## 4 SF-PPP Performance Analysis of Android Mobile Phones
### Positioning Performance Analysis of Android Mobile Phones  
Weak signal strength and high measurement noise present a great challenge to precise GNSS positioning for the smartphones. We further investigated the SF-PPP performance by utilizing the dataset collected from P40-EXT and P40-INT. Figure 7 displays the number of available satellites (ASAT) as well as the position dilution of precision (PDOP) for different GNSS system combinations. The satellites used in SF-PPP solution are denoted as ASAT in the case of gross errors. With a geodetic-grade antenna, P40-EXT could generally track five more satellites than P40-INT. With multi-GNSS availability, the average number of ASAT of P40-EXT varied from 20 to 30 while that of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Devices**} & \multicolumn{5}{c}{**Pseudorange Noise RMS (m)**} \\ \cline{2-6}  & **GPS-L1** & **BDS-B1I** & **BDS-B1C** & **Galileo-E1** & **Average** \\ \hline P40-EXT & 0.56 & 0.36 & 0.28 & 0.36 & 0.40 \\ P40-INT & 0.99 & 0.57 & 0.41 & 0.60 & 0.67 \\ \hline \hline \multirow{2}{*}{**Devices**} & \multicolumn{5}{c}{**Carrier-Phase Noise RMS (cycle)**} \\ \cline{2-6}  & **GPS-L1** & **BDS-B1I** & **BDS-B1C** & **Galileo-E1** & **Average** \\ \hline P40-EXT & 0.03 & 0.02 & 0.03 & 0.03 & 0.02 \\ P40-INT & 0.03 & 0.03 & 0.03 & 0.03 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSs of pseudorange and carrier-phase noise for different smartphone antenna devices. Figure 6: Pseudorange (left panel) and carrier-phase (right panel) noise RMS versus satellite elevation (top panel) and C/N0 value (below panel) for different smartphone antenna devices. P40-INT varied from 16 to 26, considering different frequency combinations. It should be noted five to six more BDS satellites could be observed at the B1I frequency than that at the B1C frequency for both P40-EXT and P40-INT. As a result, the PDOP of the GPS L1, BDS B1C, and Galileo E1 frequency combinations showed more dramatic changes than the case of using the B1I frequency, especially for P40-INT, where the PDOP even jumped from 0.9 to above 1.3. Although the B1C signal manifested a smaller code noise level than the B1I signal, it was still recommended to adopt the B1I signal to ensure more available satellites and better satellite geometry. With the GPS L1, BDS B1I, and Galileo E1 combination, the average GNSS ASAT numbers reached 27.3 and 23.9 for P40-EXT and P40-INT, respectively, while the resulting average PDOPs were 0.826 and 0.934, respectively. The P40-EXT positioning performance of the two SF-PPP approaches was evaluated using observations from GPS L1, BDS B1I, and Galileo E1 frequencies. The left panel of Figure 8 shows the epoch-wise positioning errors in the east, north, and up components for the GRAPHIC and uncombined solutions of P40-EXT, while the right panel is the corresponding RMS values every 5 min. The positioning errors of the GRAPHIC and uncombined approaches were at the same order of magnitude; both could reach sub-meter level positioning accuracy after convergence. However, the uncombined model had a slightly higher accuracy in the up component. When the GRAPHIC approach was applied, the positioning errors of P40-EXT were within a few meters during the first 20 min, and it took about 40 min to stabilize. In contrast, the uncombined model could achieve accuracy within 1 m in the horizontal direction and 2 m in the vertical direction during a few minutes. The remarkable improvement in terms of convergence performance of the uncombined model should be attributed to the fact that the carrier phase observation precision is much higher than the GRAPHIC combination and that the ionospheric parameters could absorb part of observational errors. Figure 7: The number of available satellites and the PDOP in different smartphone antenna devices. Considering the code noise correlation with respect to C/N0, the P40-INT SF-PPP was evaluated using a C/N0-dependent weighting model in addition to the elevation-dependent model for comparison.