## 8 Conclusions  
In this paper, we investigated the effects of different GNSS transmitters' antenna patterns assumptions on the transmitted signals' characteristics, in a trajectory that starts from LEO, crossing the SSV and ending at the Moon altitude. In particular, the analysis was carried out by simulating signal power levels, availability, GDOP, code tracking jitter, and, finally, the single-epoch least squares position and velocity solutions, assuming the receiver's characteristics of the SANAG spaceborne receiver proof-of-concept, under development in our laboratory. For the transmitters' antenna patterns of Block IIR and IIR-M L1 we used detailed information, available in the literature, while we were forced to make an assumption (although conservative) on the L1 IIF Block transmitters' patterns. We analyzed the GPS L1 availability in case the assumed patterns vary as a function of elevation and azimuth (3D pattern) and in case they vary only as a function of the elevation (2D pattern). The results show that the variation in the number of satellites is smaller when a 2D pattern is used. The higher variation in number of available observations when using a pattern changing in both elevation and azimuth causes very big GDOP peaks, which are then reflected in the navigation solution. When the spacecraft is orbiting along the SSV regions only 0.23 satellites per epoch (1 s) on average is the difference in availability (with a maximum of two satellites), while above 200,000 km it is 1.24 satellites per epoch (a maximum of five satellites). Hence, the approximation of the antenna gain pattern does not impact the SSV, but mainly very high altitudes. We investigated the effect on the SANAG receiver navigation performance for different assumptions on the L5 transmitters' patterns, for which little information is currently available. Figure 46: Zoomed-in version of Figure 45 between 80,000 km and 105,000 km. Figure 47: Zoomed-in version of Figure 45 between 170,000 km and 190,000 km. From our results we can state that the assumption on the L5 antenna pattern has a small influence on the availability (and consequently on the GDOP) for the two regions of the SSV, where there are always more than seven satellites. However, it is obvious that at very high altitudes, such as the last part of the assumed MTO, the number of available observations is more sensitive to the L5 pattern assumptions; the same happens to the GDOP, which worsens for the third assumed pattern, resulting in a large least-squares solution error. We can conclude that it is important to model the transmitters' antenna patterns dependency on the azimuth (since using a constant average value is not conservative) and also that for the GPS L5 signal, as expected, assuming a pattern with lower gain values for the side lobes is conservative. We analyzed the number of available GNSS observations for each receiver antenna elevation during the full mission; 62.8% of the signals are received between 1.5\({}^{\circ}\) and 7\({}^{\circ}\) from the receiver's antenna boresight and above 150,000 km only within 10\({}^{\circ}\). Below 150,000 km many signals reach the receiver's antenna between 10\({}^{\circ}\) and 30\({}^{\circ}\) elevation, but fortunately with stronger power and without the need for a strong receiver's antenna gain. Furthermore, we investigated the relationships between the availability and the elevation (the angle from the antenna boresight) at which the signals are transmitted during the full MTO; all the signals transmitted within an angle below 30\({}^{\circ}\) from the transmitters' antenna boresight should be included in the search space for the entire MTO and the ones below 75\({}^{\circ}\) should always be included in the search space up to 150,000 km. With the increase in the altitude, the number of available signals transmitted from elevations 30\({}^{\circ}\) to 90\({}^{\circ}\) is lower and lower than the number of satellites visible in the LOS, making any acquisition aiding strategy harder.