# Bayesian Filtering Multi-Baseline Phase Unwrapping Method Based on a Two-Stage Programming Approach
## 4 Results and Discussion
### Experiment 1  
In the first experiment, the performance of the TSPAEKF, TSPACKF, and TSPAUIF methods is verified with a simulated InSAR dataset, and compared with traditional TSPA. Figure 2(a) is the reference elevation used in this experiment. We can see that the simulated data has complicated terrain fluctuations. Figure 2(b) shows the reference unwrapped phases with a baseline length of 389.20 m, whereas Figure 2(c) shows the reference unwrapped phases with a baseline length of 112.10 m. Figure 2(d) shows the simulated wrapped phases of Figure 2(b), and Figure 2(e) shows the simulated wrapped phases of Figure 2(c). From Table 1, we can see the parameters of simulated InSAR data. Figure 2(f) is the PU result of Figure 2(d) by TSPA, while Figure 2(g)-i illustrate the unwrapped phase of Figure 2(d) obtained by the TSPAEKF, TSPACKF, and TSPAUIF methods, respectively. Figure 2(j)-m illustrates the errors between Figures 2(f)-i and 2(b). It can be seen from the figure that TSPA produces a significant error transmission phenomenon, due to the influence of noise. Although TSPAEKF, TSPACKF, and TSPAUIF also produce error transmission phenomena, their error transmission areas are significantly smaller than that of TSPA. We can see that different methods produce errors in areas with large gradient changes. This is due to the low interference phase quality in areas with large gradient changes. Although they limit the range of error transmission to a small range, they produce obvious over-smoothing in areas with large gradient changes. Figure 2(n) is the PU result of Figure 2(d) by TSPA, while Figure 2(o)-q illustrates the unwrapped phase of Figure 2(b) obtained by the TSPAEKF, TSPACKF, and TSPAUIF methods, respectively. Figure 2(r)-u illustrates the errors between Figures 2(n)-p and 2(c). From the results of the short baseline, it can be seen that these interferograms can obtain better PU results than long baseline interferograms, but that there is still an error transmission phenomenon in the areas of dense noise. The MBPU method of this Bayesian filtering method has better accuracy. In comparison, several Bayesian filtering MBPU methods can obtain more accurate results. From Table 2, we can see that the long baseline results obtained by TSPA are 3.2803 radians, while the results of TSPAEKF, TSPACKF, and TSPAUIF are 1.6736 radians, 1.6856 radians, and 1.6530 radians, respectively. The short baseline results are similar to the long baseline results. However, the short baseline interferogram is less difficult to unwrap, so the accuracy of these PU methods is very close. Nevertheless, the accuracy of the proposed MBPU methods is still better than that of traditional TSPA. It can be seen from the results that the TSPA-based Bayesian filtering MBPU methods proposed in this paper have a better noise robustness than TSPA. In this experiment, the TSPA consumes 40.55 s, while the TSPAEKF, TSPACKF, and TSPAUIF consume 13.84 s, 11.67 s, and 8.38 s, respectively. The efficiency of proposed TSPA-based Bayesian filtering MBPU methods are better than TSPA.