# Improved Least Squares Phase Unwrapping Method Based on Chebyshev Filter
## 3 Results
### The Real InSAR Phase Unwrapping Results of Sentinel-1  
We selected two sentinel-1 IW data from 12 January 2023 and 24 January 2023 covering the position (30.43 N, 103.02 E), and the experimental data are distributed over strip 6 of IW2. The Sentinel-1 satellite is a C-band SAR launched by ESA in 2014; its data are currently available for free on the Copernicus Data Space Ecosystem. It has been widely used in marine environment monitoring, land change detection, earthquake detection, and landslide detection. Using real Sentinel-1 InSAR phase data for phase unwrapping experiments can better reflect the advantages and disadvantages of the phase unwrapping algorithm.  
The terrain data located in Yaan City, Sichuan Province, China, with a maximum and minimum elevation difference of about 500 m was used. Before phase unwrapping, 1 \(\times\) 5 multi-looking was applied to the data in azimuth and range. Phase interference was performed after image registration. Then the reference ellipsoid phase was removed, and then the Goldstein filter [31] with a coefficient of 0.5 was selected for phase filtering, and finally, a 500 \(\times\) 500 wrapped phase map in the horizontal and vertical was obtained. As shown in Figure 7a, it can be seen that the phase interference fringes are relatively dense and there is a large amount of noise residue, which provides favorable conditions for verifying the effectiveness of this method. Figure 7b shows the real-terrain simulated phase, which uses the Digital Elevation Model of Shuttle Radar Topography Mission [32] information and was generated under the same conditions as the InSAR phase data.  
Using the same unwrapping methods as the simulated test, the unwrapping error results are shown in Figure 8 and Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Times (s)** & **Error Range (rad)** & **RMSE (rad)** \\ \hline LS & 0.0483 & [\(-\)13.4945, 10.9733] & 4.6728 \\ PCUA & 8.1418 & [\(-\)11.0035, 8.4564] & 2.6099 \\ RPUA & 3.4221 & [\(-\)13.5213, 9.5692] & 3.6979 \\ Proposed & 3.0237 & [\(-\)9.2915, 6.9055] & 1.6866 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The times, error range, and RMSE of the true phase unwrapping.  
Figure 7: The wrapped phase data and the real phase data. (**a**) The wrapped phase. (**b**) The real phase data.  
It can be seen from Figure 8a that the incompletely unwrapped phase range in the error map obtained by the LS phase unwrapping method is the highest. From Table 2, it can be seen that the RMSE obtained by the LS phase unwrapping method is the largest and the error range is the widest; its biggest advantage is that it can be quickly unwrapping. It can be seen from Figure 8b,c that PCUA and RPUA reduce the incompletely unwrapped area and phase range compared to the LS phase unwrapping method, but there will still be more incompletely unwrapped areas and larger phase error. As can be seen from Table 2, PCUA takes the most phase unwrapping time but has a lower RMSE than LS and RPUA. Although RPUA reduces the processing time, it has a larger RMSE and a wider error range than PCUA. As can be seen from Figure 8d and Table 2, the proposed method has the smallest incomplete unwrapping area and the smallest incomplete unwrapping phase range, and the unwrapping time is about 62.86% and 11.64% shorter than PCUA and RPUA, respectively. Compared with LS, PCUA, and RPUA, the proposed method has the smallest RMSE, which is reduced by 63.91%, 35.38%, and 54.39%, respectively.