# Bayesian Filtering Multi-Baseline Phase Unwrapping Method Based on a Two-Stage Programming Approach
## 4 Results and Discussion
### Experiment 3  
In this experiment, we validate the proposed TSPA-based Bayesian filtering MBPU method with a real MB InSAR datasets. Figure 5a shows the real surface conditions of the study area. From the figure, we can see that the study area contains a large number of high mountains. In Table 4, we can see the major parameters of the real dataset. Figure 5b is an interferogram with a baseline length of \(-370.46\) m, and Figure 5c is an interferogram with a baseline length of \(-127.79\) m. From Figure 5b,c, the white lines are composed of the ICESat points. The accuracy of these ICESat points is about 14 cm. It can be seen from Figure 5a that the research area has obvious mountain undulations, and it was proved [30] that the SBPU method cannot obtain high-precision PU results. Figure 5d-g illustrates the unwrapped phase of Figure 5b obtained by TSPA, and the proposed TSPA-based Bayesian filtering MBPU methods, respectively. Figure 5h-k illustrates the unwrapped phase of Figure 5c obtained by TSPA, and the proposed TSPA-based Bayesian filtering MBPU method, respectively. It can be seen at a glance that the results obtained by different MBPU methods are very similar. This is because the experimental data have less noise and a larger study area. To further compare the performance of different MBPU methods, we provide the DEMs generated from the data of different MBPU results, and use ICESat data points to verify the accuracy of the results of different methods. As can be seen from Table 5, the standard deviations obtained by traditional TSPA method are 3.25 m for Figure 5d and 3.73 m for Figure 5h. The results of TSPAEKF are better than the TSPA method. The standard deviations of the obtained results are 3.08 m for Figure 5e and 3.04 m for Figure 5f. Similar to the previous simulation data results, TSPACKF also has better noise robustness. However, the accuracy of the results is the worst of the three proposed TSPA-based Bayesian filtering MBPU methods. The standard deviations obtained are 3.10 m for Figure 5f and 3.10 m for Figure 5i. TSPAUF is an improved algorithm, based on TSPAUKF. This method can obtain better results than other methods. Its standard deviations are 3.05 m  
Figure 4: (**a**) Digital elevation model (DEM) for simulation data. (**b,c**) Reference unwrapped phases ((**b**) long and (**c**) short baseline length). (**d,e**) Simulated wrapped phases of (**b,c**). (**f–i**) PU results of (**b**) obtained by (**f**) TSPA, (**g**) TSPAEKF, (**h**) TSPACKF, and (**i**) TSPAUIE. (**j–m**) Errors between (**b**) and PU results (**f–i**). (**n–q**) PU results of (**c**) obtained by (**n**) TSPA, (**o**) TSPAEKF, (**p**) TSPACKF, and (**q**) TSPAUIF. (**r–u**) Errors between (**c**) and PU results (**n–q**).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PU Method**} & \multicolumn{2}{c}{**Long Baseline**} & \multicolumn{2}{c}{**Short Baseline**} \\ \cline{2-5}  & **Figure** & **RMSE** & **Figure** & **RMSE** \\ \hline
**TSPA** & Figure 4j & 2.5464 & Figure 4r & 1.7760 \\
**TSPAEKF** & Figure 4k & 0.2865 & Figure 4s & 0.2354 \\
**TSPACKF** & Figure 4l & 0.3731 & Figure 4t & 0.2795 \\
**TSPAUIF** & Figure 4m & 0.2929 & Figure 4u & 0.2408 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The results of different PU methods in Figure 4j–m,r–u (unit: radians).