标题： 扰动时空中的相对论定位系统 显示英文标题

标题： Relativistic Positioning System in Perturbed Space-time

摘要： 我们提出了一种称为相对论定位系统（RPS）的全球导航卫星系统的变体，该系统基于发射坐标。我们在地球周围的时空中对RPS动力学进行了建模，该时空由受扰的施瓦茨希尔德度规描述，其中包含了由于地球多极矩（最高到第六阶）、月球、太阳、金星、木星、固体潮汐、海洋潮汐和克尔旋转效应引起的扰动。卫星与用户之间的信号交换是通过在施瓦茨希尔德时空中的射线追踪方法计算的。我们发现，在受扰的时空中进行定位是可行的，并且使用标准数值过程即可达到很高的精度：用于将发射坐标转换为用户施瓦茨希尔德坐标的定位算法非常精确且时间效率高——在笔记本电脑上，分别以相对精度$10^{-28}-10^{-26}$和$10^{-32}-10^{-30}$确定用户的时空坐标需要0.04秒。 显示英文摘要

摘要： We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild space-time. We find that positioning in a perturbed space-time is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient -- on a laptop it takes 0.04 s to determine the user's spatial and time coordinates with a relative accuracy of $10^{-28}-10^{-26}$ and $10^{-32}-10^{-30}$, respectively.