## 3 Results
### Positioning Results of Vehicle Kinematic Experiments  
In the vehicle-mounted kinematic experiment based in Wuhan, PPP-RTK performance was assessed alongside PPP-AR and RTK using dual-frequency PPP and GEC constellations. The definitions of convergence time and TTFF were the same as used in the static experiments. Figure 5 displays the positioning error sequences of dual-frequency PPP, PPP-AR, PPP-RTK, and RTK. Table 3 provides the corresponding RMS values of the positioning error, success rate of ambiguity resolution (AR), and the convergency time. From Figure 5, it is evident that PPP had a long initialization time and slow reconvergence speed after occlusion. The positioning accuracies in the north, east, and up directions were measured at 10.8 cm, 10.8 cm, and 30.9 cm, respectively, with a convergence time of more than 20 min. PPP-AR had reduced convergence time, but it still took more than 10 min. However, the GNSS signals from fast-moving carriers tend to be noisy, increasing the possibility of incorrect ambiguity resolution and reducing positioning availability. The overall accuracies in the respective directions were 11.5 cm, 11.6 cm, and 29.3 cm. The reduced accuracy of PPP-AR may have been due to error-fixed narrow-lane (NL) ambiguity. In contrast, PPP-RTK, with high-precision atmospheric product constraints, had a significantly reduced convergence time compared with PPP and achieved improved positioning accuracies of 2.6 cm, 2.6 cm, and 7.5 cm. These accuracies represent a more than 75% improvement compared with float PPP. Additionally, the successful fix rate was enhanced from 75.50% in PPP-AR to 97.96%. Unlike PPP-RTK, the RTK algorithm mitigates errors in the observation domain, enabling rapid and high-precision positioning. In the vehicle-mounted experiment, a base station was established at the starting position, supporting a baseline length of up to 20 km. Throughout the experiment, the RTK achieved positioning accuracies of 3.1 cm, 4.3 cm, and 6.3 cm in the three respective directions. The successful fix rate of RTK was slightly higher than that of PPP-RTK. Overall, both RTK and PPP-RTK can achieve instantaneous fixing of ambiguity in open environments. Dual-frequency multi-constellation PPP-RTK demonstrated better horizontal positioning accuracy compared with RTK; however, there was a slight decrease in vertical accuracy. This could be attributed to the presence of unmodeled errors in the line-of-sight direction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**System** & **Method** & **N (cm)** & **E (cm)** & **U (cm)** & **TTFF (s)** \\ \hline \multirow{3}{*}{C} & PPP-Float & 4.18 & 3.06 & 8.83 & 2303 \\  & PPP-AR & 1.54 & 1.71 & 4.79 & 1039 \\  & PPP-RTK & 1.31 & 1.12 & 4.73 & 25 \\ \hline \multirow{3}{*}{GEC} & PPP-Float & 4.18 & 2.44 & 5.87 & 955 \\  & PPP-AR & 1.08 & 0.94 & 2.97 & 166 \\ \cline{1-1}  & PPP-RTK & 1.03 & 0.94 & 2.62 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The statistical values of convergence time and positioning error for PPP-Float, PPP-AR, and PPP-RTK, respectively. Figure 6 shows the distribution of 3D positioning errors for the three dual-frequency schemes. Due to the long convergence time of PPP-Float, the accuracy distribution was relatively dispersed, and about half of the epochs could only achieve decimeter-level accuracy. PPP-AR achieved centimeter-level positioning accuracy in most cases, but in kinematic scenarios, the ambiguity-fixing reliability was relatively low, leading to incorrect solutions and reducing the positioning accuracy [40]. The accuracy of PPP-RTK was generally greater than 0.2 m, demonstrating a high reliability and stability similar to that of RTK. The percentages of 3D positioning errors within 0.2 m for the three schemes were 60.67%, 80.97%, and 98.46%, respectively. PPP-RTK improved by 37.79% and 17.49% compared to PPP-Float and PPP-AR, respectively. In summary, PPP-RTK exhibited a remarkably high level of position availability and was able to meet the requirements for decimeter-level lane positioning.