## 4 Experiment and Result
### PPP/INS Solutions on the Playground and Sidewalk
Compared with Figure 12a, the offset of trajectory was significantly improved in Figure 13a. In Table 2, the RMS of Mate 30 GPS/BDS PPP/INS horizontal errors decreases by 33.24% from 5.367 to 3.583 m, and the maximum horizontal positioning error decreases from 15.041 to 7.294 m. The RMS of Mate 30 GPS/BDS PPP/INS vertical errors decreases by 24.64% from 7.359 to 5.546 m. Previously, the average C/N\({}_{0}\) value observed on the west side of the playground was significantly lower than that on the east side, as shown in Figure 4a. Comparing the PPP solutions on the west and east sides of the playground, the RMS of Mate 30 GPS/BDS PPP horizontal errors on the west side is 6.515 m, which is 27.17% higher than the 5.123 m on the east side. However, based on the INS-aided and RKF parameter estimation model, the RMS of Mate 30 GPS/BDS positioning horizontal errors on the west side of the playground decreases by 41.21% to 3.830 m, and the RMS of Mate 30 GPS/BDS positioning horizontal errors on the east side of the playground can reach 3.073 m. Subsequently, the IMU data of ADIS16405 were used with Huawei Mate 30 in the experiment on the sidewalk, and the GNSS PPP and PPP/INS solutions are shown in Figure 14. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dir**} & \multicolumn{6}{c}{**Smartphone Kinematic Positioning Error RMS (m)**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Huawei Mate 10**} & \multicolumn{2}{c}{**Huawei Mate 30**} & \\ \cline{2-7}  & **G(PPP)** & **G(PPP/INS)** & **G(PPP)** & **G(PPP/INS)** & **GB(PPP)** & **GB(PPP/INS)** \\ \hline E & 12.157 & 8.112 & 4.732 & 5.318 & 3.666 & 2.546 \\ N & 11.403 & 8.304 & 3.682 & 2.849 & 3.920 & 2.521 \\ H & 16.668 & 11.293 & 5.996 & 6.033 & 5.367 & 3.583 \\ V & 29.509 & 23.717 & 12.274 & 7.389 & 7.359 & 5.546 \\
3D & 33.891 & 26.269 & 13.660 & 9.539 & 9.108 & 6.603 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMS of GNSS PPP and PPP/INS positioning error using smartphones on the playground. Dir denotes direction. G and B denote GPS and BDS, respectively. H, V, and 3D denote horizontal, vertical, and three-dimensional. Figure 14: GPS/BDS PPP and PPP/INS solutions from Huawei Mate 30 on the sidewalk. (**a**) Trajectories of GPS/BDS PPP and PPP/INS solutions. (**b**) Comparison of GPS/BDS PPP, PPP/INS, and PPP/INS–ADIS solutions with reference points. PPP/INS–ADIS denotes that the data of ADIS16405 were used in the PPP/INS coupled model instead of the IMU data of smartphone. Although the GNSS signals are significantly degraded due to the buildings and trees on both sides in Figure 14, the PPP solutions of Mate 30 still can be outputted with GPS and BDS. However, compared with the PPP solutions on the playground, the RMS of PPP horizontal and vertical errors increases to 9.200 and 13.389 m, respectively. In Figure 14, the RMS of PPP/INS horizontal errors decreases by 29.53% to 6.483 m, and the RMS of PPP/INS vertical errors decreases by 41.98% from 13.389 to 7.768 m. Meanwhile, compared with the positioning trajectories between PPP/INS and PPP/INS-ADIS, it can be found that the trajectory of PPP/INS-ADIS fits more closely to the reference trajectory, especially on the northwest side. As shown in Table 3, the RMS of PPP/INS-ADIS horizontal errors is 5.336 m, which is lower than that of PPP/INS, and the RMS of PPP/INS-ADIS vertical errors is approximate to that of PPP/INS.