Single-Satellite Lunar Navigation via Doppler Shift Observables for the NASA Endurance Mission

<h3>Abstract</h3> The National Aeronautics and Space Administration (NASA) Endurance rover mission concept is designed to enable the exploration and collection of samples along a 2000-km traverse within the Moon’s South Pole-Aitken (SPA) impact basin. Precise geotagging of these samples will be critical to the mission’s scientific objectives, which include characterizing the Solar System’s chronology and the Moon’s geological evolution. Concurrently, the European Space Agency (ESA) and Surrey Satellite Technology Ltd. (SSTL) are partnering to launch the Lunar Pathfinder satellite to provide communication services to lunar surface users, including the NASA Endurance rover. To enable precise absolute localization of the rover throughout its 2000-km traverse, we have investigated the achievable position estimation by opportunistically leveraging the Doppler shift observables from the Lunar Pathfinder’s downlink communication signals with no navigation payload. With only one satellite available, we accumulated Doppler shift measurements over time while the rover was stationary and refined the rover’s position estimate through a weighted batch filter framework. Through simulations, we modeled the effects of Doppler shift measurement uncertainty, which includes the frequency error of the rover clock as well as errors due to carrier tracking as a function of the carrier-to-noise ratio <i>C</i>/<i>N</i>₀. The state estimation performance is evaluated at different key locations of the SPA basin under varying degrees of satellite ephemeris uncertainty and clock stability. With this framework of using the Doppler shift as the only navigation observable, we find that the Lunar Pathfinder is able to opportunistically localize the Endurance rover with sub-10-m accuracy, on average, within two orbital periods of the Lunar Pathfinder. To the best of the authors’ knowledge, this paper is the first to examine the achievable localization of a lunar surface asset using only a single satellite that is not equipped with a navigation payload.