## 4 Performance Assessment of Single Point Positioning with Smartphone Code Pseudoranges
### Positioning Methodology
Red crosses represent the outliers. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**GPS**} & \multicolumn{4}{c}{**Multi-GNSS**} \\ \cline{2-10}
**Smartphone** & \multicolumn{2}{c}{**el. Weighting**} & \multicolumn{2}{c}{\(C/N_{0}\) Weighting**} & \multicolumn{2}{c}{**el. Weighting**} & \multicolumn{2}{c}{\(C/N_{0}\) Weighting**} \\ \cline{2-10}  & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\  & **[m]** & **[m]** & **[m]** & **[m]** & **[m]** & **[m]** & **[m]** & **[m]** \\ \hline Xiaomi Mi 8 & 10.61 & 8.25 & 7.77 & 4.57 & 7.50 & 4.63 & 6.13 & 3.52 \\ Xiaomi Mi 9 & 14.85 & 17.15 & 9.62 & 5.15 & 9.87 & 5.71 & 7.21 & 3.58 \\ Huawei P 30 & 7.72 & 4.73 & 6.25 & 3.38 & 6.72 & 3.73 & 5.07 & 2.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Three-dimensional coordinate error statistics (mean and STD) for GPS and multi-GNSS solutions with elevation and \(C/N_{0}\)-dependent weighting schemes. The complete computation of all statistics is shown in Table 3 (where the mean and STDs of the positioning errors are listed) and Table 4 where the RMSs of the horizontal, vertical, and three-dimensional coordinate errors are reported. The results shown in the tables confirm what was previously stated. Here, for the sake of brevity, we will only comment on the results obtained using the best weighting scheme (\(C/N_{0}\)). The best performance is obtained by the Huawei P30. If the multi-GNSS signals are used, the horizontal, vertical, and three-dimensional RMS error are 3.24 m, 4.73 m, and 5.73 m, respectively. Even in the case of using only the GPS constellation, this smartphone shows the best performance with horizontal, vertical, and three-dimensional RMS errors of 4.47 m, 5.52 m, and 7.10 m, correspondingly. The performance of the Xiaomi Mi 8 is slightly worse than that of the Huawei P30 but still comparable: the errors of the Mi 8 are higher than those of the P30 by about 1.5 m (the maximum difference recorded is less than 2 m while the minimum is 0.9 m). Finally, the worst performances are obtained by the Xiaomi Mi 9 as predicted in the section where we analyzed the observables. For this smartphone, we get a three-dimensional RMS error of 10.92 m in the GPS configuration and of 8.05 m in the multi-GNSS configuration compared to the 7.10 m and 5.73 m obtained by the Huawei P30. Figure 12: Horizontal coordinate component error scatter plots for single point positioning: elevation (represented in blue marker) versus \(C/N_{0}\) (represented in red marker) dependent weighting schemes for multi-GNSS (first row) and GPS (second row) solutions. Xiaomi Mi 8, Xiaomi Mi 9, and Huawei P30 smartphones are shown in the left, middle, and right panels, respectively. Figure 13: Time series of vertical coordinate component error for single point positioning: elevation (represented in blue marker) versus \(C/N_{0}\) (represented in red marker) dependent weighting schemes for GPS (first column) and multi-GNSS (second column) solutions. Xiaomi Mi 8, Xiaomi Mi 9 and Huawei P30 smartphones are shown in the top, middle, and bottom rows, respectively. The results, as it was legitimate to expect, also highlight the clear improvement obtained when using the multi-constellation observations. The advancement is significant for all three smartphones: if we refer to the horizontal RMS error, we pass from the values equal to 5.61 m, 6.82 m, 4.47 m (for the Xiaomi Mi 8, Xiaomi Mi 9, Huawei P30, respectively) to the values equal to 4.14 m, 4.90 m, and 3.24 m (for the same smartphones). This type of improvement is also obtained for the vertical component.