High Performance Orbit Determination and Time Synchronization for Lunar Radio Navigation Systems

This paper presents a concept for the orbit determination and time synchronization (ODTS) of a lunar radio navigation system. The proposed approach utilizes small ground antennas that simultaneously track all satellites in the constellation using K-band frequency links. The work describes the architecture and performance of the radio system, highlighting the implementation of the multiple spacecraft per aperture (MSPA) concept. This configuration ensures sufficient data rates and achieves high accuracy in Doppler and range observables, enabling precise orbit determination. One notable outcome of this configuration is the availability of a new observable quantity, the differential phase of the two-way signals received by the ground station from any pair of satellites, also known as single-beam interferometry (SBI). The paper examines the achieved time transfer accuracies with different onboard clocks and evaluates the standard asynchronous two-way satellite time and frequency transfer (TWSTFT) method. Additionally, a novel time transfer method is proposed, leveraging onboard code epoch timestamping and precise spacecraft range information. Through the analysis of realistic test cases, the study demonstrates that orbit determination accuracies consistently remain below 10 meters (root sum square). Furthermore, the findings indicate that ephemerides aging and clock drifts align well with a navigation message repeat time of approximately three hours (99% confidence level), while maintaining a signal-in-space error (SISE) of 25 meters.