Location Problem in Relativistic Positioning: Relative Formulation

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-07-17 DOI:10.3390/universe10070299

Ramón Serrano Montesinos, J. J. Ferrando, J. A. Morales-Lladosa

引用次数: 0

Abstract

A relativistic positioning system is a set of four emitters broadcasting their proper times by means of light signals. The four emitter times received at an event constitute the emission coordinates of the event. The covariant quantities associated with relativistic positioning systems are analysed relative to an observer in Minkowski space-time by splitting them in their relative space-like and time-like components. The location of a user in inertial coordinates from a standard set of emission data (emitted times and satellite trajectories) is solved in the underlying 3+1 formalism. The analytical location solution obtained by Kleusberg for the GPS system is recovered and interpreted in a Minkowskian context.

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相对论定位中的位置问题：相对公式

相对论定位系统是一套由四个发射器组成的系统，通过光信号广播它们的适当时间。在某一事件中接收到的四个发射器时间构成了该事件的发射坐标。相对于闵科夫斯基时空中的观察者，与相对论定位系统相关的协变量是通过将它们拆分为相对的类空间和类时间分量来分析的。根据一组标准发射数据（发射时间和卫星轨迹），在惯性坐标中求解用户的位置。克莱斯贝格（Kleusberg）为全球定位系统获得的分析定位解在明科夫斯基（Minkowskian）背景下得到恢复和解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.