# A Combined Elevation Angle and C/N0 Weighting Method for GNSS PPP on Xiaomi MI8 Smartphones
## 4 Experimental Results and Discussion
### Kinematic Experiment in an Open Sky Environment  
A kinematic GNSS experiment was conducted using the Xiaomi M18 smartphone on an open playground of Central South University, China on 2 December 2021. Its trajectory and experiment equipment are shown in Figure 6. A Trimble NetR9 GNSS receiver with a geodetic antenna is employed to acquire the precise kinematic position for use as a benchmark value. The horizontal distance between the geodetic-type antenna and the smartphone is less than one decimeter. The experimental platform was lifted by a pedestrian over the head. A base station is set up at about one kilometer away from the rover station. Thus, the position of the geodetic receiver at the rover station can be precisely determined by the real-time kinematic (RTK) technique. The entire data collection lasts about 24 min, with a sampling rate of 1 HZ. The elevation mask is set to 10 degrees. Figure 7 shows the total number of satellites received, the total number of satellites used and the number of satellites for different constellations of GPS, GLONASS, BDS and Galileo in the PPP. The number of GPS and BDS satellites observed is obviously more than GLONASS and Galileo. At the same time, the total number of satellites received is 23.8 on average, which is apparently less than the Trimble NetR9 receiver at an average number of 36.0. In contrast, the total number of satellites used for PPP on the Xiaomi M18 smartphone is only 17.5 on average with an STD of 2.8 due to a lack of parts of observations. Taking the GPS G01 satellite at the L5 frequency and the GLONASS R09 satellite at the G1 frequency as examples, Figure 8 depicts the variations in elevation angle and C/N0 in the time domain, which shows that the elevation angle steadily changes for both satellites. In contrast, the C/N0 severely fluctuates with a range exceeding 10 dB-Hz for both satellites, which suggests that the C/N0 is prone to be affected by the outer environment due to a polarized antenna embedded inside the smartphone. Figure 9 shows the observation variances derived from Equations (5), (6) and (8) for the GPS G01 at the L5 frequency and the GLONASS R09 at the G1 frequency. The observation variances are displayed in the top, middle and bottom panels, derived from three different weighting scenarios, namely \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Processing Strategies** \\ \hline Estimation method & Kalman filter \\ Constellations & GPS (L1, L5)/GLONASS (G1)/BDS (B1)/Galileo (E1, E5a) \\ Weighting scheme & Combined elevation angle and C/N0 weighting method \\ Satellite orbit and clock & Real-time precise satellite orbit and clock products from Centre National d’Etudes Spatiales (CNES) [30] \\ Ionospheric delay & Estimated as random walk process and GIM products are used as pseudo-observations \\ Tropospheric delay & Hydrostatic delay uses Saastamoinen model correction [31], and zenith wet delay \\ Receiver position & Estimated as random walk process \\ Receiver clock offset & Estimated as white noise \\ Inter-system bias & Estimated as white noise \\ Ambiguities & Estimated as constants \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PPP processing strategy. elevation-angle-only, C/N0-only and combined elevation angle and C/N0. As can be seen, the C/N0-derived observation variances severely vary, whereas the observation variances derived from the combined elevation angle and C/N0 are more stable. Figure 8: Elevation angle and C/N0 variations for GPS G01 satellite at L5 frequency and GLONASS R09 satellite at G1 frequency. Figure 6: Kinematic experimental trajectory (**a**) and equipment setup (**b**) on an open-sky playground. Figure 7: Number of satellites for quad-constellations on 2 December 2021. Figure 10 shows the positioning errors in the east, north and up components using the three weighting scenarios. It can be seen that the positioning error curve derived from the combined weighting method is closer to the zero axis, especially in the east direction.