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

TL;DR

This work develops a fully relativistic framework for GNSS navigation in the Earth–Moon system by unifying the GCRS and BCRS formalism and introducing the LCRS for cislunar use. It derives direct and inverse coordinate-time transformations, along with practical, screened formulas for transforming position, velocity, and acceleration to achieve $O(c^{-2})$ accuracy and cm/ps performance, validated in GipsyX with DE440. The framework confirms that relativistic corrections are essential for cm-level orbit determination and sub-ns timing in both Earth-orbiting and cislunar contexts, enabling decimeter-level orbital accuracy and sub-nanosecond timing in the Earth–Moon regime. A NRHO-like minimal case study demonstrates end-to-end BCRS↔LCRS transformations and light-time modeling, and a concrete plan outlines three pathways to mature LCRS into a flight-ready capability for future lunar missions and deep-space GNSS operations.

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.

Figures (1)

• Figure 1: Millimeter‑level closure test of the BCRS implementation with JPL GipsyX. Panels show radial/along‑track/cross‑track closure residuals in meters (note the $10^{-3}$ scale, i.e., millimeter range) versus integration time (hours).