# Time to First Fix Robustness of Global Navigation Satellite Systems: Comparison Study
## 3 Results
### Positioning Error  
Obtaining a low TTFF is useful as long as the accuracy of the position provided by the receiver is sufficient for the intended purposes of the corresponding application. For this reason, to evaluate the robustness of the TTFF, the positioning error obtained in the first fix also needs to be analysed. Taking into account that most mass-market applications are performed on the ground, this study specifically focuses on the horizontal error. The horizontal error is derived by converting the first fixed position, calculated through standard point positioning (SPP), into Universal Transverse Mercator (UTM) coordinates and comparing them with the georeferenced position of the GNSS antenna.  
In Figure 8, the outcome of the horizontal error as a function of attenuation is depicted for the different GNSSs. The associated statistics (mean, standard deviation, minimum, and maximum) are also provided in Table 3. In those cases where no fix is achieved, the horizontal error assigned is the highest value obtained in any other run of the same recording for that specific GNSS. However, this limitation imposed on the maximum value gives rise to an artificial reduction in the standard deviation for high attenuation levels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Horizontal Error**} & \multirow{2}{*}{**GNSS**} & \multicolumn{10}{c}{**Attenuation (dB)**} \\ \cline{3-13}  & & **0** & **2** & **4** & **6** & **8** & **10** & **12** & **14** & **16** & **18** & **20** \\ \hline \multirow{4}{*}{Mean (m)} & BeiDou & 2.62 & 2.72 & 3.20 & 3.95 & 4.87 & 4.14 & 3.70 & 4.66 & 5.34 & 6.40 & 7.71 \\  & Galileo & 3.21 & 3.43 & 3.26 & 3.44 & 3.76 & 4.57 & 5.17 & 6.59 & 8.42 & 10.3 & 13.9 \\  & GLONASS & 5.29 & 5.83 & 6.98 & 9.94 & 13.5 & 18.6 & 22.0 & 27.0 & 30.3 & 32.5 & 43.6 \\  & GPS & 2.24 & 2.16 & 2.11 & 2.15 & 2.19 & 2.37 & 2.46 & 2.71 & 2.66 & 2.69 & 3.42 \\ \hline \multirow{4}{*}{Standard deviation (m)} & BeiDou & 1.62 & 1.71 & 2.96 & 5.18 & 7.51 & 3.23 & 2.28 & 3.85 & 3.33 & 4.41 & 5.15 \\  & Galileo & 3.65 & 4.12 & 3.79 & 3.75 & 3.56 & 3.95 & 4.50 & 6.09 & 7.27 & 9.78 & 16.8 \\  & GLONASS & 3.94 & 4.70 & 6.14 & 10.4 & 11.0 & 15.7 & 20.7 & 27.3 & 30.8 & 30.9 & 37.1 \\  & GPS & 1.47 & 1.37 & 1.32 & 1.35 & 1.36 & 1.60 & 1.78 & 1.79 & 1.71 & 1.83 & 2.32 \\ \hline \multirow{4}{*}{Minimum (m)} & BeiDou & 0.22 & 0.37 & 0.44 & 0.50 & 0.42 & 0.67 & 0.70 & 0.54 & 0.74 & 1.01 & 1.61 \\  & Galileo & 0.25 & 0.32 & 0.46 & 0.63 & 0.62 & 0.71 & 0.64 & 0.52 & 1.22 & 1.57 & 2.58 \\  & GLONASS & 0.62 & 0.71 & 1.10 & 1.56 & 1.68 & 1.78 & 4.28 & 4.04 & 2.59 & 3.69 & 3.49 \\  & GPS & 0.21 & 0.21 & 0.22 & 0.26 & 0.41 & 0.23 & 0.40 & 0.85 & 0.59 & 0.58 & 0.99 \\ \hline \multirow{4}{*}{Maximum (m)} & BeiDou & 11.5 & 10.7 & 26.3 & 48.6 & 66.4 & 21.2 & 12.6 & 32.3 & 18.1 & 23.2 & 29.9 \\  & Galileo & 29.3 & 31.0 & 26.5 & 23.7 & 24.9 & 26.6 & 28.3 & 36.4 & 40.2 & 68.3 & 131 \\ \cline{1-1}  & GLONASS & 30.4 & 37.5 & 46.8 & 63.3 & 69.2 & 72.2 & 114 & 155 & 173 & 155 & 226 \\ \cline{1-1}  & GPS & 8.30 & 6.71 & 6.45 & 7.26 & 7.59 & 8.45 & 10.5 & 10.3 & 9.80 & 12.6 & 17.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical results for the horizontal error.  
Figure 7: TTFF versus attenuation for the different GNSSs.  
Under optimal conditions, all GNSSs achieve similar results regarding the horizontal error, except for GLONASS. GLONASS presents larger errors, which are already above 5 metres without any attenuation. As attenuation increases, GPS exhibits the lowest degradation of its horizontal positioning. BeiDou and Galileo also present acceptable results, with those of Galileo being more stable. However, their horizontal errors increase with attenuation at a higher rate in comparison with those of GPS.