# Preliminary Results on Tropospheric ZTD Estimation by Smartphone
## 3 Results
### Case Study 1  
The elaboration results carried out for Case study 1 are reported below, starting with the one obtained with CSRS-PPP. In the CSRS-PPP solution, after the initialization phase, lasting about 20-30 min, both the positioning solutions (Figure 2) and the ZTD estimations (Figure 3) become more stable, with a standard deviation of a few millimeters in this last case. As it is possible to see from Figures 2 and 3, there is a lack of measurements of  
Figure 1: Layout for Case study 2.  
about 13 min at about 12:45 UTC, due to unexpected events. Despite that, after a second initialization phase, the solution converges quicker than the first one. It is worth highlighting that, considering TOSM, CSRS-PPP is not able to estimate ZTD, but it provides the values coming from the Vienna Mapping Function (VMF) model due to the poor quality of the observation and noisy data collected and saved in the RINEX file, which contains long gaps. To check the behavior of different software, RTKLIB was considered on the same data. As expected, RTKLIB highlights a poor quality of the solution, obtained from the smartphone observations (TOSM), for both Up positioning component and ZTD (Figures 4 and 5, respectively). The residuals of the three positioning components of TORI and TOSM with respect to the corresponding reference positions, i.e., the convergence solution, are reported in Figures 6 and 7, respectively. Table 2 summarizes the statistics deriving from Figures 6 and 7. Figure 3: ZTD values for TORI (estimated, blue) and TOSM (Xiaomi Mi 8—modelled, orange) obtained with CSRS-PPP. Figure 2: TORI (blue) and TOSM (Xiaomi Mi 8—orange) Up component estimated with CSRS-PPP. Figure 4: Differences between estimated and reference coordinates for TORI (blue) and TOSM (Xiaomi Mi 8—orange) receivers, obtained with RTKLIB. Figure 5: ZTD estimates for TORI (blue) and TOSM (Xiaomi Mi8—orange) obtained with RTKLIB. Figure 6: Residuals of positioning components for TORI with respect to the reference position, as obtained with RTKLIB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Average (m)** & **Standard Deviation (m)** & **Root Mean Square (m)** \\ \hline \multirow{3}{*}{TORI} & E-W & \(0.16\) & \(0.29\) & \(0.33\) \\  & N-S & \(-0.10\) & \(0.20\) & \(0.22\) \\  & U-D & \(-0.04\) & \(0.14\) & \(0.14\) \\  & E-W & \(-0.45\) & \(0.56\) & \(0.72\) \\ \multirow{3}{*}{TOSM} & N-S & \(0.30\) & \(0.34\) & \(0.45\) \\  & U-D & \(0.85\) & \(1.36\) & \(1.60\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical parameters for the position outputs for TORI and TOSM with respect to the corresponding reference positions. The solution instability in the initial time span (approximately the starting 20-30 min) is particularly evident in Figure 4. This corresponds to the solution needing time to converge. After this phase, the positioning solution becomes more stable, and it is coherent with those available in the literature. The average difference between TORI and TOSM is about 0.8 m in the vertical component, while the ZTD estimation is at the order of 0.2 m. In this case, RTKLIB is able to estimate ZTD, for both TORI and TOSM, without introducing the VMF model as CRSR-PPP did. To analyze the differences of the ZTD estimations with the two types of considered software and to verify the independence of the software used, Figure 8 shows the comparison of tropospheric delay values obtained with the CSRS-PPP (in blue) and RTKLIB (in orange) software. Figure 9 shows the differences in ZTD values for the TOSM station, considering the CSRS-PPP and RTKLIB software. Figure 7: Residuals of positioning components for TOSM with respect to the reference position, as obtained with RTKLIB.