24,068 research outputs found
A relativistic navigation system for space
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 fourdimensional grid covering the whole spacetime and made of the null hypersurfaces representing the propagating pulses. In our first approach to the problem of positioning we consider radio-pulsars at infinity as primary sources of the required signals. The reason is that, besides being very good clocks, pulsars can be considered as being fixed stars for reasonably long times. The positioning is obtained linearizing the worldline of the observer for times of the order of a few periods of the signals. We present an exercise where the use of our method applied to the signals from four real pulsars permits the reconstruction of the motion of the Earth with respect to the fixed stars during three days. The uncertainties and the constraints of the method are discussed and the possibilities of using mov- ing artificial sources carried around by celestial bodies or spacecrafts in the Solar System is also discusse
A null frame for spacetime positioning by means of pulsating sources
We introduce an operational approach to the use of pulsating sources, located
at spatial infinity, for defining a relativistic positioning and navigation
system, based on the use of four-dimensional bases of null four-vectors, in
flat spacetime. As a prototypical case, we show how pulsars can be used to
define such a positioning system. The reception of the pulses for a set of
different sources whose positions in the sky and periods are assumed to be
known allows the determination of the user's coordinates and spacetime
trajectory, in the reference frame where the sources are at rest. We describe
our approach in flat Minkowski spacetime, and discuss the validity of this and
other approximations we have considered.Comment: 19 pages, revised to match the version accepted for publication in
Advances in Space Researc
A relativistic positioning system exploiting pulsating sources for navigation across the Solar System and beyond
We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of null four-vectors in a flatMinkowskian spacetime. We describe our approach and discuss the validity of it and of the other approximations we have considered in actual physical situations. As a prototypical case, we show how pulsars can be used to define such a positioning system: the reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user's coordinates and spacetime trajectory, in the reference frame where the sources are at rest. In order to confirm the viability of the method, we consider an application example reconstructing the world-line of an idealized Earth in the reference frame of distant pulsars: in particular we have simulated the arrival times of the signals fromfour pulsars at the location of the Parkes radiotelescope in Australia. After pointing out the simplifications we have made, we discuss the accuracy of the method. Eventually, we suggest that the method could actually be used for navigation across the Solar System and be based on artificial sources, rather than pulsar
Efficient AoA-based wireless indoor localization for hospital outpatients using mobile devices
The motivation of this work is to help outpatients find their corresponding departments or clinics, thus, it needs to provide indoor positioning services with a room-level accuracy. Unlike wireless outdoor localization that is dominated by the global positioning system (GPS), wireless indoor localization is still an open issue. Many different schemes are being developed to meet the increasing demand for indoor localization services. In this paper, we investigated the AoA-based wireless indoor localization for outpatients’ wayfinding in a hospital, where Wi-Fi access points (APs) are deployed, in line, on the ceiling. The target position can be determined by a mobile device, like a smartphone, through an efficient geometric calculation with two known APs coordinates and the angles of the incident radios. All possible positions in which the target may appear have been comprehensively investigated, and the corresponding solutions were proven to be the same. Experimental results show that localization error was less than 2.5 m, about 80% of the time, which can satisfy the outpatients’ requirements for wayfinding
Emitter Location Finding using Particle Swarm Optimization
Using several spatially separated receivers, nowadays positioning techniques, which are implemented to determine the location of the transmitter, are often required for several important disciplines such as military, security, medical, and commercial applications. In this study, localization is carried out by particle swarm optimization using time difference of arrival. In order to increase the positioning accuracy, time difference of arrival averaging based two new methods are proposed. Results are compared with classical algorithms and Cramer-Rao lower bound which is the theoretical limit of the estimation error
Pulsars as celestial beacons to detect the motion of the Earth
In order to show the principle viability of a recently proposed relativistic
positioning method based on the use of pulsed signals from sources at infinity,
we present an application example reconstructing the world-line of an idealized
Earth in the reference frame of distant pulsars. The method considers the null
four-vectors built from the period of the pulses and the direction cosines of
the propagation from each source. Starting from a simplified problem (a
receiver at rest) we have been able to calibrate our procedure, evidencing the
influence of the uncertainty on the arrival times of the pulses as measured by
the receiver, and of the numerical treatment of the data. The most relevant
parameter turns out to be the accuracy of the clock used by the receiver.
Actually the uncertainty used in the simulations combines both the accuracy of
the clock and the fluctuations in the sources. As an evocative example the
method has then been applied to the case of an ideal observer moving as a point
on the surface of the Earth. The input have been the simulated arrival times of
the signals from four pulsars at the location of the Parkes radiotelescope in
Australia. Some substantial simplifications have been made both excluding the
problems of visibility due to the actual size of the planet, and the behaviour
of the sources. A rough application of the method to a three days run gives a
correct result with a poor accuracy. The accuracy is then enhanced to the order
of a few hundred meters if a continuous set of data is assumed. The method
could actually be used for navigation across the solar system and be based on
artificial sources, rather than pulsars. The viability of the method, whose
additional value is in the self-sufficiency, i.e. independence from any control
from other operators, has been confirmed.Comment: 11 pages, 3 eps figures; revised to match the version accepted for
publication in IJMP
Measuring emission coordinates in a pulsar-based relativistic positioning system
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 event in spacetime can be fully described by emission coordinates: the
proper emission time of each pulse measured at the event. The proper emission
time of each pulse from four different pulsars---interpolated as
necessary---provides the four spacetime coordinates of the reception event in
the emission coordinate system. If more than four pulsars are available, the
redundancy can improve the accuracy of the determination and/or resolve
degeneracies resulting from special geometrical arrangements of the sources and
the event.
We introduce a robust numerical approach to measure the emission coordinates
of an event in any arbitrary spacetime geometry. Our approach uses a continuous
solution of the eikonal equation describing the backward null cone from the
event. The pulsar proper time at the instant the null cone intersects the
pulsar world line is one of the four required coordinates. The process is
complete (modulo degeneracies) when four pulsar world lines have been crossed
by the light cone.
The numerical method is applied in two different examples: measuring emission
coordinates of an event in Minkowski spacetime using pulses from four pulsars
stationary in the spacetime; and measuring emission coordinates of an event in
Schwarzschild spacetime using pulses from four pulsars freely falling toward a
static black hole.
These numerical simulations are merely exploratory, but with improved
resolution and computational resources the method can be applied to more
pertinent problems. For instance one could measure the emission coordinates,
and therefore the trajectory, of the Earth.Comment: 9 pages, 2 figures, v3: replaced with version accepted by Phys. Rev.
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