## 4 Experiment and Result
### PPP/INS Solutions on the Playground and Sidewalk  
While the pitch and roll angle were calculated by accelerometer, the yaw angle of smartphones was estimated by position and speed provided by GNSS solutions for PPP/INS initial alignment in dynamic mode. The INS parameters would be initialized while both the velocity of the receiver and the PDOP of the GNSS reached corresponding thresholds. Meanwhile, considering the convergence velocity and precision of smartphones PPP initialization, the yaw angle is directly estimated by the geodetic receiver with differential positioning during INS initial alignment in the experiments. Moreover, some reference coordinates which cannot be outputted by the geodetic receiver with GNSS integer ambiguities estimated as a fix solution were estimated by the post-processing fitting method. The conventional PPP method adopted the standard Kalman filter parameter estimation model while the robust Kalman filter was used in the PPP/INS coupled model, and both adopted the C/N\({}_{0}\)-dependent stochastic model. The PPP and PPP/INS positioning trajectories of Huawei Mate 10 are shown in Figure 11a, and the corresponding positioning errors in terms of east, north, and up directions are shown in Figure 11b. In Figure 11a, the positioning errors of single-frequency GPS PPP of the Huawei Mate 10 show a significant fluctuation at the beginning even in the open area, and then the smartphone enters the area marked by the yellow box successively in about 50 epochs and 180 epochs. In Figure 11b, the RMS of GPS PPP/INS horizontal errors is 11.293 m, which decreases by 32.24% compared with that of GPS PPP horizontal errors, and the RMS of PPP/INS vertical errors is 23.717 m, which decreases by 19.63% compared with that of GPS PPP vertical errors. However, although the positioning accuracy of the Huawei Mate 10 is improved with INS, its absolute positioning accuracy is still closely related to positioning accuracy of the smartphone PPP. For the early single-frequency smartphones such as Mate 10, an amount of raw carrier phase measurements cannot be logged due to many cycle slips in GNSS-degraded environments, and the weak positioning performance makes it difficult to meet the requirements of a high-precision location service even in the open area. In contrast, the dual-frequency smartphone Mate 30 has significantly better positioning performance, as shown in Figure 12. The RMS of Mate 30 GPS PPP horizontal errors can reach 5.996 m in the same environment. Figure 11: GPS PPP and PPP/INS solutions from Huawei Mate 10 on the playground. (**a**) Trajectories of GPS PPP and PPP/INS solutions. (**b**) Comparison of GPS PPP and PPP/INS solutions with reference points. The E and N denote east and north direction, respectively. From Figure 12b, although the Mate 30 GPS PPP/INS maximum horizontal positioning error decreases by 32.08% from 16.407 to 11.144 m, the horizontal positioning accuracy did not improve significantly with INS, and the RMS of Mate 30 PPP/INS horizontal errors is 6.033 m which is almost the same as that of PPP. Meanwhile, in Figure 12a, it can be found that the trajectory of PPP/INS positioning is still flat while the smartphone is in the area marked by the yellow box, but the offset is also increasing. However, the RMS of GPS PPP/INS vertical positioning errors decreases by 39.80% from 12.274 to 7.389 m, and the RMS of three-dimensional positioning errors is 9.539 m. Then, the BDS observations of Mate 30 were used in the GNSS PPP/INS experiment, and the results are shown in Figure 13.  
Figure 12: GPS PPP and PPP/INS solutions from Huawei Mate 30 on the playground. (**a**) Trajectories of GPS PPP and PPP/INS solutions. (**b**) Comparison of GPS PPP and PPP/INS solutions with reference points. Figure 13: GPS/BDS PPP and PPP/INS solutions from Huawei Mate 30 on the playground. (**a**) Trajectories of GPS/BDS PPP and PPP/INS solutions. (**b**) Comparison of GPS/BDS PPP and PPP/INS solutions with reference points.