## 4 Results and Discussion
### Performance of the Presented Smartphone Static PPP  
Based on the ultra-rapid precise orbit/clock products, these static smartphone's GPS+BDS data were processed by (1) GPS PPP based on the hybrid weight function and the mixed-frequency measurements for L1 and L5 (GPS-MF-Com), (2) GPS+BDS PPP based on the elevation-dependent weight function and measurements for L1 and B1 (GB-SF-Ele), (3) GPS+BDS PPP based on the C/N0-dependent weight function and measurements for L1 and B1 (GB-SF-CN0), (4) GPS+BDS PPP based on the hybrid weight function and measurements for L1 and B1 (GB-SF-Com), and (5) GPS+BDS PPP based on the hybrid weight function and the mixed-frequency measurements for L1, L5, and B1 (GB-MF-Com), respectively.  
The positioning errors of these five schemes are presented in Figure 10, and the corresponding RMS values are listed in Table 4. From Figure 10, it can be seen that the convergence speed of the smartphone PPP is invisible due to the low-quality GNSS observations. According to the statistical results, the positioning errors based on the elevation-dependent weight function are more difficult to converge to zero. However, the positioning errors of the smartphone PPP based on the hybrid weight function converge quickly. As is shown in Table 4, the positioning accuracy of GPS+BDS PPP based on the hybrid weight function and the mixed-frequency measurements (GB-MF-Com) is the highest among the five schemes, with the RMS values of 0.51 m, 0.67 m, and 0.71 m in the east,  
Figure 9: Number of visible GPS+BDS satellites and the corresponding PDOP for M8 in the static experiment (**above**) and the dynamic experiment (**below**).  
north, and vertical directions, respectively. In contrast, the GB-SF-Ele scheme provides the worst positioning accuracy among these five schemes, even worse than the results of the GPS-MF-Com scheme. Compared to the results of the GB-SF-Ele scheme, the positioning accuracy of the GB-SF-Com scheme was improved from 1.88 m, 2.48 m, and 3.61 m to 0.61 m, 0.69 m, and 0.83 m in the east, north, and vertical components, respectively, with position improvement percentages of 67.55%, 72.18%, and 77.01%. Such position improvement percentages are 20.69% and 15.31% in the north and vertical components, compared with the results of the GB-SF-C/N0 scheme. The GB-MF-Com scheme brings about 16.39%, 2.9%, and 14.46% improvements to the GB-SF-Com scheme and also offers 59.52%, 22.99%, and 33.64% to the GPS-MF-Com scheme in the three components. These results indicate that (1) neither the elevation-dependent weight function nor the C/N0-dependent weight function can represent the quality of smartphones' GNSS observations accurately, and the presented hybrid weight function is one of the effective tools; (2) the mixed-frequency measurement model can increase the available measurements and further improve the smartphone positioning accuracy.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Positioning Modes** & **East (m)** & **North (m)** & **Up (m)** \\ \hline GPS-MF-Com & 1.26 & 0.87 & 1.07 \\ GB-SF-Ele & 1.88 & 2.48 & 3.61 \\ GB-SF-CN\({}_{0}\) & 0.61 & 0.87 & 0.98 \\ GB-SF-Com & 0.61 & 0.69 & 0.83 \\ GB-MF-Com & 0.51 & 0.67 & 0.71 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Position RMS of static PPP for MI8 based on different positioning modes.  
Figure 10: Positioning errors of different PPP modes based on different weight functions in the static test.