## 1 Introduction
Evidently, correctly modeling the side lobes of the transmitters' antennas is very important as it would directly affect the navigation performance at the high altitudes obtained in simulation. In the case of GPS L1 and L2, antenna gain data and relative phase data has been released for Blocks IIR and IIR-M [3]. On the other side, Boeing, which is responsible for building GPS Block IIF satellites, has not released any similar document yet. Even more obscure is the information regarding GPS L5 antenna directivity data. Existing information used by researchers is usually an approximation of the expected patterns using the information in [4]. No definite data have been released so far, causing possible inaccuracies in the results of the published researches. In [5], for instance, only an example of L5 pattern for only one PRN (PRN 5, from block IIR-M) is reported, and without detailing how this pattern was approximated from the available data. In our previous research [6], we investigated the feasibility of using GNSS as navigation system to reach the Moon; in [7] we described the implementation of an orbital filter in order to improve the navigation accuracy; in [8] we detailed how such a filter can be used for aiding purposes; in [9] we demonstrated the GNSS accuracy at GEO altitude achieved with the developed orbital filter considering that the receiver is able to process different signal combinations. However, the lack of information about the transmitters' antenna patterns has always limited the level of accuracy. Considering the importance of the antenna pattern assumptions, in this research we aim to evaluate the effects of different antenna pattern assumptions when simulating the performance of a GNSS-based navigation system for space missions, in order to identify the most conservative assumptions to be used in our future simulations and tests. Elements like experienced signal levels, availability, GDOP and ranging error were computed for different antenna patterns assumptions. Moreover, the impact of different antenna pattern assumptions on the navigation solutions obtained using the single-point least squares technique and an orbital filter was analyzed. Initially, we evaluated the effect of averaging the gain pattern in azimuth for the GPS L1 signals and then we explored the impact of assuming different GPS L5 patterns available from the literature. Furthermore, information on the elevation angles of the transmitter and receiver antenna patterns of the available GNSS signals is also considered and analyzed. Figure 1: Elevation angle of the global positioning system (GPS) antenna pattern from which the signals are received, for the assumed moon transfer orbit (MTO) in Section 2.1. Figure 2: Number of GPS satellites received from main and side lobes of the transmitters’ antenna pattern, for the assumed MTO in Section 2.1. These evaluations were carried out considering the characteristics of the \"SANAG\" (spaceborne autonomous navigation based on GNSS) receiver, a proof-of-concept GPS receiver under development in our laboratory, specifically for lunar missions. The considered MTO is an interesting trajectory case, as it includes the signals' characteristics of the SSV and beyond, up to the Moon. Following a description of the models and assumptions (in Section 2), in the first part of the paper (in Sections 3 and 4), we analyze the effect of assuming different transmitter antenna patterns on the signal power level at the receiver's position, on the availability, on the GDOP, and finally on the navigation accuracy. The analysis was performed for the signals that the SANAG receiver can process and then for GPS L1 C/A (in Section 3) and for GPS L5 (Section 4), for which we considered different antenna patterns information publically available.