Real-Time Position, Velocity, and Timing Estimation of Lunar Surface Users with Joint Doppler and Ranging

Future lunar missions will require onboard, real-time position, velocity, and timing (PVT) knowledge for surface users. This paper introduces accurate, real-time, and onboard PVT estimation for a moving lunar surface user with a three satellite lunar navigation constellation using Joint Doppler and Ranging (JDR). Utilizing one-way measurements, JDR enables autonomous navigation for a scalable number of surface users around a self-positioned reference station. First, this study introduces the generalized JDR equations that account for user and reference station velocity. Infeasible regions are possible with the JDR equations, resulting in complex values that can lead to computational errors and numerical instabilities. However, a brief analysis demonstrates the unlikeliness of these infeasible regions. Then, this analysis simulates PVT performance of JDR with measurement differencing using a well-known reference station and one-way range and Doppler measurements from a few orbiters. The study compares the PVT accuracy of JDR with measurement differencing relative to traditional pseudorange and Doppler measurement differencing assuming a highly dynamic surface user. The lunar surface user traverses 12.8 km over a 32-hour trajectory that includes continuous turns and both positive and negative accelerations in user velocity magnitude. During the entire interval, the orbiters broadcast one-way ranging codes to both the user and reference station in S-Band. The reference station also broadcasts a separate ranging code in UHF to its local region. The simulation generates Doppler shift measurements including instrumentation and propagation error sources with a space qualified chip-scale atomic clock as the user's local oscillator. A Monte Carlo analysis with an extended Kalman filter implementing double differencing with JDR (DD-JDR) estimates PVT with a root sum-squared (RSS) accuracy of 9 m for position, 17 mm/s for velocity, and 230 ns for timing errors at 95% confidence. Using the same measurements, measurement errors, and navigation architecture, traditional double differencing (Trad DD) achieves 23 m, 17 mm/s, and 250 ns of RSS position, velocity, and timing error at 95% confidence. DD-JDR improves positioning performance by more than a factor of two with no additional measurements or changes in navigation architecture.