Relativistic Framework for High-precision GNSS Processing in Geocentric and Barycentric Celestial Reference Systems with Extension to Cislunar Space

Abstract We present an implementation-oriented relativistic modeling framework for high-precision GNSS processing consistent with the IAU-adopted Geocentric and Barycentric Celestial Reference Systems (G CRS /B CRS ) and their associated timescales ( TCB/TDB and TCG/TT ). We derive explicit O ( c − 2 ) transformations for position, velocity, and acceleration between TT -compatible GCRS quantities and TDB -compatible BCRS quantities, and provide screened operational forms with conservative remainder bounds that quantify state-map truncation errors for centimeter-class orbit modeling. For 10 −16 -class fractional-frequency transfer, the O ( c − 4 ) clock-rate terms identified below must be retained or explicitly included in the observable error budget. We implement a BCRS -native processing option in JPL’s GipsyX and verify it internally via a 24 hr round-trip GCRS → BCRS → GCRS propagation-and-transform closure test at the few-millimeter level, demonstrating consistency of the implemented dynamical model and state transformations under matched force-model assumptions. To support emerging Earth–Moon applications, we define a Lunicentric Celestial Reference System ( LCRS ), its coordinate time ( TCL ), and a scaled lunar-surface time ( TL ), and specify a minimal near-rectilinear halo orbit ( NRHO )-like regression test that exercises the BCRS ↔ LCRS transformation chain together with the first post-Newtonian barycentric light-time model. End-to-end cislunar navigation performance additionally depends on signal availability and estimation strategy; the present work provides the relativistic reference-frame and time-transfer infrastructure needed to model observables at the centimeter and tens-of-picoseconds level.