Autonomous orbit determination and timekeeping in lunar distant retrograde orbits by observing X-ray pulsars

A server satellite that is parked in a stable distant retrograde orbit (DRO) in the vicinity of the Moon can provide navigation service for satellites in the Earth-Moon system. In this study, X-ray pulsar navigation (XPNAV) is investigated to determine the server's orbital position and velocity, and maintain its onboard timing autonomously to ensure the autonomy of the server. First, the feasibility and potential advantages of XPNAV in DRO are analyzed qualitatively based on the unique properties of DRO: long-term orbital stability and short-term, nearly uniform-velocity rectilinear motion. Second, high-fidelity X-ray photon timestamps are simulated to serve as the original measurements for XPNAV. A classical extended Kalman filter is used to estimate the orbital states (i.e., position and velocity) and the clock timing of the satellite in DRO, wherein the pulse phase and Doppler frequency are estimated as intermediate measurements. Finally, Monte Carlo simulations are conducted to assess the variation in the XPNAV performance with the DRO orbital period, clock noise, and detector effective area. The simulation results show that XPNAV in DRO can achieve considerably improved position accuracy than that in low Earth orbit using the same hardware while maintaining the long-term stability of the satellite onboard clock, thus demonstrating the capability of XPNAV to be used in an operational spaceflight mission around or beyond the Moon.