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

Abstract

We present an implementation-oriented relativistic modeling framework for high-precision {\tt 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 state-map truncation errors for cm-class orbit modeling. For $10^{-16}$-class fractional-frequency transfer, the ${\cal O}(c^{-4})$ 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~h round-trip GCRS$\rightarrow$BCRS$\rightarrow$GCRS propagation-and-transform closure test at the few-mm 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$\leftrightarrow$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.