发表机构
The Stephen B. Klein Faculty of Aerospace Engineering, Technion – Israel Institute of Technology; Rafael Advanced Defense Systems / Department of Computer Science, Technion – Israel Institute of Technology（以色列理工学院斯宾塞·B·克莱恩航空航天工程学院; 拉斐尔先进防御系统公司/以色列理工学院计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对低轨卫星多普勒导航中GDOP与伪距导航不同的难题，本文建立几何基础，推导闭式参数化，用Schur补分解得出GDOP膨胀公式，证明几何耦合与协方差膨胀的关系，并指出高度多样性可降低共线性。
AI 中文摘要
全球导航卫星系统日益增长的脆弱性激发了人们对利用低地球轨道卫星进行多普勒导航的新兴趣，这种导航方式可以从载波多普勒测量中确定位置、速度、时钟偏差和时钟漂移。然而，在这个八状态问题中，几何精度因子（GDOP）的行为与基于伪距导航中的GDOP有着根本性的不同。特别是，基于体积的卫星选择方法，虽然对基于伪距的GDOP最小化有效，但经验上发现其对多普勒GDOP表现不佳。本文为多普勒GDOP的表征建立了几何基础。推导了多普勒测量雅可比矩阵关于仰角、方位角、轨道倾角和高度比的闭式几何参数化表达式。研究表明，时钟偏差灵敏度取决于仰角、高度以及卫星速度矢量与视线之间的夹角。这种灵敏度产生了与时钟漂移的相关性，任何几何排列都无法消除这种相关性。对八状态信息矩阵进行了Schur补分解，得出了一个精确的GDOP膨胀公式，该公式由一个共线性系数控制，该系数衡量时钟偏差列与七状态子空间之间的对齐程度。证明了使时钟偏差可观测的几何耦合正是膨胀估计协方差的同一耦合，并且卫星高度多样性通过将等仰角卫星分离到不同的灵敏度带上而减少了共线性。一个采用双壳卫星配置的示例说明了上述分析。
英文摘要
The increasing vulnerability of Global Navigation Satellite Systems has motivated renewed interest in Doppler-based navigation using low Earth orbit satellites, which can determine position, velocity, clock bias, and clock drift from carrier Doppler measurements. However, the geometric dilution of precision (GDOP) in this eight-state problem behaves fundamentally differently from the GDOP in pseudorange-based navigation. In particular, volume-based satellite selection, effective for pseudorange-based GDOP minimization, has been empirically found to perform poorly for Doppler GDOP. This paper establishes a geometric foundation for Doppler GDOP characterization. A closed-form geometric parameterization of the Doppler measurement Jacobian in terms of elevation, azimuth, inclination, and altitude ratio is derived. It is shown that the clock bias sensitivity depends on elevation, altitude, and the angle between the satellite velocity vector and the line of sight. This sensitivity produces a correlation with the clock drift that no geometric arrangement can remove. A Schur complement decomposition of the eight-state information matrix is performed, yielding an exact GDOP inflation formula, governed by a collinearity coefficient that measures the alignment between the clock bias column and a seven-state subspace. It is proven that the geometric coupling that renders clock bias observable is the same coupling that inflates estimation covariance, and that satellite altitude diversity reduces the collinearity by separating satellites at equal elevation onto distinct sensitivity bands. An example employing a two-shell satellite configuration illustrates the analysis.
