## 3 Results
### Velocity Domain Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Novatel**} & \multicolumn{4}{c}{**uBlox**} & \multicolumn{4}{c}{**Xiaomi**} \\ \hline  & & **Mean** & **rms** & **Max** & **Mean** & **rms** & **Max** & **Mean** & **rms** & **Max** \\ \hline \multirow{2}{*}{**GPS**} & Doppler & 0.018 & 0.020 & 0.072 & 0.027 & 0.032 & 0.173 & 0.009 & 0.013 & 0.232 \\  & TDCP & 0.002 & 0.002 & 0.017 & 0.002 & 0.003 & 0.032 & 0.005 & 0.007 & 0.055 \\ \hline \multirow{2}{*}{**GLO**} & Doppler & - & - & - & 0.057 & 0.072 & 0.802 & 0.045 & 0.049 & 0.207 \\  & TDCP & - & - & - & 0.009 & 0.079 & 3.572 & 0.011 & 0.014 & 0.040 \\ \hline \multirow{2}{*}{**GAL**} & Doppler & - & - & - & 0.035 & 0.042 & 0.187 & - & - & - \\  & TDCP & - & - & - & 0.003 & 0.004 & 0.025 & - & - & - \\ \hline \multirow{2}{*}{**BDS**} & Doppler & - & - & - & 0.108 & 0.149 & 1.234 & 0.043 & 0.050 & 0.323 \\  & TDCP & - & - & - & 0.012 & 0.019 & 0.395 & 0.022 & 0.028 & 0.228 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Horizontal velocity error (m/s): mean, root mean square, and maximum errors for single devices and single GNSSs. RAIM is applied. Figure 9: Horizontal Doppler-based and TDCP-based velocity error with RAIM applied. Each panel refers to a single device and to a single GNSS. Panels in the first row, (**a**–**c**), refer to GPS; panels in the second row, (**d**,**e**), to Glonass; panels in the third row, (**f**,**g**), to Galileo; and panels in the fourth row, (**h**,**i**), to BeiDou. The panel in the first column, (**a**), refers to the Novatel device; panels in the second column, (**b**,**d**,**f**,**h**), to uBlox; and panels in the third column, (**c**,**e**,**g**,**i**), to Xiaomi. Figure 10: Vertical Doppler-based and TDCP-based velocity error with RAIM applied. Each panel refers to a single device and to a single GNSS. Panels in the first row, (**a**–**c**), refer to GPS satellites; panels in the second row, (**d**,**e**), to Glonass; panels in the third row, (**f**,**g**), to Galileo; and panels in the fourth row, (**h**,**i**), to BeiDou. The panel in the first column, (**a**), refers to the Novatel device; panels in the second column, (**b**,**d**,**f**,**h**), to uBlox; and panels in the third column, (**c**,**e**,**g**,**i**), to Xiaomi. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Novatel**} & \multicolumn{3}{c}{**uBlox**} & \multicolumn{3}{c}{**Xiaomi**} \\ \hline  & & **Mean** & **rms** & **Max** & **Mean** & **rms** & **Max** & **Mean** & **rms** & **Max** \\ \hline \multirow{2}{*}{**GPS**} & Doppler & 0.029 & 0.036 & 0.117 & 0.042 & 0.054 & 0.283 & 0.031 & 0.045 & 0.781 \\  & TDCP & 0.003 & 0.004 & 0.055 & 0.004 & 0.006 & 0.116 & 0.009 & 0.014 & 0.209 \\ \hline \multirow{2}{*}{**GLO**} & Doppler & - & - & - & 0.072 & 0.099 & 1.579 & 0.129 & 0.132 & 0.272 \\  & TDCP & - & - & - & 0.011 & 0.109 & 4.957 & 0.017 & 0.021 & 0.057 \\ \hline \multirow{2}{*}{**GAL**} & Doppler & - & - & - & 0.045 & 0.057 & 0.318 & - & - & - \\  & TDCP & - & - & - & 0.004 & 0.006 & 0.052 & - & - & - \\ \hline \multirow{2}{*}{**BDS**} & Doppler & - & - & - & 0.110 & 0.170 & 1.728 & 0.074 & 0.085 & 0.349 \\  & TDCP & - & - & - & 0.012 & 0.025 & 0.822 & 0.023 & 0.031 & 0.252 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Vertical velocity error (m/s): mean, root mean square, and maximum errors for single devices and single GNSSs. RAIM is applied. RAIM-FDE has no impact on both Doppler shift and TDCP velocities using the Novatel device, as is evident from the identical figures of merit reported in Tables 7 and 8, because no blunders were detected. The benefits coming from RAIM-FDE can be clearly appreciated when using the measurements of low-cost devices. For the GPS case with uBlox, the benefits of RAIM-FDE are evident in the TDCP solution where several spikes have been eliminated, improving all the figures of merit; no benefits are evident for Doppler velocity. A similar behavior is demonstrated for the Galileo-only case with uBlox.