GNSS, Special Relaltivity, General Relativity.

Geolocation satellites are currently of crucial importance for countless people and economic activities. With the launch of the last satellites of the GALILEO constellation, and the new generations of GLONASS and COMPASS, the integration of these systems becomes relevant. Wich brings back old questions and how they should be addressed now from the perspective of a single integrated GNSS system. Although there are articles in the literature discussing the effects of relativity on those, a study that looks at the issue from the perspective of the proper time is absent. This might be interesting because it is independent of the construction and operation of each of the systems. And above all, it lacks a study that takes into account more than one of the constellations, let alone, all of them. Hence, we set out to analytically solve the temporal distortion in a manner that embrace all these satellites.

In this context we investigated the following constellations: GPS, GLONASS, GA- LILEO, COMPASS, IRNSS and QZSS. Through the ephemeris data, extracted from the navigation messages of the systems, we were able to evaluate the effects of relativity in- dividually for each satellite of the constellations mentioned above. We were able to find a constant dilation, due to the combined effects of Special Relativity and General Relativity, which for GPS, for example, is 445.6 ps for each second elapsed on the ground. Although it seems little, this could compromise all the investment made. Today, this correction is made, for example, in the cases of GPS and IRNSS, by an offset in the frequency step of the atomic clocks pre-flight. In the cases of GALILEO and COMPASS, it is let to be done by the user segment.

It is added to this effect a periodic dilation that depends on the eccentricity of the orbits and is mainly related to the speed of translation and Special Relativity. It is intended for us to investigate it in a later stage of this study, with the bases built here. In the literature it can be found that for GPS, this dilation has an amplitude up to 0.2 ns/day. We are expected to find even more significant values for QZSS, since its orbit is highly eccentric. Periodic corrections are done at the user level, so that each receiver device processes the data locally and compensates for the effects of relativity separately for each satellite in its sight. Taking this into account, we pursuit an correction wich could be made automatically and that can be applied to the different constellations.