###### Abstract  
In recent years, global navigation satellite system (GNSS)-based navigation in high earth orbits (HEOs) has become a field of research interest since it can increase the spacecraft's autonomy, thereby reducing the operating costs. However, the GNSS availability and the GNSS-based navigation performance for a spacecraft orbiting above the GNSS constellation are strongly constrained by the signals' power levels at the receiver position and the sensitivity. The simulated level of signal power at the receiver's position may considerably increase or decrease when assuming different gain/attenuation values of the transmitter antenna for a certain azimuth and elevation. Assuming a slightly different antenna pattern therefore may significantly change the simulated signal's availability results and accordingly the simulated navigation accuracy, leading to an inexact identification of the requirements for the GNSS receiver. This problem particularly concerns the case of orbital trajectories above the GNSS constellation, where most of the signals received are radiated from the secondary lobe of the transmitters' antennas, for which typically very little information is known. At the time of this study, it was possible to model quite accurately the global positioning system (GPS) L1 antenna patterns for the IIR and IIR-M Blocks because of the precise information available. No accurate information was available for the GPS L1 antenna patterns of the IIF Block. Even less accurate information was available on the GPS L5 antenna patterns. In this context, this paper aims at investigating the effect of different antenna pattern assumptions on the simulated signal availability and on the consequent simulated navigation performance of a spaceborne receiver orbiting in a very highly elliptical orbit from the Earth to the Moon. Initially the impact of averaging the transmitter's antenna gain over the azimuth, a typical assumption in many studies, is analyzed. Afterwards, we also consider three different L5 antenna patterns assumed in the literature (the precise L5 patterns are unfortunately not yet fully available). For each of the considered antenna pattern assumptions, we simulate received signal power level, availability, geometric dilution of precision (GDOP), and navigation accuracy in order to evaluate their different effects. After identifying the most conservative assumptions for the transmitters' antenna patterns, for each elevation of the receiver antenna, we also compute the number of available GNSS observations and analyze their distribution. Moreover, possible aiding of the acquisition process using the prediction of the elevation at which the signal is transmitted, as well as the elevation at which the signal is received, are discussed. Finally, the impact on the GDOP of using only signals transmitted from certain angle intervals of the transmitter antenna pattern and the importance of selecting the transmitters that provide the best GDOP (in the case of a receiver with a limited number of channels) are considered and discussed.  
keywords: global navigation satellite system (GNSS); global positioning system (GPS); antenna patterns; availability; navigation +
Footnote †: journal: Journal of Geomechanics and Physics