Design of the broadcast ephemerides for the Lunar Communication and Navigation Services system

The last few years have brought extensive growth of interest in the Earth's natural satellite-the Moon. The lunar surface, especially the surroundings of its south pole, is supposed to become a getaway for space exploration including Mars in the first place. The European Space Agency initiated the Moonlight activity to provide services connected to navigation and communication with future lunar infrastructure. One of the key aspects of every navigation system is the design of the broadcast ephemerides for the orbiters. We investigate two methods of the navigation message representation for the future lunar navigation system. We conduct simulations of the lunar orbiter trajectory which is subject to a complex force model including gravitational and non-gravitational forces. The initially proposed orbit parameters assume a high eccentricity of the orbit which introduces challenges in the modeling of the satellite trajectory when passing above the periselene regions of the orbit. Further, we test the representation of the navigation message using the model which consists of the Keplerian elements and empirical accelerations, as well as Chebyshev polynomials. To obtain a sub-decimeter quality of the orbit recovery, one needs to use either model which considers six Keplerian elements together with nine empirical accelerations or Chebyshev polynomials of degree 10 with 11 coefficients, both within the 1 h time window. The navigation message represented using Chebyshev polynomials demands a higher bit storage, i.e., 576, when compared to the Keplerian elements and empirical accelerations with 401 bits. On the other hand, the Keplerian elements together with the empirical accelerations introduce computation complexities for the end user requiring a numerical integration algorithm to compute the satellite position in the given time window. However, the Keplerian elements can be used outside the validity time window, which is impossible for the Chebyshev representation. For 95% of the cases, the quality of the orbit recovery is better than 6.7, and 3.2 cm when using Keplerian elements together with empirical accelerations and Chebyshev polynomials, respectively. As a result, both methods can potentially be used to represent the navigation message for the designed Lunar Communication and Navigation Services system.