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).

翻译：本文提出了一种基于地面全球导航卫星系统（GNSS）的月球导航卫星轨道与钟差估计框架。为在月球距离所面临的低可观测性条件下实现高精度估计，我们开发了一种随机克隆UD分解滤波器及延迟状态平滑器，该算法在处理精密时间差分载波相位（TDCP）观测值时具有更强的数值稳定性。本文构建了完整的动力学与观测模型，明确考虑了轨道与钟差状态之间的相对论性耦合、月球时标转换以及包括电离层、等离子体层和夏皮罗效应在内的信号传播延迟。通过高保真蒙特卡洛仿真对所提方法进行评估，仿真中融合了真实的多星座GNSS几何构型、广播星历误差、月球卫星动力学特性，以及基于经验电子密度模型计算的电离层与等离子体层延迟。仿真结果表明，结合无电离层伪距与TDCP观测值可实现米级轨道精度和亚毫米/秒级速度精度，满足未来月球增强导航服务（LANS）对空间信号误差的严苛要求。