## 4 PIESAT-01 Digital Surface Model (DSM) Production Techniques
Additionally, adaptive filtering is employed for phase denoising to remove residual points caused by spatial decorrelation noise between the master and slave SAR images and system thermal noise. Phase unwrapping is a crucial step in obtaining high-precision terrain elevation information in InSAR imaging, and the unwrapped interferometric phase directly affects the accuracy of terrain elevation extraction. In this paper, the minimum cost flow algorithm is used for phase unwrapping. By utilizing the unwrapped phase, radar system parameters, and the geometric relationships in InSAR, height information for each pixel in the image can be calculated based on elevation conversion formulas. Through terrain correction, the DSM can be reconstructed using InSAR data processing. Finally, using the multi-baseline DSM data fusion technique compensates for low coherence, shadowing, and high-error areas, enhancing the accuracy of the DSM [31]. The weights commonly used in traditional weighted averaging methods are mostly based on the ratio of coherence coefficients or vertical baselines [32]. In this paper, theoretical height errors corresponding to interferometric phases of different baselines are utilized to achieve the fusion of multi-baseline DSMs. The weights are determined based on the statistical characteristics of the probability distribution of interferometric phases, taking into account the height error determined by jointly considering various InSAR geometric parameters such as incidence angle, vertical baseline, slant range, etc., involved in different interferometric combinations, making this approach more rational. Assuming a multi-baseline spaceborne InSAR system acquires \(n\) sets of interferometric phases, according to the conversion formula between interferometric phase and elevation, where any unwrapped interferometric phase and theoretical terrain elevation satisfy the following equation:  
\[h=\frac{\lambda R_{i}\sin\theta_{i}}{2\pi B_{\perp i}}\varphi_{i}\ \ \ i=1,2,\ldots,n \tag{12}\]  
where \(\varphi_{i}\) represents the \(i\)th set of interferometric phases, \(h\) denotes terrain elevation information, \(\lambda\) represents wavelength, \(R_{i}\) is the slant range of the \(i\)th interferometric pair, \(\theta\) stands for the incidence angle of the \(i\)th interferometric pair, and \(B_{\perp i}\) represents the vertical baseline length of the \(i\)th interferometric pair. Elevation ambiguity resolution, as an important evaluation metric in InSAR imaging technology, has a certain reference value for assessing the performance of multi-baseline InSAR height estimation. In theory, elevation ambiguity resolution can be utilized to invert the height phase into terrain elevation. After obtaining the standard deviation of phase noise, elevation ambiguity can be used to approximate the DSM theoretical error. The elevation ambiguity resolution corresponding to different baseline lengths in multi-baseline InSAR is as follows:  
\[H_{amb,i}=\frac{\lambda R_{i}\sin\theta_{i}}{B_{\perp i}} \tag{13}\]  
The standard deviation of height estimation \(\sigma_{h,i}\) caused by the estimation error \(\sigma_{\phi,i}\) of the \(i\)th (\(i=1,\ldots,\) N) observed interferometric phase is calculated as follows:  
\[\sigma_{h,i}=\frac{H_{amb,i}}{2\pi}\sigma_{\phi,i} \tag{14}\]  
Weight \(W_{i}\) is constructed using the height errors \(\sigma_{h,i}\) corresponding to different baselines according to the following:  
\[W_{i}=\frac{1}{\sigma_{h,i}^{2}}/\sum_{i=1}^{N}\frac{1}{\sigma_{h,i}^{2}} \tag{15}\]  
Finally, the weights constructed from the height error of each interferometric phase group are used to perform weighted fusion on the terrain elevation information \(h\) obtained from single-baseline interferometric processing of the \(i\)th group, as follows:  
\[\overline{h}=\sum_{i=1}^{N}W_{i}\cdot h_{i} \tag{16}\]  
For quantitative evaluation of DSM accuracy, mean error (ME) and root mean square error (RMSE) are commonly used.