Related papers: The Relativistic framework of Positioning systems
4 emitters broadcasting an increasing electromagnetic signal generate a system of relativistic coordinates for the space-time, called emission coordinates. Their physical realization requires an apparatus similar to the one of the Global…
This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated…
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in…
The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the…
Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a…
A {\em relativistic positioning system} consists in a set of four clocks broadcasting their respective proper time by means of light signals. Among them, the more important ones are the {\em auto-located positioning systems,} in which every…
Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian spacetime, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of…
We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on…
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic…
Fully relativistic coordinates have been proposed for (relativistically) running a "GPS" system. These coordinates are the arrival times of the light signals emitted by four "satellites" (clocks). Replacing the signals emitted by four…
A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
We present here a method for the relativistic positioning in spacetime based on the reception of pulses from sources of electromagnetic signals whose worldline is known. The method is based on the use of a four-dimensional grid covering the…
Starting from the description of space-time as a curved four-dimensional manifold, null Gaussian coordinates systems as appropriate for relativistic positioning will be discussed. Different approaches and strategies will be reviewed,…
A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…
A general approach to the problem of positioning by means of pulsars or other pulsating sources located at infinity is described. The counting of the pulses for a set of different sources whose positions in the sky and periods are assumed…
Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in…
A relativistic positioning system has been proposed by Bartolom\'e Coll in 2002. Since then, several group developed this topic with different approaches. I will present a work done in collaboration with Ljubljana University and the ESA…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…