## 4 Experiment and Result
### Multi-GNSS Static PPP Solution  
In view of the differences in measurement noise of GPS, BDS, and GLONASS observations of smartphone, the \(C_{S}\) values of the C/\(N_{0}\)-dependent stochastic model with step function variance of GPS, BDS, and GLONASS were calculated separately based on the previous experimental data of multi-GNSS pseudorange and carrier phase variance of the Huawei Mate30. Meanwhile, the appropriate weight matrix \(P_{S}\) was set according to the measurement residuals of multi-GNSS observations and the orbit of satellites. Tests on the static PPP algorithms with elevation- and C/\(N_{0}\)-dependent stochastic models were conducted with respect to different combinations of GPS, BDS, and GLONASS. It should be noted that the multi-GNSS observations of the Huawei Mate30 were collected in an open sky environment, which is less affected by multipath. The positioning errors of GPS, GPS/BDS, and GPS/BDS/GLONASS are shown in Figure 6a,c,e in terms of east, north and up directions of the coordinate system, and the corresponding three-dimensional deviation points in the initial 10 min are shown in Figure 6b,d,f. According to the comparison of GNSS(CR) and GNSS(EK) in Figure 6b,d,f, it can be found that the positioning errors of GNSS(CR) are even higher than GNSS(EK) in the first few epochs, but the convergence rate of GNSS(CR) is obviously faster than that of GNSS(EK) with time in Figure 6a,c,e. In Figure 6a, the first time for the horizontal error of GPS(CR) convergence to 0.5 m is 156 epochs, which is much faster than 516 epochs of GPS(EK). The RMS of vertical error decreases from 1.850 m of GPS(EK) to 0.878 m of GPS(CR). The mean horizontal and vertical errors of GPS(CR) reach 0.234 and 0.502 m, respectively, which are lower than 0.267 and 1.205 m of GPS(EK). For the GPS/BDS and GPS/BDS/GLONASS positioning in Figure 6c,e, it should be emphasized that we had to weaken the allocation of carrier phase residuals correction of BDS in both of PPP methods, so as to improve the stability and accuracy of multi-GNSS positioning. The maximum vertical error decreases from 6.204 m for GPS(EK) to 4.607 m for GPS/BDS(EK) and 4.656 m for GPS/BDS/GLONASS(EK). Moreover, the RMS of vertical errors decreases from 1.333 m for GPS/BDS(EK) and 1.545 m for GPS/BDS/GLONASS(EK) to 0.817 m for GPS/BDS(CR) and 0.761 m for GPS/BDS/GLONASS(CR), respectively. The comparison of RMS of GPS, GPS/BDS, and GPS/BDS/GLONASS positioning errors in each direction during different periods is shown in Figure 7, and the RMS of single and dual frequency PPP errors of the geodetic receiver are added for reference. In the first 10 min, the RMS of three-dimensional positioning errors of GPS(CR), GPS/BDS(CR), and GPS/BDS/GLONASS(CR) are 2.44, 2.160 and 1.386 m respectively, which are much lower than 4.726, 2.969 and 3.488 m for GPS(EK), GPS/BDS(EK), and GPS/BDS/GLONASS(EK). Meanwhile, the RMS of horizontal and vertical errors of GPS/BDS/GLONASS(CR) is 0.474 and 1.302 m, respectively, which are close to 0.661 and 1.119 m for GEO(SF). Then the RMS of GPS/BDS/GLONASS(CR) positioning errors gradually decreases with time, of which the horizontal and vertical parts decrease continuously from 0.306 and 0.798 m within 60 min to 0.250 and 0.761 m within 100 min, respectively. However, the three-dimensional positioning errors of the proposed static PPP algorithm based on C/\(N_{0}\)-dependent step function variance stochastic model decrease by different levels, no matter which group of GPS, GPS/BDS, and GPS/BDS/GLONASS is considered. The RMS values of static PPP errors with respect to GPS, GPS/BDS, and GPS/BDS/GLONASS observed by the Huawei Mate30 and the geodetic receiver are shown in Table 2. Compared with GPS(EK), GPS/BDS(EK), and GPS/BDS/GLONASS(EK), the RMS of the three-dimensional positioning errors of GPS(CR), GPS/BDS(CR), and GPS/BDS/GLONASS(CR) decrease by 50.72%, 36.95%, and 49.06% to 0.928, 0.852, and 0.801 m in 100 min.