  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.
