Abstract
Uncertainties in the satellite world lines lead to dominant positioning errors. In the present work, using the approach presented in Puchades and Sáez (Astrophys. Space Sci. 352, 307–320, 2014), a new analysis of these errors is developed inside a great region surrounding Earth. This analysis is performed in the framework of the so-called Relativistic Positioning Systems (RPS). Schwarzschild metric is used to describe the satellite orbits corresponding to the Galileo Satellites Constellation. Those orbits are circular with the Earth as their centre. They are defined as the nominal orbits. The satellite orbits are not circular due to the perturbations they have and to achieve a more realistic description such perturbations need to be taken into account. In Puchades and Sáez (Astrophys. Space Sci. 352, 307–320, 2014) perturbations of the nominal orbits were statistically simulated. Using the formula from Coll et al. (Class. Quantum Gravity. 27, 065013, 2010) a user location is determined with the four satellites proper times that the user receives and with the satellite world lines. This formula can be used with any satellite description, although photons need to travel in a Minkowskian space-time. For our purposes, the computation of the photon geodesics in Minkowski space-time is sufficient as demonstrated in Puchades and Sáez (Adv. Space Res. 57, 499–508, 2016). The difference of the user position determined with the nominal and the perturbed satellite orbits is computed. This difference is defined as the U-error. Now we compute the perturbed orbits of the satellites considering a metric that takes into account the gravitational effects of the Earth, the Moon and the Sun and also the Earth oblateness. A study of the satellite orbits in this new metric is first introduced. Then we compute the U-errors comparing the positions given with the Schwarzschild metric and the metric introduced here. A Runge-Kutta method is used to solve the satellite geodesic equations. Some improvements in the computation of the U-errors using both metrics are introduced with respect to our previous works. Conclusions and perspectives are also presented.
Highlights
The numerical codes developed in Puchades and Sáez (2014) are used to compute the positioning errors due to uncertainties in the satellite world lines, which are defined as the U-errors
Our results show that the greatest effect comes from the Earth quadrupole, the second one from Moon and the third one from Sun
The main purpose of this paper is to study the U-errors obtained as the difference in Relativistic Positioning Systems (RPS) by using Schwarzschild and a more accurate metric to describe the Galileo satellite world lines
Summary
The numerical codes developed in Puchades and Sáez (2014) are used to compute the positioning errors due to uncertainties in the satellite world lines, which are defined as the U-errors. The description of the perturbed satellite world lines is made using a metric that takes into account the gravitational effects of the Earth, the Moon, the Sun, as well as the Earth oblateness (Earth quadrupole effect). This analysis is performed in the framework of the so-called Relativistic Positioning Systems (RPS). Both the satellite world lines and the user location are numerically computed and the corresponding U-errors are calculated. Part of the work shown here was presented in Fullana i Alfonso et al (2019)
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