Related papers: Relativistic Positioning System in Perturbed Space…
Uncertainties in the satellite world lines lead to dominant positioning errors. In the present work, using the approach presented in \cite{neu14}, a new analysis of these errors is developed inside a great region surrounding Earth. This…
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…
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…
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating…
For reliable operation, next generation autonomous agents will need enhanced situational perception as well as precise navigation capabilities. The global navigation satellite system (GNSS) signals that are utilized by practically all…
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…
We extend to three dimensions the proposal of a completely relativistic positioning system (rPS). The system does not rely on approximations, in fact, it works at a few Schwarzschild radii from a black hole, and it does not rely on…
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…
In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated 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,…
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…
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…
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…
The Global Positioning System (GPS) is a U.S. space-based radionavigation system that provides reliable positioning, navigation, and timing services to civilian users on a continuous worldwide basis -- freely available to all. GPS provides…
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities…
A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and…
This paper considers the localization problem in a 5G-aided global navigation satellite system (GNSS) based on real-time kinematic (RTK) technique. Specifically, the user's position is estimated based on the hybrid measurements, including…
Emission relativistic coordinates are a class of spacetime coordinates defined and generated by four emitters (satellites, pulsars) broadcasting their proper time by radio signals. They are the main ingredient of the simplest conceivable…
We propose a quantum experiment to measure with high precision the Schwarzschild space-time parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth's space-time. As a…
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…