Terrestrial GPS Time-Differenced Carrier-Phase Positioning of Lunar Surface Users

To support the increasing interest in lunar exploration, the future lunar users will require precise position, velocity, and timing (PVT) services on the Moon. Active efforts are being invested in utilizing terrestrial GPS signals at lunar distances to achieve precise lunar surface localization. Compared to conventional pseudoranges of terrestrial GPS satellites, carrier phase measurements are 1000 times more accurate when integer ambiguities (unknown number of cycles) are accurately resolved. We propose a precise localization technique for lunar users, wherein we design a tightly-coupled Kalman filter framework that utilizes the terrestrial GPS time-differenced carrier phase (TDCP) measurements and inertial measurement unit (IMU)-based motion dynamics. To account for the time-correlation across TDCP measurements, we design an augmented state vector that incorporates consecutive rover states and perform fixed point smoothing before each measurement update. Through high-fidelity Monte-Carlo simulations, we validate that our framework not only isolates the TDCP measurements suffering from cycle slips but also demonstrates precise localization on the lunar surface.