fan areas, and 29 are in the mountainous region. Figure 5: The relationship between the elevation-related geolocation error in range and on the ground. The range error is \(\Delta s_{de}=\Delta hcos\theta\), while on the ground it is \(|OB|=\Delta hcot\theta\). Figure 6: The geographical distribution of the measurement points. This study used 11 TerraSAR-X images and a pair of Tianhui-2 images. The TerraSAR-X satellite constellation operates in the X-band at a frequency of 9.65 GHz. It comprises two identical satellites, TerraSAR-X and TanDEM-X, which exhibit nearly the same performance. The two satellites were launched in June 2007 and June 2010. The TerraSAR-X images we used were acquired by the TanDEM-X satellite, from 3 July 2018 to 29 May 2019, and are Level 1B single-look complex (SLC), slant-range, and HH-polarized images in the stripmap mode. The ground resolution is azimuth 3.3 m \(\times\) range 2.2 m, the pixel size is azimuth 1.8 m \(\times\) range 0.9 m, and the swath is azimuth 50 km \(\times\) range 30 km. The Tianhui-2 satellite constellation, similar to TerraSAR-X, comprises two identical satellites that operate in the X-band at a frequency of 9.60 GHz. The reference and secondary satellites acquired the selected images on October 28 th, 2019, and are Level 1B SLC, slant-range, and HH-polarized images. They share the same image parameters. The ground resolution is 3.0 m in both azimuth and range, the pixel size is azimuth 2.0 m \(\times\) range 0.9 m, and the swath is azimuth 30 km \(\times\) range 30 km. The orbit accuracy of the Tianhui-2 satellites is lower than that of TerraSAR-X, with potential errors reaching up to 2 m [41,42]. We first verified the completeness of the geolocation error decomposition in Equations (1) and (2). In Section 3.1, we geolocate the measurement points based on the GNSS elevations, correct the tropospheric delay through the RT method, implement the ionospheric correction, and evaluate the results. When performing tropospheric correction, we utilize ERA5 data and the WRF program. ERA5 is a reanalysis dataset for the troposphere derived from global meteorological observations [25], dividing the troposphere into 37 layers according to the pressure, providing the pressure, temperature, and vapor partial pressure for each layer, with a horizontal resolution of 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) and a temporal resolution of 1 h. The WRF is a high-accuracy numerical weather model widely applied in InSAR research [43]. We input the ERA5 data as the initial condition into the WRF to obtain atmospheric parameters at the imaging time with a resolution of 0.01\({}^{\circ}\)\(\times\) 0.01\({}^{\circ}\). For the ionospheric correction, we utilize the TEC products from the International GNSS Service (IGS). The TEC product, recorded in units of 0.1 TECU (10\({}^{15}\)/m\({}^{2}\)), comes with a spatial resolution of 2.5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) and a temporal resolution of 2 h [44]. Section 3.2 checks the validity of ERA5, analyzes the characteristics of the tropospheric delay, and compares the performances of the RT method and the ZDM method. Owing to a lack of in situ data, we verify ERA5 using the ZPD data from the BJFS station near the study area.