## 3 Results
### Positioning Results of Vehicle Kinematic Experiments
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **N (cm)** & **E (cm)** & **U (cm)** & \
\begin{tabular}{c} **Success Rate** \\ **of AR (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Convergence** \\ **Time (s)** \\ \end{tabular} \\ \hline PPP & 10.8 & 10.8 & 30.9 & - & 1394 \\ PPP-AR & 11.5 & 11.6 & 29.3 & 75.50 & 712 \\ PPP-RTK & 2.6 & 2.6 & 7.5 & 97.96 & \(1\) \\ RTK & 3.1 & 4.3 & 6.3 & 98.89 & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The statistical values of convergence time and positioning error for four algorithms for vehicle kinematic positioning, tested in the Wuhan area. Figure 5: The time series of positioning errors for PPP-Float, PPP-AR, PPP-RTK, and RTK solutions in the north, east, and up directions, respectively. The yellow dashed lines represent outages of GNSS. The cumulative distribution functions (CDFs) of the horizontal and vertical positioning errors for the three schemes are depicted in Figure 7. The percentages of horizontal positioning errors better than 0.1 m for the three schemes were 64.50%, 82.86%, and 99.54%, respectively. It is evident that the CDF of PPP outperformed that of PPP-AR when the horizontal positioning error was below 0.2 m. This discrepancy can be attributed to the NL ambiguity fixing error, highlighting the lower robustness of dual-frequency PPP-AR in dynamic data. Compared with the horizontal positioning error, the vertical positioning accuracy was comparatively poorer. However, PPP-RTK continued to demonstrate superior positioning accuracy and availability, with more than 99% of positioning errors within 0.2 m. On the other hand, both PPP and PPP-AR exhibited significantly lower availability in terms of vertical positioning. Another advantage of PPP-RTK is its ability to achieve rapid convergence after signal loss or the blocking of GNSS. Figures 8 and 9 show the positioning errors and satellite number of the three algorithms in regions A and B in Figure 2. Figure 8 shows that on Route (1), the receiver experienced a brief loss of lock for 6 s while the vehicle passed through the tunnel. It is evident that PPP had relatively large positioning errors, with RMS values of 0.57 m, 0.37 m, and 1.21 m in the north, east, and up directions, respectively. PPP-AR required a longer convergence time, and the positioning accuracy fluctuated significantly. PPP-RTK demonstrated outstanding positioning performance, swiftly achieving precise ambiguity resolution once a sufficient number of satellites were reacquired. The RMS statistical values for the north, east, and up directions were 0.18 m, 0.19 m, and 0.68 m, respectively. Route (2) also experienced a 5 s outage. Even after normal tracking was restored, PPP and PPP-AR  
Figure 6: The 3D position error distribution histogram for the kinematic positioning experiment with the three algorithms. Figure 7: Cumulative distribution function of 2D and up direction positioning error in kinematic experiments, for PPP-Float/PPP-AR/PPP-RTK. continued to exhibit slower and less stable convergence. Fortunately, the PPP-RTK solution achieved reconvergence with high reliability, demonstrating accuracies of 0.03 m, 0.03 m, and 0.1 m in the three directions. From Figure 9, it can be observed that in Region B, the tunnel crosses the railway, leading to a gradual decrease in satellite lock. Although the three algorithms continued to provide positioning, significant fluctuations in error were also noted. The duration of the sharp change in the number of satellites on Route (1) lasted for 4 s, whereas the entire  
Figure 8: The positioning errors for vehicles passing through tunnels. From top to bottom, the PPP, PPP-AR, PPP-RTK, and satellite numbers. From left to right, vehicles traveling from north to south (route 1) and from south to north (route 2) in Region A (In Figure 1), respectively. Figure 9: The positioning error for vehicles passing through tunnels.