## 4 PIESAT-01 Digital Surface Model (DSM) Production Techniques  
The InSAR technique is a technology that utilizes interferometric phase information to process two SAR single-look complex images of the same area, generating digital surface model (DSM) data [30]. The interferometric phase consists of the deformation phase, atmospheric delay error phase, topographic phase, orbit error phase, and noise phase. To obtain high-precision topographic phase results, effective estimation and elimination of the other components are necessary. Since the PIESAT-01 constellation can capture four sets of images of the same area in one imaging session, there is no deformation phase or atmospheric delay error phase caused by different acquisition times during the InSAR processing. The data exhibit extremely high coherence, which can significantly enhance the accuracy of DSM from the source. The DSM acquisition process of PIESAT-01 is illustrated in Figure 3, including coregistration of master and slave images, interferogram generation, flat-earth phase removal, interferogram filtering, phase unwrapping, raw DSM generation, and DSM fusion. The complex images coregistration is the first step in interferometric processing. Due to the incomplete overlap of satellite orbits and slight differences in the incident angles of satellite antennas, there are certain degrees of translation, rotation, and stretching in the corresponding pixel positions of the multiple SAR images used for coherent processing. To improve the coherence between SAR images, it is necessary to perform coregistration and resampling operations on SAR images to ensure that the same pixel points in SAR images obtained from different baselines correspond to the same target points on the ground. The coregistration accuracy of the two images should be better than 0.2 pixels to achieve the correct interferometric phase information between image pairs. The second step involves interferogram generation. The coregistered master and slave SAR images are conjugately multiplied, and their phase is extracted to obtain the interferogram. The interferometric phase reflects the slant range difference between the antennas of the master and slave satellites to the imaging scene. Due to the periodic nature of trigonometric functions, the interferometric phase is wrapped within the interval of \((-\pi,\pi]\). The coherence coefficient is a key parameter used in interferometric SAR processing to assess the coregistration accuracy between the master and slave SAR images and the  
Figure 3: The flowchart of PIESAT-01 DSM generation. quality of the interferometric phase. The expression for calculating the coherence coefficient is as follows:  
\[\gamma=\frac{E[S_{1}S_{2}^{*}]}{\sqrt{E\Big{[}\big{|}S_{1}\big{|}^{2}\Big{|}E \Big{[}\big{|}S_{2}\big{|}^{2}\Big{]}}} \tag{10}\]  
where \(S_{1}\) and \(S_{2}\) represent the master and slave SAR images, respectively. A higher value of the coherence coefficient \(\gamma\) indicates a higher quality of the interferometric phase, which is more beneficial for subsequent interferometric processing. In the interferometric phase, the relationship between the signal-to-noise ratio and coherence coefficient is as follows:  
\[SNR=\frac{\gamma}{1+\gamma} \tag{11}\]  
indicating that as the coherence coefficient increases, the signal-to-noise ratio of the interferometric phase also increases, leading to a higher-quality interferometric phase. Due to the presence of a flat-earth phase, the interferometric phase generated through the aforementioned steps exhibits regular stripe variations in the range direction, resulting in excessive phase wrapping and overly dense stripes in the interferometric phase map, significantly impacting the accuracy of phase unwrapping. To reduce the density of interferometric stripes and alleviate the difficulty of phase filtering and unwrapping, this paper eliminates the flat-earth phase, retaining only the height phase reflecting topographic changes in the imaging scene.