ECLIPSE-X：作为航天器导航相对论天体测量约束的底片比例尺校准

中文摘要 AI 辅助

太阳附近的精密恒星天体测量可以通过引力光偏折来约束参数化后牛顿（PPN）参数γ。本研究开发了ECLIPSE-X，一种局部多帧估计架构，其中一个持久的相对论参数与依赖于帧的航天器视线和滚动状态同时估计，通过它们不同的空间特征以及γ在帧间的持久性来区分。目的不是对γ进行竞争性测定，而是评估这种联合解及其形式协方差在现实天体测量模型误差下是否保持统计有效性。在40帧、5秒节奏下观测了一个包含250颗恒星、覆盖1.22-8个太阳视半径的合成视场；加权最小二乘估计γ，每帧有三个导航状态，通过Schur补余边缘化给出导航耦合后γ的形式不确定性。名义解恢复γ = 1.0001198167，σγ = 3.075104e-4，1000次实现集成确认了校准。估计器未知的扰动将底片比例尺失配识别为主要失效机制：仅300 ppm的比例尺误差就将经验与形式不确定性之比膨胀到7126.6，且1σ和2σ覆盖率为零，而星表坐标失配为2.18，帧相干径向扰动为1.12，同时每次实现都数值收敛：收敛并不保证统计有效性。用底片比例尺参数增强状态可恢复一致性，但代价是γ的精度固定损失21.2%，该精度由两个持久参数之间的相关性决定。校准扫描显示，未增强的估计器仅在σp = 2.7884e-8以下具有协方差一致性，因此增强状态是近太阳相对论天体测量估计器的要求，而非改进。

英文摘要

Precision stellar astrometry near the Sun can constrain the parametrized post-Newtonian (PPN) parameter gamma through gravitational light deflection. This study develops ECLIPSE-X, a localized multi-frame estimation architecture in which one persistent relativistic parameter is estimated simultaneously with frame-dependent spacecraft line-of-sight and roll states, separated by their differing spatial signatures and by the persistence of gamma across frames. The aim is not a competitive determination of gamma, but an assessment of whether such a joint solution and its formal covariance stay statistically valid under realistic astrometric model error. A synthetic field of 250 stars spanning 1.22-8 apparent solar radii is observed over 40 frames at 5-s cadence; weighted least squares estimates gamma with three navigation states per frame, and Schur-complement marginalization gives the formal uncertainty in gamma after navigation coupling. The nominal solution recovers gamma = 1.0001198167 with sigma_gamma = 3.075104e-4, and a 1000-realization ensemble confirms calibration. Perturbations unknown to the estimator identify plate-scale mismatch as the dominant failure mechanism: a 300-ppm scale error alone inflates the empirical-to-formal uncertainty ratio to 7126.6 with zero 1-sigma and 2-sigma coverage, against 2.18 for catalog-coordinate mismatch and 1.12 for a frame-coherent radial perturbation, while every realization converges numerically: convergence does not guarantee statistical validity. Augmenting the state with a plate-scale parameter restores consistency, at a fixed 21.2% cost in the precision of gamma set by the correlation between the two persistent parameters. A calibration sweep shows the unaugmented estimator is covariance-consistent only below sigma_p = 2.7884e-8, so the augmented state is a requirement, not a refinement, for near-Sun relativistic astrometric estimators.

发表机构

• Embry-Riddle Aeronautical University（埃姆布里-里德尔航空大学）

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