Positioning and Timing of Distributed Lunar Satellites via Terrestrial GPS Differential Carrier Phase Measurements

Relative positioning, navigation, and timing (PNT) are crucial to support proximity operations of multiple spacecraft in lunar orbit, which is expected to play a key role in upcoming lunar missions. We propose a relative positioning and timekeeping technique in lunar orbit that leverages differential carrier phase measurements of the terrestrial GPS signals. However, using GPS signals in the lunar orbit is challenging due to 1) the clustered GPS satellite direction leading to a low-observable system, 2) the nonexistence of ionosphere delay models for lunar orbit, and 3) the possibility of cycle slips in the low C/N0 signals. We designed a PNT framework that tackles the three challenges above. First, to robustly make the filter converge in a low-observable system, the proposed PNT framework estimates the absolute and relative states in two separate filters, where filter settings (e.g., process noise) can be tuned separately. Second, to remove the signal-in-space errors, the proposed filter utilizes three different differential measurements. The absolute filter estimates time-differenced carrier phase (TDCP) measurements in combination with the pseudorange and pseudorange rate measurements, avoiding the need for estimating the integer ambiguity terms that are low observable. The relative filter estimates the relative orbit and clock offsets by processing the single difference carrier phase (SDCP) measurements, where signal-in-space errors are removed thanks to the short inter-satellite distance compared to the Earth-Moon distance. Using the obtained single difference float ambiguity estimate, the relative filter also fixes the integer ambiguities in double difference carrier phase (DDCP) measurements to improve the relative orbit estimates. Finally, cycleslip corrupted carrier-phase measurements are removed by observing the residuals in the TDCP measurements. We demonstrate the filter’s performance through simulations of two closely operating lunar satellites with different clock grades in the elliptical lunar frozen orbit (ELFO), wherein we showcase higher positioning and timing accuracy compared to code phase-only PNT methods.