Relativistic Corrections in the European GNSS Galileo (original) (raw)

Relevance of the relativistic effects in satellite navigation

2016

Position determination of Global Navigation Satellite Systems (GNSS) depends on the stability and accuracy of the measured time. However, since satellite vehicles (SVs) travel at velocities significantly larger than the receivers and, more importantly, the electromagnetic impulses propagate through changing gravitational potentials, enormous errors stemming from relativity-based clock offsets would cause a position error of about 11 km to be accumulated after one day. Based on the premise of the constancy of light, two major relativistic effects are described: time dilation and gravitational-frequency shift. Following the individual interests of the author, formulas of both are scrupulously derived from generaland special-relativity theory principles; moreover, in the penultimate section, the equations are used to calculate the author’s own numerical values of the studied parameters for various GNSSs and one Land Navigation Satellite System (LNSS).

RELEVANCE OF THE RELATIVISTIC EFFECT IN SATELLITE NAVIGATION

GNSSs’ position determination depends on the stability and accuracy of the measured time. However, since SVs travel at velocities significantly larger than the receivers and, more importantly, the electromagnetic impulses propagate through changing gravitational potentials, enormous errors stemming from relativity-based clock offsets would cause the position mistake of about 11 km accumulated after one day. Basing on the premise of the constancy of light two major relativistic effects are described: time dilation and gravitational frequency shift. Following the individual interests of the author formulas of both are scrupulously derived from general and special relativity theories’ principles; moreover in the last but one section the equations are used to calculate author’s own numerical values of studied parameters for various GNSS and one LNSS.

Introducing relativity in global navigation satellite systems

Annalen der Physik, 2007

Today, the Global Navigation Satellite Systems, used as global positioning systems, are the GPS and the GLONASS. They are based on a Newtonian model and hence they are only operative when several relativistic effects are taken into account. The most important relativistic effects (to order 1/c 2 ) are: the Einstein gravitational blue shift effect of the satellite clock frequency (Equivalence Principle of General Relativity) and the Doppler red shift of second order, due to the motion of the satellite (Special Relativity). On the other hand, in a few years the Galileo system will be built, copying the GPS system unless an alternative project is designed. In this work, it will be also shown that the SYPOR project, using fully relativistic concepts, is an alternative to a mere copy of the GPS system. According to this project, the Galileo system would be exact and there would be no need for relativistic corrections.

GGSP: Realisation and maintenance of the Galileo Terrestrial Reference Frame

Advances in Space Research, 2011

The realisation and maintenance of a Galileo Terrestrial Reference Frame (GTRF) is the main function of the Galileo Geodetic Service Provider (GGSP). The GTRF shall be compatible with the latest International Terrestrial Reference Frame (ITRF) within a precision level of 3 cm (2 sigma). The connection to the ITRF is realized and validated by stations of the International GNSS Service (IGS) and by geodetic local ties to stations equipped with other geodetic techniques. It is demonstrated that this GTRF can be maintained by including the Galileo Signal-in-Space data, once Galileo reaches its operational stage. The GGSP will also provide additional products, such as Earth Rotation Parameters, satellites orbits, clock corrections for satellites and stations, which will be offered to the Galileo user community to have most precise access to the GTRF and will be used to monitor the accuracy of the corresponding Galileo Mission Segment. The GGSP was built up in time, and for a final demonstration the full system was operated for an interval of 6 months. During that time also microwave data from the two active GIOVE satellites were used. The GGSP Consortium followed the most up to date IGS standards of weekly processing during seven monthly campaigns (November 2006 to June 2008) and a continuous processing from September 2008 to February 2009 delivering several versions of the GTRF. The latest GTRF solution (GTRF09v01) has an RMS position difference with respect to the ITRF2005 computed over the 71 common stations of 1.1 and 2.9 mm in the horizontal and vertical components, respectively. The RMS velocity differences are 0.3 and 0.6 mm/y, respectively. The GGSP GPS satellite orbits and clock corrections agree with the IGS Final products at a level of 5-11 mm and 0.02-0.03 ns, respectively. The quality of the GIOVE orbits is at a level of 20-30 cm. The Hydrogen-Maser on board of GIOVE-B is nearly one order of magnitude better than the GPS satellite clocks.

Relativistic Effects in the Global Positioning System

1985

The Global Positioning System (GPS) provides a superb opportunity to introduce relativity concepts to undergraduate students, including non-physics majors. Familiarity with the numerous applications of GPS motivates students to understand relativity. A few fundamental principles need to be introduced, including the postulates of special relativity and the universality of free fall. Then a series of thought experiments leads to the breakdown of simultaneity, the Sagnac effect, the first-order Doppler effect, gravitational frequency shifts, and time dilation. This article presents this chain of thought and explains the essential role of special and general relativity in the GPS. I. INTRODUCTION This paper develops a series of thought experiments based on a few fundamental relativity principles, and discusses how the predicted effects are incorporated into the GPS. Important relativistic effects on GPS satellite clocks include gravitational frequency shifts and time dilation. These effects are so large that if not accounted for, the system would not be effective for navigation. Reference clocks on earth's geoid are similarly influenced by time dilation (due to earth's rotation) and gravitational frequency shifts, relative to clocks at infinity. The frequency differences between clocks in orbit, and reference clocks on earth's surface, are very important in the GPS. Constancy of the speed of light is essential for navigation using GPS. This principle also leads directly to the relativity of simultaneity and to the Sagnac effect, that must be accounted for when synchronizing clocks in the neighborhood of

Spacecraft clocks and relativity: Prospects for future satellite missions

Physical Review D, 2014

The successful miniaturization of extremely accurate atomic clocks invites prospects for satellite missions to perform precise timing experiments. This will allow effects predicted by general relativity to be detected in Earth's gravitational field. In this paper we introduce a convenient formalism for studying these effects, and compute the fractional timing differences generated by them for the orbit of a satellite capable of accurate time transfer to a terrestrial receiving station on Earth, as proposed by planned missions. We find that (1) Schwarzschild perturbations would be measurable through their effects both on the orbit and on the signal propagation, (2) frame-dragging of the orbit would be readily measurable, and (3) in optimistic scenarios, the spin-squared metric effects may be measurable for the first time ever. Our estimates suggest that a clock with a fractional timing inaccuracy of 10 −16 on a highly eccentric Earth orbit will measure all these effects, while for a low Earth circular orbit like that of the Atomic Clock Ensemble in Space Mission, detection will be more challenging.

With classical physics it is also possible the correction of the clocks on the GPS.

The correction of the clocks on the GPS is announced as one of the biggest hits of the theory of general relativity, but this work exposes that the clocks in the satellite systems, not only can be corrected with Albert Einstein's theory of relativity, but also with the theory of classical physics. Based on a mathematical formula that has been published by Paul Gerber in 1898, as the solution to explain the anomaly of the perihelion of mercury, it also makes a relationship in the theoretical explanation of classical physics, and the techniques of parabolic flight, as the experimental way to confirm the theory of Gerber. Finally concludes that the correction of the clocks on the GPS has two theoretical ways to express themselves, but a single mathematical form.

An assessment of relativistic effects for low Earth orbiters: the GRACE satellites

Metrologia, 2007

The GRACE mission consists of two identical satellites orbiting the Earth at an altitude of ∼500 km. Dual-frequency carrier-phase Global Positioning System (GPS) receivers are flying on both satellites. They are used for precise orbit determination and to time-tag the K-band ranging system used to measure changes in the distances between the two satellites. The satellites are also flying ultra-stable oscillators (USOs) to achieve the mission's need for short-term (<1 s) oscillator stability. Because of the high quality of both the GPS receivers and the oscillators, relativistic effects in the GRACE GPS data can be examined. An expression is developed for relativistic effects that explicitly includes the effects of the Earth's oblateness (J 2). Use of this expression significantly reduces the twice per orbital period energy in the GRACE clock solutions, indicating that the effect of J 2 can be significant and should be modeled for satellite clocks in low Earth orbit. After relativistic effects have been removed, both GRACE USOs show large (2 ns to 3 ns) once per orbital period signatures that correlate with voltage variations on the spacecraft.

The global positioning system, relativity, and extraterrestrial navigation

Proceedings of the International Astronomical Union, 2009

Relativistic effects play an important role in the performance of the Global Positioning System (GPS) and in world-wide time comparisons. The GPS has provided a model for algorithms that take relativistic effects into account. In the future exploration of space, analogous considerations will be necessary for the dissemination of time and for navigation. We discuss relativistic effects that are important for a navigation system such as at Mars. We describe relativistic principles and effects that are essential for navigation systems, and apply them to navigation satellites carrying atomic clocks in orbit about Mars, and time transfer between Mars and Earth. It is shown that, as in the GPS, relativistic effects are not negligible.