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In order to show the principle viability of a recently proposed relativisticpositioning method based on the use of pulsed signals from sources at infinity,we present an application example reconstructing the world-line of an idealizedEarth in the reference frame of distant pulsars. The method considers the nullfour-vectors built from the period of the pulses and the direction cosines ofthe propagation from each source. Starting from a simplified problem (areceiver at rest) we have been able to calibrate our procedure, evidencing theinfluence of the uncertainty on the arrival times of the pulses as measured bythe receiver, and of the numerical treatment of the data. The most relevantparameter turns out to be the accuracy of the clock used by the receiver.Actually the uncertainty used in the simulations combines both the accuracy ofthe clock and the fluctuations in the sources. As an evocative example themethod has then been applied to the case of an ideal observer moving as a pointon the surface of the Earth. The input have been the simulated arrival times ofthe signals from four pulsars at the location of the Parkes radiotelescope inAustralia. Some substantial simplifications have been made both excluding theproblems of visibility due to the actual size of the planet, and the behaviourof the sources. A rough application of the method to a three days run gives acorrect result with a poor accuracy. The accuracy is then enhanced to the orderof a few hundred meters if a continuous set of data is assumed. The methodcould actually be used for navigation across the solar system and be based onartificial sources, rather than pulsars. The viability of the method, whoseadditional value is in the self-sufficiency, i.e. independence from any controlfrom other operators, has been confirmed.

Pulsars as celestial beacons to detect the motion of the Earth