Error analysis for the Global Positioning System: Difference between revisions

Revision as of 10:55, 14 March 2025

Revision as of 16:15, 9 May 2025

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'''Ionospheric delay''' of a microwave signal depends on its frequency. It arises from ionized atmosphere (see [[Total electron content]]). This phenomenon is known as [[dispersion (optics)|dispersion]] and can be calculated from measurements of delays for two or more frequency bands, allowing delays at other frequencies to be estimated.<ref>The same principle, and the math behind it, can be found in descriptions of [[Dispersion measure|pulsar timing by astronomers]].</ref> Some military and expensive survey-grade civilian receivers calculate atmospheric dispersion from the different delays in the L1 and L2 frequencies, and apply a more precise correction. This can be done in civilian receivers without decrypting the P(Y) signal carried on L2, by tracking the [[carrier wave]] instead of the [[modulation|modulated]] code. To facilitate this on lower cost receivers, a new civilian code signal on L2, called L2C, was added to the Block IIR-M satellites, which was first launched in 2005. It allows a direct comparison of the L1 and L2 signals using the coded signal instead of the carrier wave.

The effects of the ionosphere generally change slowly, and can be averaged over time. Those for any particular geographical area can be easily calculated by comparing the GPS-measured position to a known surveyed ___location. This correction is also valid for other receivers in the same general ___location. Several systems send this information over radio or other links to allow L1-only receivers to make ionospheric corrections. The ionospheric data are transmitted via satellite in [[Satellite Based Augmentation System]]s (SBAS) such as [[Wide Area Augmentation System]] (WAAS) (available in North America and Hawaii), [[EGNOS]] (Europe and Asia), [[Multi-functional Satellite Augmentation System]] (MSAS) (Japan), and [[GPS Aided Geo Augmented Navigation]] (GAGAN) (India) which transmits it on the GPS frequency using a special pseudo-random[[pseudorandom noise]] sequence (PRN), so only one receiver and antenna are required.

[[Humidity]] also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the [[troposphere]]. This effect is more localized than ionospheric effects, changes more quickly and is not frequency dependent. These traits make precise measurement and compensation of humidity errors more difficult than ionospheric effects.<ref>[https://web.archive.org/web/20140522193825/http://www.navipedia.net/index.php/Earth_Sciences#Troposphere_Monitoring Navipedia: Troposphere Monitoring]</ref>

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GPS formerly included a feature called ''Selective Availability'' (''SA'') that added intentional, time varying errors of up to 100 meters (328&nbsp;ft) to the publicly available navigation signals. This was intended to deny an enemy the use of civilian GPS receivers for precision weapon guidance.

SA errors are actually [[Pseudorandomness|pseudorandom]], generated by a cryptographic algorithm from a classified ''seed'' [[key (cryptography)|key]] available only to authorized users (the U.S. military, its allies and a few other users, mostly government) with a special military GPS receiver. Mere possession of the receiver is insufficient; it still needs the tightly controlled daily key.

Before it was turned off on May 2, 2000, typical SA errors were about 50&nbsp;m (164&nbsp;ft) horizontally and about 100&nbsp;m (328&nbsp;ft) vertically.<ref>Grewal (2001), p. 103.</ref> Because SA affects every GPS receiver in a given area almost equally, a fixed station with an accurately known position can measure the SA error values and transmit them to the local GPS receivers so they may correct their position fixes. This is called [[Differential GPS]] (DGPS). DGPS also corrects for several other important sources of GPS errors, particularly ionospheric delay, so it continues to be widely used even though SA has been turned off. The ineffectiveness of SA in the face of widely available DGPS was a common argument for turning off SA, and this was finally done by order of President [[Bill Clinton|Clinton]] in 2000.<ref>{{Cite web |title=President Clinton Orders the Cessation of GPS Selective Availability |url=https://clintonwhitehouse4.archives.gov/WH/EOP/OSTP/html/0053.html }}</ref>