## 4 GPS L1/L5 Receiver: L5 Pattern Assumption
### Availability and GDOP  
In this case, according to the dual frequency L1/L5 capabilities of the SANAG receiver, the \(i\)-th GPS observation is considered available at time \(t_{k}\) if:  
1. At time \(t_{k}\), the corresponding \(i\)-th GPS L1 C/A signal is acquired (i.e., according to the conditions already specified in Section 3.2). Figure 21: Third-highest received power level of GPS L5 signals, during the considered MTO, for a 0 dBi receiver gain pattern. Figure 22: Fourth-highest received power level of GPS L5 signals, during the considered MTO, for a 0 dBi receiver gain pattern. In case the \(i\)-th GPS signal does not cross the ionosphere: the corresponding \(i\)-th GPS L5Q signal is tracked (i.e., the corresponding signal power is equal to or stronger than 12 dB-Hz). 3. In case the \(i\)-th GPS signal crosses the ionosphere: the corresponding \(i\)-th GPS L5Q and GPS L1 C/A signals are both tracked (i.e., the corresponding signal power is equal to or stronger than 12 dB-Hz for GPS L5Q and 15 dB-Hz for GPS L1 C/A). In Figure 23 is illustrated the availability of satellites as a function of the altitude, for the three considered L5 antenna patterns, during the entire MTO, assuming 10 dBi antenna gain for the receiver. The total number of available observations at each altitude is shown in Figure 24, where we can see clearly that at the end of the trajectory the availability is lower when assuming L5 pattern 3. Indeed, in this case, at the end of the considered MTO, the number of available observations is often less than 4, which is never the case for the other two assumed patterns (i.e., L5 pattern 1 and L5 pattern 2). Table 6 reports the precise information on the availability for the full trajectory and the three considered representative portions, such as percentage of availability, mean, max, and min number of available satellites, and percentage of time when more than four satellites are available. The GDOP for the three considered L5 patterns is shown in Figure 25. What is interesting to notice is that up to 250,000 km the GDOP has similar values for the three considered cases. As displayed in Figure 25, in the case of L5 pattern 3, the GDOP very often reaches values larger than 10,000 (at the end of the MTO). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Portion**} & \multicolumn{3}{c}{**L5 Antenna Pattern 1**} & \multicolumn{3}{c}{**L5 Antenna Pattern 2**} & \multicolumn{3}{c}{**L5 Antenna Pattern 3**} \\ \cline{2-11}  & **1** & **2** & **3** & **MTO** & **1** & **2** & **3** & **MTO** & **1** & **2** & **3** & **MTO** \\ \hline Average availability (\%) & 63.42 & 33.70 & 22.99 & 32.17 & 63.42 & 32.00 & 20.05 & 30.16 & 63.35 & 35.03 & 12.06 & 27.65 \\ Mean & 19.66 & 10.45 & 7.13 & 9.97 & 19.66 & 9.92 & 6.21 & 9.35 & 19.64 & 10.86 & 3.74 & 8.57 \\ Max & 26 & 13 & 10 & 26 & 26 & 12 & 9 & 26 & 26 & 13 & 7 & 26 \\ Min & 11 & 8 & 5 & 5 & 11 & 8 & 4 & 4 & 11 & 8 & 1 & 1 \\ \(\geq\)4 sats (\%) & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 62.52 & 88.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistics for the number of available observations. Figure 23: Available GPS L5 signals, during the assumed MTO, for a 10 dBi receiver gain pattern. Meanwhile, the continuity in terms of percentage of continuous time intervals with a duration equal to or longer than time interval T is shown in Figure 26 for the full MTO and the three considered portions. We can see that for the first portion the continuity curves are almost the same for the three considered L5 patterns, while for the two other portions and the entire trajectory they are different. Figure 24: Number of available observations during the assumed MTO. Figure 25: GDOP in log scale during the assumed MTO. From Table 6 we can conclude that the third assumed L5 (i.e., L5 pattern 3) patterns leads to worse availability mainly in the third considered portion compared to L5 pattern 1 and L5 pattern 2.