GNSS-based Lunar Orbit and Clock Estimation With Stochastic Cloning UD Filter

TL;DR

This paper introduces a GNSS-based lunar orbit and clock estimation framework using a stochastic-cloning UD filter and delayed-state smoother, achieving high-precision results under challenging lunar conditions.

Contribution

It develops a novel stochastic-cloning UD filter and smoother tailored for lunar GNSS navigation, explicitly modeling relativistic and delay effects for improved accuracy.

Findings

Achieves meter-level orbit accuracy in simulations.

Attains sub-millimeter-per-second velocity accuracy.

Demonstrates robustness under realistic GNSS error conditions.

Abstract

This paper presents a terrestrial GNSS-based orbit and clock estimation framework for lunar navigation satellites. To enable high-precision estimation under the low-observability conditions encountered at lunar distances, we develop a stochastic-cloning UD-factorized filter and delayed-state smoother that provide enhanced numerical stability when processing precise time-differenced carrier phase (TDCP) measurements. A comprehensive dynamics and measurement model is formulated, explicitly accounting for relativistic coupling between orbital and clock states, lunar time-scale transformations, and signal propagation delays including ionospheric, plasmaspheric, and Shapiro effects. The proposed approach is evaluated using high-fidelity Monte-Carlo simulations incorporating realistic multi-constellation GNSS geometry, broadcast ephemeris errors, lunar satellite dynamics, and ionospheric and plasmaspheric delay computed from empirical electron density models. Simulation results demonstrate that combining ionosphere-free pseudorange and TDCP measurements achieves meter-level orbit accuracy and sub-millimeter-per-second velocity accuracy, satisfying the stringent signal-in-space error requirements of future Lunar Augmented Navigation Services (LANS).