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Measuring emission coordinates in a pulsar-based relativistic positioning system
General Relativity and Quantum Cosmology · Submitted 8 Jul 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. | background 1.00 | 0.07 | 0.06 | asserted 0.87 |
| s1 | (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. | background 1.00 | 0.08 | 0.06 | asserted 1.00 |
| s2 | 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. | background 0.89 | 0.14 | 0.16 | asserted 1.00 |
| s3 | 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. | background 0.90 | 0.09 | 0.07 | hedged possibility 0.90 |
| s4 | We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. | contribution 0.98 | 0.92 | 0.22 | asserted 1.00 |
| s5 | Our approach uses a continuous solution of the eikonal equation describing the backward null cone from the event. | method 0.99 | 0.82 | 0.07 | asserted 1.00 |
| s6 | The pulsar proper time at the instant the null cone intersects the pulsar world line is one of the four required coordinates. | method 1.00 | 0.48 | 0.08 | asserted 1.00 |
| s7 | The process is complete (modulo degeneracies) when four pulsar world lines have been crossed by the light cone. | method 0.99 | 0.47 | 0.09 | asserted 1.00 |
| s8 | 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. | contribution 0.55 | 0.94 | 0.10 | asserted 1.00 |
| s9 | These numerical simulations are merely exploratory, but with improved resolution and computational resources the method can be applied to more pertinent problems. | limitation 0.80 | 0.67 | 0.08 | hedged possibility 0.68 |
| s10 | For instance one could measure the emission coordinates, and therefore the trajectory, of the Earth. | future work 1.00 | 0.06 | 0.09 | hedged possibility 0.97 |
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The paper
Original abstract
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.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 4 sentences without a confident label
Compares with 1 paper
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By contrast the analysis of [ref] (based on a different approach) is carried out essentially to machine precision for the Schwarzschild case.
Mapping the spacetime metric with GNSS: a preliminary study · Computational Accuracy · 1.00
Cites as background 4 papers
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It was treated extensively by Delva and Olympio [ref] ; they have in mind that the source is a navigational satellite in the Schwarzschild spacetime representing the Earth's gravitational field.
Mapping the spacetime metric with GNSS: a preliminary study · Introduction · 0.90
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A number of authors have developed the idea of a completely relativistic satellite positioning system; see [ref] .
Gravimetry, Relativity, and the Global Navigation Satellite Systems · Introduction · 0.86
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A number of authors have developed the idea of a completely relativistic satellite positioning system; see [ref] .
A principal positioning system for the Earth · Introduction · 0.86
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