# Bayesian Filtering Multi-Baseline Phase Unwrapping Method Based on a Two-Stage Programming Approach
## 4 Results and Discussion
### Experiment 2  
In this experiment, the performance of TSPA and TSPA-based Bayesian filtering MBPU methods was verified using the simulation data in Figure 4d,e. Figure 4a is the employed digital elevation model in the experiment. The data are obtained by MATLAB simulation. Figure 4b,c show the reference unwrapped phases with different normal baseline lengths. Figure 4d shows the simulated wrapped phases of Figure 4b, with added phase noise using 0.95 mean correlation coefficient, and Figure 4e shows the simulated wrapped phases of Figure 4c, with added phase noise using 0.9 mean correlation coefficient. Figure 4f illustrates the unwrapped phase of Figure 4d obtained by TSPA, while Figure 4g-i  
\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 3j & 3.2803 & Figure 3r & 0.5734 \\
**TSPAEKF** & Figure 3k & 1.6736 & Figure 3s & 0.4576 \\
**TSPACKF** & Figure 3l & 1.6856 & Figure 3t & 0.4489 \\
**TSPAUIF** & Figure 3m & 1.6530 & Figure 3u & 0.4442 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The results of different PU methods in Figure 3j–m,r-u (unit: radians).  
Figure 3: (**a**) Digital elevation model (DEM) for simulation data (unit: m). (**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**) extended Kalman filter (TSPAEKF), (**h**) cubature Kalman filter (TSPACKF), and (**i**) unscented information filter (TSPAUIF). (**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**) TSPAUF. (**r–u**) Errors between (**c**) and PU results (**n–q**).  
illustrates the unwrapped phase of Figure 4d obtained by the TSPA-based Bayesian filtering MBPU methods, respectively. Figure 4j-m illustrates the errors between Figures 4f-i and 4b. From the Figure 4f, we can see that the traditional TSPA can obtain the PU results. However, due to the influence of noise, an obvious PU error has been generated in the upper right corner. From Figure 4g-I,k-m, it can be seen that the proposed TSPA-based Bayesian filtering MBPU methods can obtain better results than traditional TSPA, and obviously have better noise robustness. However, there is still a small amount of over-smoothing in the gradient-change regions. Figure 4n illustrates the unwrapped phase of Figure 4e obtained by TSPA, while Figure 4o-q illustrates the unwrapped phase of Figure 4e obtained by the TSPA-based Bayesian filtering MBPU methods, respectively. Figure 4r-u illustrates the errors between Figures 4n-q and 4c. It can be seen from the results that, although the short baseline interferogram is easier to unwrap, the result of the traditional TSPA is still not ideal, due to the influence of noise. However, the TSPA-based Bayesian filtering MBPU methods not only obtain great PU results, but have better noise robustness. As can be seen from Table 3, the long and short baseline PU accuracy of traditional TSPA are 2.5464 radians and 1.7760 radians, respectively. Due to the influence of noise, the accuracy of traditional TSPA is not very good. The TSPA-based Bayesian filtering MBPU methods proposed in this study, especially the TSPAEKF and TSPAUF methods, can obtain better results. The PU results of TSPACKF are relatively ineffective, but have better noise robustness. The efficiency of proposed TSPA-based Bayesian filtering MBPU methods are 7.97 s, 7.13 s, and 5.28 s, respectively. The efficiency of TSPA is 8.23 s, and it can be seen from the experiment that the proposed methods not only have better robustness, but also have better efficiency.  
Figure 4: Cont.