## 4 Experiment and Result
### PPP/INS Solutions for Tunnel and Long Trajectory  
Considering that few GNSS satellites signals can be observed by smartphones in some areas such as tunnels, the solutions of the current epoch would be output by INS when the number of satellites could not meet the requirements of GNSS positioning, and other parameters, such as ambiguity, are usually initialized at the beginning, which are the same as before. As shown in Figure 15, the experiment was conducted in a tunnel shown on the right with a length of about 80 m, and the vertical drop is more than 10 m. The trajectories of Mate 30 GPS/BDS PPP and PPP/INS solutions are shown on the left, and the gaps between the positioning points are preserved in the trajectory. Figure 15: GPS/BDS PPP and PPP/INS solutions from Huawei Mate 30 in the tunnel. (**a**) Left: trajectories of GPS/BDS PPP and PPP/INS solutions. Right: the realistic environment marked in the red box. (**b**) Comparison of GPS/BDS PPP and PPP/INS solutions with reference points, and the red box shows the GPS/BDS PPP/INS solutions in the tunnel. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Direction**} & \multicolumn{3}{c}{**Huawei Mate 30 Kinematic Positioning Error RMS (m)**} \\ \cline{2-4}  & **GB(PPP)** & **GB(PPP/INS)** & **GB(PPP/INS-ADIS)** \\ \hline E & 6.589 & 4.903 & 3.470 \\ N & 6.420 & 4.241 & 4.054 \\ H & 9.200 & 6.483 & 5.336 \\ V & 13.389 & 7.768 & 7.859 \\
3D & 16.245 & 10.118 & 9.499 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMS of GPS/BDS PPP and PPP/INS positioning errors using Huawei Mate 30 on the sidewalk. In fact, the GNSS satellite signals were blocked gradually before the smartphone entered the tunnel, the PDOP value of GNSS satellites increased gradually, and the horizontal and vertical errors were shown to fluctuate significantly for 25 to 40 epochs in Figure 15b. From 41 to 77 epochs, the number of GNSS satellites observed by Mate 30 was insufficient to meet the requirement of the PPP method. Nevertheless, the position of the smartphone can still be obtained continuously with the PPP/INS coupled method while inside the tunnel, and the horizontal deviation from the reference point is more than 8 m at 29 epochs. Then, the positioning points of PPP/INS gradually approach the reference trajectory after leaving the tunnel. The RMS of horizontal deviation in the tunnel is 6.700 m, and the maximum horizontal and vertical deviation are 8.139 and 7.996 m, respectively. Compared with the RMS of PPP/INS horizontal errors from 1 to 40 epochs, the RMS of PPP/INS horizontal errors in the tunnel increases only 21.99%. Meanwhile, it should be noted that the deviation will increase significantly with the further increase of the length of tunnel. Finally, a long trajectory experiment with PPP, PPP/INS, and PPP/INS-ADIS was conducted, and the trajectories are shown in Figure 16.  
In the areas marked by purple boxes 1 and 3, it can be found that the trajectory of GPS/BDS PPP is not smooth, and the maximum horizontal errors of GPS/BDS PPP in the areas even reached 49.813 m and 27.627 m, respectively. This can be attributed to the measurement residuals of some satellites with low signal quality, which belong to outliers and are not eliminated in the process of iteration. With the INS-aided and RKF parameter estimation model, as shown in Figure 17, the maximum horizontal errors of GPS/BDS PPP/INS in the areas marked by purple boxes 1 and 3 are 20.662 and 8.933 m, which are decreased by 58.52% and 67.67%, respectively. Figure 16: The long trajectories of GPS/BDS PPP, PPP/INS, and PPP/INS–ADIS solutions using Huawei Mate 30 and ADIS16405. Left: the realistic environment marked in the purple box 3. Right: the realistic environment marked in the purple box 1. The areas where the number of satellites cannot meet the requirements of GNSS positioning are marked by red boxes 2 and 4.