# Assessment of Hongtu-1 Multi-Static X-Band SAR Constellation Interferometry
## 3 Results  
### Height Update  
The phase of the detrended differential interferograms corresponds primarily to residual topographic phase and phase noise. There is no deformation phase due to the simultaneous acquisition of both images in the interferometric pair. The atmospheric path delay phase [41; 42; 43; 44] is also negligible and only non-zero because of the slight spatial separation of the observation paths (by up to a few hundred meters). The residual topographic phase depends linearly on the difference between the true effective height of the scatterer and the assumed height based on the used DEM and linearly on the baseline component that is perpendicular to the line of sight. For a longer perpendicular baseline, the same height difference results in a larger differential interferometric phase--accordingly, pairs with longer baselines have higher phase-to-height sensitivity. While this has the positive effect of more precise height estimation, it also means that the higher phase gradients make phase unwrapping more challenging. Figure 4 shows the geocoded differential interferogram phase of a smaller section of the scene for three pairs with different baseline lengths. A significant non-zero phase is observed for forest areas and for areas where the topography has changed, e.g., due to mining or landfill. While the deviations from the zero phase are smaller than half a phase cycle for the shortest baseline--which makes phase unwrapping trivial--more significant phases are present in the pairs with longer baselines. The determined height corrections are shown in Figure 5. Positive values indicate that the height estimated with the HT1 data of 5 September 2023 is higher than the \(1^{\prime\prime}\) Copernicus DEM height. Both positive and negative height corrections are observed. No height correction was estimated for water areas and radar shadow, where the signal noise dominates. In the updating of the DEM, the height of the pre-existing DEM was used for these areas. Figure 4: Images showing 9 km \(\times\) 9 km sections of geocoded, detrended, multi-static HT1 differential interferograms. The sensor combination and the estimated perpendicular baseline are indicated below the images. One color cycle corresponds to one phase cycle. For a more detailed illustration of the different reasons for height changes, Figure 6 shows a smaller area of about 4.2 km \(\times\) 3.3 km that includes Zuomu Village and a section of the Liangzhu River. The 1\" Copernicus DEM used as topographic reference and the HT1 multi-static acquisition used to calculate height differences correspond to different dates. The Copernicus DEM is generated based on TanDEM-X/WorldDEM data acquired between December 2010 and January 2015 and ICESat GLAS reference point data acquired between 2003 and  
Figure 5: Height corrections relative to 1” Copernicus DEM heights. The image brightness corresponds to the shaded relief calculated from the corrected terrain heights. In areas without color, no height correction was determined. In the updating of the DEM, the height of the pre-existing DEM was used for these areas. Figure 6: A 4.2 km \(\times\) 3.3 km section of height corrections relative to 1” Copernicus DEM heights, derived from multi-static HT1 acquisition. The image brightness corresponds to the radar backscatter. Different color scales are used in the two visualizations. With the finer color scale used in the image to the right, small, meter-scale corrections become visible. The letters A to D indicate areas with different types of height changes (A: mining area; B: forest area; C: agricultural field; D: trees/hedges along a road) further discussed in the text. 2009. A more detailed description of the Copernicus DEM is provided in the Copernicus DEM Product Handbook [45]. The HT1 multi-static dataset used in this work was acquired on 5 September 2023. During the more than eight years between the acquisition of the two datasets, the terrain height changed in some areas.