Relativistic Effects and Geolocation Satellite Systems

The greater stability of the atomic clocks in the new generation’s satellites and the improvements in corrections are enabling applications of navigation systems at activities of increasingly higher level precision. We’ve recently witnessed the launch of the latest GALILEO satellites, the completion of the QZSS constellation, and the new generations of GLONASS and Beidou. All this made the need to integrate the navigation satellite systems an even more pressing matter. Therefore old questions are brought back and it’s important to know how they should be addressed now from the perspective of a single integrated GNSS. This study approaches the relativistic effects on the onboard atomic clocks in all six navigation constellations in operation nowadays. Hence, we set out to find the temporal distortion for each one of the 118 vehicles in the following constellations: GPS (USA), GLONASS (Russia), GALILEO (EU), Beidou (China), IRNSS (India), and QZSS (Japan).

Through the ephemeris data, extracted from the constellations almanacs and the analy- tical equations of Special and General relativity, we found a fixed and two periodic offsets, influenced by the orbit’s semi-major axis, eccentricity, and inclination. For GPS, e.g., the fixed offset is 445.6 ps for each second elapsed on the ground. More importantly, when considering each satellite individually, we found that deviations from the average can go up to about 50 nanoseconds per day. For PRN 21 of the same constellation, we found a periodic effect due to the orbit’s eccentricity with an amplitude of 56.6 ns with a period equal to the orbital one. i.e., depending on the satellite’s position within the orbit the clock might be offset up to 56.6 ns. This may impact applications requiring precisions of tens of meters. Among the six constellations, 38.9% of the satellites require corrections for precision in the order of meters. Yet another periodic effect was found, one caused by the Earth’s oblateness with a period of half the orbital one and an amplitude that, from MEO satellites, goes from 60 to 100 ps, and thus causes trouble for applications that require centimeter-level precision. These estimations help us better understand the importance of applying the correct relativistic corrections for specific applications.