Relativistic framework for high-precision GNSS-based navigation in cislunar space

We present a relativistic modeling framework for GNSS-based navigation in geocentric and barycentric coordinate reference systems, i.e., GCRS and BCRS, respectively. Using the IAU-adopted GCRS and BCRS conventions, we derive closed-form transformations for position, velocity, and acceleration that are required to achieve fractional-frequency transfer precision of 10 16 and sub-centimeter positional accuracy. We introduce the Lunicentric Coordinate Reference System (LCRS) and its associated time scale to extend GNSS-based navigation into cislunar space. Numerical simulations with GipsyX validate centimeter-level orbit determination and timing stability within tens of picoseconds across GCRS, BCRS, and LCRS. These results underscore the necessity of relativistic corrections for high-precision GNSS throughout the Earth–Moon system and demonstrate that GNSS signals can support a decimeter-level orbit accuracy and sub-nanosecond-scale timing synchronization in cislunar space, establishing a robust framework for future operations. We present a minimal cislunar case study (NRHO-like geometry) that applies the improved position/velocity/acceleration transformations, the LCRS transformations, and the light-time model. We also define and verify a frame-closure metric between BCRS and LCRS, providing an implementation-ready approach for cislunar navigation.