Error analysis for the Global Positioning System: Difference between revisions

Revision as of 01:44, 26 April 2012

Revision as of 20:24, 30 April 2012

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When combining the time dilation and gravitational frequency shift, the discrepancy is about 38 microseconds per day, a difference of 4.465 parts in 10¹⁰.<ref name=Rizos>Rizos, Chris. [[University of New South Wales]]. [http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap3/312.htm GPS Satellite Signals]. 1999.</ref> Without correction, errors in the initial pseudorange of roughly 10&nbsp;km/day would accumulate. This initial pseudorange error is corrected in the process of solving the [[GPS#Navigation equations|navigation equations]]. In addition the elliptical, rather than perfectly circular, satellite orbits cause the time dilation and gravitational frequency shift effects to vary with time. This eccentricity effect causes the clock rate difference between a GPS satellite and a receiver to increase or decrease depending on the altitude of the satellite.

To compensate for the discrepancy, the frequency standard on board each satellite is given a rate offset prior to launch, making it run slightly slower than the desired frequency on Earth; specifically, at 10.22999999543&nbsp;MHz instead of 10.23&nbsp;MHz.<ref name=Nelson>[http://www.aticourses.com/global_positioning_system.htm The Global Positioning System by Robert A. Nelson Via Satellite], November 1999</ref> Since the atomic clocks on board the GPS satellites are precisely tuned, it makes the system a practical engineering application of the scientific theory of relativity in a real-world environment.<ref>Pogge, Richard W.; [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html “Real"Real-World Relativity: The GPS Navigation System”System"]. Retrieved 25 January 2008.</ref> Placing atomic clocks on artificial satellites to test Einstein's general theory was proposed by [[Friedwardt Winterberg]] in 1955.<ref>{{cite web|url=http://bourabai.kz/winter/satelliten.htm |title=Astronautica Acta II, 25 (1956). |date=1956-08-10 |accessdate=2009-10-23}}</ref>

=== Calculation of time dilation ===

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Since GPS signals at terrestrial receivers tend to be relatively weak, natural radio signals or scattering of the GPS signals can [[Desensitization (telecommunications)|desensitize]] the receiver, making acquiring and tracking the satellite signals difficult or impossible.

[[Space weather]] degrades GPS operation in two ways, direct interference by solar radio burst noise in the same frequency band<ref>Cerruti, A., P. M. Kintner, D. E. Gary, A. J. Mannucci, R. F. Meyer, P. H. Doherty, and A. J. Coster (2008), Effect of intense December 2006 solar radio bursts on GPS receivers, Space Weather, {{doi:|10.1029/2007SW000375}}, October 19, 2008</ref> or by scattering of the GPS radio signal in ionospheric irregularities referred to as scintillation.<ref>{{cite journal | author=Aarons, Jules and Basu, Santimay | title=Ionospheric amplitude and phase fluctuations at the GPS frequencies | work=Proceedings of ION GPS | volume=2 | year=1994 | pages=1569–1578}}</ref> Both forms of degradation follow the 11 year [[solar cycle]] and are a maximum at sunspot maximum although they can occur at anytime. Solar radio bursts are associated with [[solar flares]] and Coronal Mass Ejections (CMEs)<ref>S. Mancuso and J. C. Raymond, "Coronal transients and metric type II radio bursts. I. Effects of geometry, 2004, Astronomy and Astrophysics, v.413, p.363-371'</ref> and their impact can affect reception over the half of the Earth facing the sun. Scintillation occurs most frequently at tropical latitudes where it is a night time phenomenon. It occurs less frequently at high latitudes or mid-latitudes where magnetic storms can lead to scintillation.<ref>{{cite journal | author=Ledvina, B. M., J. J. Makela, and P. M. Kintner | year=2002 | title=First observations of intense GPS L1 amplitude scintillations at midlatitude | journal=Geophysical Research Letters | work=Geophys. Res. Lett. | volume=29 | page=1659 | doi=10.1029/2002GL014770 | issue=14 | bibcode=2002GeoRL..29n...4L}}</ref> In addition to producing scintillation, magnetic storms can produce strong ionospheric gradients that degrade the accuracy of SBAS systems.<ref>Tom Diehl, [http://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/library/satNav/media/SATNAV_0604.PDF Solar Flares Hit the Earth- WAAS Bends but Does Not Break], SatNav News, volume 23, June 2004</ref>

== Artificial sources of interference ==