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Relativistic framework for high-precision GNSS processing in GCRS/BCRS with extension to cislunar space

We present an implementation-oriented relativistic modeling framework for high-precision GNSS processing consistent with the IAU-adopted Barycentric and Geocentric Celestial Reference Systems (BCRS/GCRS) and their associated time scales (TCB/TDB and TCG/TT). We derive explicit ${\cal O}(c^{-2})$ 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 truncation errors in sub-centimeter orbit modeling and retain the term order required by $10^{-16}$-class fractional-frequency transfer. We implement a BCRS-native processing option in JPL's GipsyX and validate it via a 24~h round-trip GCRS$\rightarrow$BCRS propagation-and-transform closure test at the few-mm level, demonstrating internal consistency of the dynamical model and the state transformations. 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$\leftrightarrow$LCRS transformation chain together with the 1PN 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.