## 4 Precise Point Positioning Results
### CNES Evaluation
However, the ambiguity resolution degrades the velocity error in the kinematic mode. The PPP-Snapshot mode plays the role of an intermediate mode between the PPP-float and the PPP-AR modes in terms of accuracy. The position results with the PPP-Snapshot mode are better than the ones for the PPP-float mode but still worse than the PPP-AR mode. This is explained by the fact that the ambiguity is reinitialized at each epoch, and the Kalman filter does not exploit the fact that the carrier-phase ambiguity is constant over a single passage. This allows a positioning without convergence, but at the price of less precise results. This accuracy could be improved by using external atmospheric corrections. In terms of convergence time, a special computation case with RT and POST products has been performed with a reinitialization of the filter every two hours. This leads to twelve convergence phases for a day, which can be sufficient to obtain a representative convergence time. Table 8 summarizes the time needed to have a permanent positioning error under 5 cm for the horizontal component and below 10 cm for the vertical one. The convergence times are always smaller using POST products than RT ones. In addition to this, the kinematic mode leads to longer convergence times than the static mode. The benefit of using the Doppler shift measurement on the user side of the PPP-WIZARD demonstrator is also assessed in this section. To do so, the Doppler shift model described in Section 2.3 has been implemented and tested on the measurements collected on a car campaign held in the city center and the surroundings of Toulouse, France, in April 2022. A car has been equipped with a Novatel antenna on the roof connected to a signal splitter. The antenna signal is directed on one hand to a ProPack 6 receiver and a Novatel Inertial Measurement Unit (IMU) in order to compute a reference trajectory, and on the other hand to a Septentrio PolaRx5 receiver, whose data have been used in this section in \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Post-Processed Products**} \\ \hline  & & & \multicolumn{2}{c}{**Horizontal**} & \multicolumn{4}{c}{**Vertical**} \\ \cline{3-8}  & & & **mean** & **std.** & **95\%** & **mean** & **std.** & **95\%** \\ \hline \multirow{3}{*}{PPP-AR} & \multirow{3}{*}{KIN} & Pos. error [cm] & 0.86 & 0.59 & 1.90 & \(-\)0.40 & 2.83 & 4.52 \\  & & Vel. error [cm/s] & 0.64 & 0.51 & 1.45 & \(-\)0.99 & 1.17 & 0.94 \\  & & STA & Pos. error [cm] & 0.87 & 0.60 & 1.90 & \(-\)0.26 & 2.81 & 4.67 \\ \hline \multirow{3}{*}{PPP-Snapshot} & \multirow{3}{*}{KIN} & Pos. error [cm] & 33.19 & 16.29 & 62.76 & 16.86 & 46.09 & 87.68 \\  & & Vel. error [cm/s] & 1.08 & 0.58 & 2.15 & \(-\)1.46 & 1.91 & 1.96 \\ \cline{1-1}  & & STA & Pos. error [cm] & 34.42 & 17.03 & 65.91 & 40.09 & 50.74 & 121.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Horizontal Convergence [min]**} & \multicolumn{2}{c}{**Vertical Convergence [min]**} \\  & **STA Mode** & **KIN Mode** & **STA Mode** & **KIN Mode** \\ \hline RT products & 54 & 55 & 72 & 73 \\ POST products & 25 & 31 & 25 & 29 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Convergence time for the positioning of the TLSG station on 14 March 2023, with the RT or the POST products, in static (STA) or kinematic (KIN) modes. order to estimate the car position. The lever arms from the IMU to the antenna have been calibrated to a centimeter level. The experimental setting is depicted in Figure 13(a) and the path traveled by the car in Toulouse city in Figure 13(b). Despite what is commonly done in the navigation community, the measures have been sampled at 10 Hz rather than 1 Hz. The trajectory of the car has been estimated with the user side of the demonstrator using the code, phase, and Doppler measurements from the GPS and Galileo satellites.