论文标题
弯曲时空中的相对论位置算法
Relativistic location algorithm in curved spacetime
论文作者
论文摘要
在本文中，我们描述并在数值上实现了一种相对论位置的方法，以略有弯曲但泛型的空间。对于在全球导航卫星系统的背景下进行陆地定位，我们的算法结合了由Gordon Metric建模的引力以及对流层和电离层效应。该算法在\ textsc {squirrel.jl}代码中实现，该代码采用了准Newton broyden算法与数值大地测量学的自动差异结合使用。我们的工作为通用时空中的相对论位置问题提供了实用的解决方案，并在单个框架中巩固了相对论和大气效应。尽管优化不是我们的主要重点，但我们的实施已经足够快地用于实际使用，从桌面计算机上的$ <1〜 {\ rm s} $从五个排放点建立了一个位置，以实现合理简单的时空几何形状。在真空中，考虑到具有陆地参数的KERR度量和子计精度，包括对流层和电离层效应，我们的实施可以实现亚毫米准确性。
In this article, we describe and numerically implement a method for relativistic location in slightly curved but otherwise generic spacetimes. For terrestrial positioning in the context of Global Navigation Satellite Systems, our algorithm incorporates gravitational as well as tropospheric and ionospheric effects modeled by the Gordon metric. The algorithm is implemented in the \textsc{squirrel.jl} code, which employs a quasi-Newton Broyden algorithm in conjunction with automatic differentiation of numerical geodesics. Our work provides a practical solution to the relativistic location problem in a generic spacetime and consolidates relativistic and atmospheric effects in a single framework. Though optimization is not our primary focus, our implementation is already fast enough for practical use, establishing a position from five emission points in $< 1~{\rm s}$ on a desktop computer for reasonably simple spacetime geometries. In vacuum, our implementation can achieve submillimeter accuracy considering the Kerr metric with terrestrial parameters and submeter accuracy including tropospheric and ionospheric effects.
