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Uncertainties in the satellite world lines lead to dominant positioningerrors. In the present work, using the approach presented in \cite{neu14}, anew analysis of these errors is developed inside a great region surroundingEarth. This analysis is performed in the framework of the so-calledRelativistic Positioning Systems (RPS). Schwarzschild metric is used todescribe the satellite orbits corresponding to the Galileo SatellitesConstellation. Those orbits are circular with the Earth as their centre. Theyare defined as the nominal orbits. The satellite orbits are not circular due tothe perturbations they have and to achieve a more realistic description suchperturbations need to be taken into account. In \cite{neu14} perturbations ofthe nominal orbits were statistically simulated. Using the formula from\cite{col10a} a user location is determined with the four satellites propertimes that the user receives and with the satellite world lines. This formulacan be used with any satellite description, although photons need to travel ina Minkowskian space-time. For our purposes, the computation of the photongeodesics in Minkowski space-time is sufficient as demonstrated in\cite{neu16}. The difference of the user position determined with the nominaland the perturbed satellite orbits is computed. This difference is defined asthe U-error. Now we compute the perturbed orbits of the satellites consideringa metric that takes into account the gravitational effects of the Earth, theMoon and the Sun and also the Earth oblateness...

astrophysics and space science

Relativistic positioning: including the influence of the gravitational  action of the Sun and the Moon and the Earth's oblateness on Galileo  satellites