## 4 Results and Validations
### ZTD Validation with the Final Tropospheric Products
Compared to the GPS-only solution, the initialization time for GFZC2 can be improved by about 5.8% and 8.1% with the dual-system and the four-system combinations, respectively. The averaged initialization time for the CLK92 RT products are 570 s (9.5 min), 522 s (8.7 min), and 510 s (8.5 min) for the GPS-only, the combined GPS/GLONASS, and the combined GPS/GLONASS/Galileo/BDS solutions, respectively, and the improvements of the dual-system and the four-system combined solutions to the GPS-only solution are about 8.4% and 10.5%, respectively. The averaged initialization time for different IGS-RT service in the single-system, the dual-system, and the four-system solutions with fixing coordinate are listed in Table 4.  
In order to evaluate the accuracy of RT ZTD estimates, their differences between the USNO final ZTD values are taken into account at each common epoch after the convergence. This will avoid the potential errors caused by the temporal interpolation of troposphere products. By processing GNSS observations on DOY 090, 2017 in the fixing coordinate mode, the accuracy of the estimated RT ZTDs derived from the five RT services are illustrated in Figure 8 for the GPS-only, the combined GPS/GLONASS, and the combined GPS/GLONASS/Galileo/BDS solutions, respectively. In the case of GPS-only, the results for CLK81 show the largest deviations with respect to the USNO final ZTD, which is followed by those for GFZD2. The CLK01 results agree slightly better with the final ZTD, compared to the CLK81 ones, while the best agreement can be obtained based \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solution** & **CLK01 (s)** & **CLK81 (s)** & **CLK92 (s)** & **GFZC2 (s)** & **GFZD2 (s)** \\ \hline GPS & 588 & 600 & 570 & 522 & 540 \\ GPS/GLONASS & 540 & 552 & 522 & 492 & 510 \\ GPS/GLONASS/Galileo/BDS & - & - & 510 & 480 & 498 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Averaged initialization time (units) for different IGS-RT service from the single-system, the dual-system, and the four-system solutions in the fixing coordinate mode. Figure 7: Averaged initialization time for all stations from the GPS-only, the combined GPS/GLONASS, and the combined GPS/GLONASS/Galileo/BDS four-system solutions with different IGS-RT service in the fixing coordinate modes. on the GFZC2 products, with less noise and fewer outliers. In the combined GPS/GLONASS and GPS/GLONASS/Galileo/BDS solutions, the GFZC2 results also agree the best with the USNO final ZTD, followed by CLK92, while the GFZD2 results reveal the largest deviations. Besides, a better agreement between the improved ZTD estimates and the reference values can be achieved in the combined GPS/GLONASS/Galileo/BDS ZTDs compared to the GPS-only ZTDs, which confirms the superiority of multi-GNSS again. Figure 9 illustrates the comparison between the RT ZTD and the USNO final ZTD products at station ONS1 in the kinematic mode for the single-, dual-, and four-system solutions. Compared to the fixing coordinate mode, the RT ZTD estimates in the kinematic mode present much larger deviations and more noise with respect to the final ZTD. Figure 8: Differences of the RT ZTD in the fixing coordinate mode, derived from the GPS-only (**a**), the combined GPS/GLONSS (**b**), and the combined GPS/GLONASS/Galileo/BDS (**c**) solutions, with the USNO final troposphere products on DOY 090, 2017 at station ONS1. The RMS values of the ZTD differences from the three solutions in the fixing coordinate and the kinematic modes with respect to the USNO final tropospheric products at station ONS1 on DOY 092, 2017 are shown in Figure 10. Generally, the RT ZTDs retrieved in the fixing coordinate mode show much  
Figure 9: Differences of the RT ZTD in the kinematic mode, derived from the GPS-only (**a**), the combined GPS/GLONSS (**b**), and the combined GPS/GLONASS/Galileo/BDS (**c**) solutions, with the USNO final troposphere products on DOY 090, 2017 at station ONS1. higher accuracy in comparison with those in the kinematic mode.