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

Abstract: We present a relativistic modeling framework for GNSS-based navigation in Geocentric and Barycentric Celestial 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-cm positional accuracy. Numerical simulations with GipsyX validate cm-level orbit determination and timing stability within tens of picoseconds across GCRS and BCRS and demonstrate mm-level round-trip GCRS <--> BCRS frame closure over 24 h. 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 introduce the Lunicentric Celestial Reference System (LCRS) and its associated time scale to extend GNSS-based navigation into cislunar space. We present a minimal cislunar case study (NRHO-like geometry) that applies the improved position/velocity/acceleration transformations and the light-time model.