# Advancing Road Infrastructure Safety with the Remotely Piloted Safety Cone
## 3 Results
### Positioning  
This test analyses GNSS positioning performance with RTK using two different providers, IGN and Smartnet, evaluated on two RPSCs located on two GCPs, respectively. The primary objective is to characterise the positioning system's convergence, stability, and precision behaviour under real-world conditions, focusing on the quality of the solution after acquiring the RTK fix, the consistency of the horizontal error, and the system's sensitivity to disturbances. Table 6 shows the results of the tests performed. The convergence of the positioning solution was measured as the number of samples required to reach a stable error zone below the 95 th percentile. In this aspect, marked differences are evident between the two evaluated services. In the case of RPSC1 with the IGN service (Figure 7), 1824 samples were required to stabilise the signal, while RPSC2 (Figure 8) needed 2045 samples with the same service, representing more than 88% of the total in both experiments. This slow convergence indicates that the GNSS system operating with IGN presents a prolonged transition before reaching a reliable RTK solution. In contrast, with the SmartNet service, both RPSC1(Figure 9) and RPSC2 (Figure 10) stabilised in around 1539 samples, showing a more efficient and consistent fix acquisition process. This improvement can be attributed to a higher frequency of correction transmission, lower latency in the Networked Transport of RTCM via Internet Protocol (NTRIP) network, or a denser base station infrastructure, all of which are crucial factors for dynamic robotic applications that require a high-precision solution in a short timeframe. The stability of the RTK solution was analyzed in terms of temporal variability, presence of jitter, and occurrence of error peaks that could indicate loss of fix. In the temporal \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Test** & **n** & **Mean** & **Median** & **P95** & **STD** & **CV** & **RMSE** & **MIN** & **MAX** & **Stabilise Samples** \\ \hline RPSC1 IGN & 2071 & 0.154 & 0.101 & 0.570 & 0.152 & 0.984 & 0.216 & 0.010 & 0.743 & 1824 \\ RPSC2 IGN & 2304 & 0.212 & 0.123 & 0.819 & 0.285 & 1.342 & 0.355 & 0.007 & 1.820 & 2045 \\ RPSC1 SmartNet & 1782 & 0.114 & 0.046 & 0.563 & 0.181 & 1.594 & 0.214 & 0.025 & 1.140 & 1539 \\ RPSC2 SmartNet & 1782 & 0.076 & 0.050 & 0.073 & 0.195 & 2.571 & 0.210 & 0.001 & 1.806 & 1403 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical summary of horizontal error for RPSC1 and RPSC2 under IGN and SmartNet correction services. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **RTK GNSS** & **Encoders** & **IMU** \\ \hline
1 (Minimum & No & No & Yes \\
2 (Relative Odometry) & No & Yes & Yes \\
3 (Absolute & Yes & Yes & Yes \\ Correction) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Field test configurations for the RPSCs. graphs of the horizontal error, it is observed that RPSC2 with IGN exhibits multiple discontinuities, with errors exceeding 1 m, suggesting sporadic losses of the fixed solution or temporary degradations in the correction quality. These losses could be related to environmental factors or insufficient GNSS coverage during specific intervals. In contrast, the error profiles associated with SmartNet, both in RPSC1 and RPSC2, show an abrupt drop in error followed by a stable plateau, without significant oscillations or evident jumps, which confirms greater robustness against external disturbances and better quality of filtering or interpolation of RTK corrections. Figure 8: Time-series analysis of horizontal positioning error for RPSC2 using IGN corrections. Figure 7: Time-series analysis of horizontal positioning error for RPSC1 using IGN corrections. Figure 9: Time-series analysis of horizontal positioning error for RPSC1 using SmartNet corrections. From a quantitative perspective, the numerical results allow for a clear comparison between the different configurations.