Error Analysis For The Global Positioning System
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The error analysis for the
Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
is important for understanding how GPS works, and for knowing what magnitude of error should be expected. The GPS makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected. GPS receiver position is computed based on data received from the satellites. Errors depend on geometric dilution of precision and the sources listed in the table below.


Overview

User equivalent range errors (UERE) are shown in the table. There is also a
numerical error In software engineering and mathematics, numerical error is the error in the numerical computations. Types It can be the combined effect of two kinds of error in a calculation. * the first is caused by the finite precision of computations involv ...
with an estimated value, \ \sigma_ , of about . The standard deviations, \ \sigma_R, for the coarse/acquisition (C/A) and precise codes are also shown in the table. These standard deviations are computed by taking the square root of the sum of the squares of the individual components (i.e.,
RSS RSS ( RDF Site Summary or Really Simple Syndication) is a web feed that allows users and applications to access updates to websites in a standardized, computer-readable format. Subscribing to RSS feeds can allow a user to keep track of many di ...
for root sum squares). To get the standard deviation of receiver position estimate, these range errors must be multiplied by the appropriate dilution of precision terms and then RSS'ed with the numerical error. Electronics errors are one of several accuracy-degrading effects outlined in the table above. When taken together, autonomous civilian GPS horizontal position fixes are typically accurate to about 15 meters (50 ft). These effects also reduce the more precise P(Y) code's accuracy. However, the advancement of technology means that in the present, civilian GPS fixes under a clear view of the sky are on average accurate to about 5 meters (16 ft) horizontally. The term user equivalent range error (UERE) refers to the error of a component in the distance from receiver to a satellite. These UERE errors are given as ± errors thereby implying that they are unbiased or zero mean errors. These UERE errors are therefore used in computing standard deviations. The standard deviation of the error in receiver position, \ \sigma_, is computed by multiplying PDOP (Position Dilution Of Precision) by \ \sigma_R, the standard deviation of the user equivalent range errors. \ \sigma_R is computed by taking the square root of the sum of the squares of the individual component standard deviations. PDOP is computed as a function of receiver and satellite positions. A detailed description of how to calculate PDOP is given in the section '' Geometric dilution of precision computation (GDOP)''. \ \sigma_R for the C/A code is given by: :3\sigma_R= \sqrt \, \mathrm \,=\,6.7 \, \mathrm The standard deviation of the error in estimated receiver position \ \sigma_, again for the C/A code is given by: :\ \sigma_ = \sqrt = \sqrt \, \mathrm The error diagram on the left shows the inter relationship of indicated receiver position, true receiver position, and the intersection of the four sphere surfaces.


Signal arrival time measurement

The position calculated by a GPS receiver requires the current time, the position of the satellite and the measured delay of the received signal. The position accuracy is primarily dependent on the satellite position and signal delay. To measure the delay, the receiver compares the bit sequence received from the satellite with an internally generated version. By comparing the rising and trailing edges of the bit transitions, modern electronics can measure signal offset to within about one percent of a bit pulse width, \frac, or approximately 10 nanoseconds for the C/A code. Since GPS signals propagate at the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, this represents an error of about 3 meters. This component of position accuracy can be improved by a factor of 10 using the higher-chiprate P(Y) signal. Assuming the same one percent of bit pulse width accuracy, the high-frequency P(Y) signal results in an accuracy of \frac or about 30 centimeters.


Atmospheric effects

Inconsistencies of atmospheric conditions affect the speed of the GPS signals as they pass through the
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
, especially the ionosphere. Correcting these errors is a significant challenge to improving GPS position accuracy. These effects are smallest when the satellite is directly overhead and become greater for satellites nearer the
horizon The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...
since the path through the atmosphere is longer (see
airmass In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere ( Green 1992). It is formulated as the integral of air density along the lig ...
). Once the receiver's approximate location is known, a mathematical model can be used to estimate and compensate for these errors. Ionospheric delay of a microwave signal depends on its frequency. It arises from ionized atmosphere (see
Total electron content Total electron content (TEC) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons integrated between two points, along a tube of one meter squared cross section, i.e., the electron columnar nu ...
). This phenomenon is known as
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
and can be calculated from measurements of delays for two or more frequency bands, allowing delays at other frequencies to be estimated. 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 In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
instead of the
modulated In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
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 Augmentation of a global navigation satellite system (GNSS) is a method of improving the navigation system's attributes, such as precision, reliability, and availability, through the integration of external information into the calculation process. ...
s (SBAS) such as
Wide Area Augmentation System The Wide Area Augmentation System (WAAS) is an air navigation aid developed by the Federal Aviation Administration to augment the Global Positioning System (GPS), with the goal of improving its accuracy, integrity, and availability. Essential ...
(WAAS) (available in North America and Hawaii),
EGNOS The European Geostationary Navigation Overlay Service (EGNOS) is a satellite-based augmentation system (SBAS) developed by the European Space Agency and EUROCONTROL on behalf of the European Commission. Currently, it supplements the GPS by rep ...
(Europe and Asia),
Multi-functional Satellite Augmentation System Multi-functional Satellite Augmentation System (MTSAT or MSAS) is a Japanese satellite based augmentation system (SBAS), i.e. a satellite navigation system which supports differential GPS (DGPS) to supplement the GPS system by reporting (then impro ...
(MSAS) (Japan), and
GPS Aided Geo Augmented Navigation The GPS-aided GEO augmented navigation (GAGAN) is an implementation of a regional satellite-based augmentation system (SBAS) by the Government of India. It is a system to improve the accuracy of a GNSS receiver by providing reference signals. T ...
(GAGAN) (India) which transmits it on the GPS frequency using a special pseudo-random noise sequence (PRN), so only one receiver and antenna are required.
Humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. Humidity depe ...
also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
. 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. The
Atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, 7 ...
can also change the signals reception delay, due to the dry gases present at the troposphere (78% N2, 21% O2, 0.9% Ar...). Its effect varies with local temperature and atmospheric pressure in quite a predictable manner using the laws of the ideal gases.


Multipath effects

GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. These delayed signals cause measurement errors that are different for each type of GPS signal due to its dependency on the wavelength. A variety of techniques, most notably narrow correlator spacing, have been developed to mitigate multipath errors. For long delay multipath, the receiver itself can recognize the wayward signal and discard it. To address shorter delay multipath from the signal reflecting off the ground, specialized antennas (e.g., a
choke ring antenna A choke ring antenna is a particular form of omnidirectional antenna for use at high frequencies ( VHF & UHF). It consists of a number of concentric conductive cylinders around a central antenna. Due to its intricate construction, it is often en ...
) may be used to reduce the signal power as received by the antenna. Short delay reflections are harder to filter out because they interfere with the true signal, causing effects almost indistinguishable from routine fluctuations in atmospheric delay. Multipath effects are much less severe in moving vehicles. When the GPS antenna is moving, the false solutions using reflected signals quickly fail to converge and only the direct signals result in stable solutions.


Ephemeris and clock errors

While the
ephemeris In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly vel ...
data is transmitted every 30 seconds, the information itself may be up to two hours old. Variability in solar radiation pressure has an indirect effect on GPS accuracy due to its effect on ephemeris errors. If a fast time to first fix (TTFF) is needed, it is possible to upload a valid ephemeris to a receiver, and in addition to setting the time, a position fix can be obtained in under ten seconds. It is feasible to put such ephemeris data on the web so it can be loaded into mobile GPS devices. See also
Assisted GPS Assisted GNSS (A-GNSS) is a GNSS augmentation system that often significantly improves the startup performance—i.e., time-to-first-fix (TTFF)—of a global navigation satellite system (GNSS). A-GNSS works by providing the necessary data to the ...
. The satellites' atomic clocks experience noise and
clock drift Clock drift refers to several related phenomena where a clock does not run at exactly the same rate as a reference clock. That is, after some time the clock "drifts apart" or gradually desynchronizes from the other clock. All clocks are subject to ...
errors. The navigation message contains corrections for these errors and estimates of the accuracy of the atomic clock. However, they are based on observations and may not indicate the clock's current state. These problems tend to be very small, but may add up to a few meters (tens of feet) of inaccuracy. For very precise positioning (e.g., in
geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
), these effects can be eliminated by
differential GPS Differential Global Positioning Systems (DGPSs) supplement and enhance the positional data available from global navigation satellite systems (GNSSs). A DGPS for GPS can increase accuracy by about a thousandfold, from approximately to . DGPSs c ...
: the simultaneous use of two or more receivers at several survey points. In the 1990s when receivers were quite expensive, some methods of ''quasi-differential'' GPS were developed, using only ''one'' receiver but reoccupation of measuring points. At the TU Vienna the method was named ''qGPS'' and post processing software was developed.


Dilution of precision


Selective availability

GPS included a (currently disabled) feature called ''Selective Availability'' (''SA'') that adds intentional, time varying errors of up to 100 meters (328 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 pseudorandom, generated by a cryptographic algorithm from a classified ''seed''
key Key or The Key may refer to: Common meanings * Key (cryptography), a piece of information that controls the operation of a cryptography algorithm * Key (lock), device used to control access to places or facilities restricted by a lock * Key (map ...
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 m (164 ft) horizontally and about 100 m (328 ft) vertically. 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 or ''DGPS''.
DGPS Differential Global Positioning Systems (DGPSs) supplement and enhance the positional data available from global navigation satellite systems (GNSSs). A DGPS for GPS can increase accuracy by about a thousandfold, from approximately to . DGPSs c ...
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 Clinton in 2000. DGPS services are widely available from both commercial and government sources. The latter include WAAS and the U.S. Coast Guard's network of LF marine navigation beacons. The accuracy of the corrections depends on the distance between the user and the DGPS receiver. As the distance increases, the errors at the two sites will not correlate as well, resulting in less precise differential corrections. During the 1990–91
Gulf War The Gulf War was a 1990–1991 armed campaign waged by a 35-country military coalition in response to the Iraqi invasion of Kuwait. Spearheaded by the United States, the coalition's efforts against Iraq were carried out in two key phases: ...
, the shortage of military GPS units caused many troops and their families to buy readily available civilian units. Selective Availability significantly impeded the U.S. military's own battlefield use of these GPS, so the military made the decision to turn it off for the duration of the war. In the 1990s, the
FAA The Federal Aviation Administration (FAA) is the largest transportation agency of the U.S. government and regulates all aspects of civil aviation in the country as well as over surrounding international waters. Its powers include air traffic m ...
started pressuring the military to turn off SA permanently. This would save the FAA millions of dollars every year in maintenance of their own
radio navigation Radio navigation or radionavigation is the application of radio frequencies to determine a position of an object on the Earth, either the vessel or an obstruction. Like radiolocation, it is a type of radiodetermination. The basic principles a ...
systems. The amount of error added was "set to zero" at midnight on May 1, 2000 following an announcement by U.S. President
Bill Clinton William Jefferson Clinton ( né Blythe III; born August 19, 1946) is an American politician who served as the 42nd president of the United States from 1993 to 2001. He previously served as governor of Arkansas from 1979 to 1981 and agai ...
, allowing users access to the error-free L1 signal. Per the directive, the induced error of SA was changed to add no error to the public signals (C/A code). Clinton's executive order required SA to be set to zero by 2006; it happened in 2000 once the U.S. military developed a new system that provides the ability to deny GPS (and other navigation services) to hostile forces in a specific area of crisis without affecting the rest of the world or its own military systems. On 19 September 2007, the
United States Department of Defense The United States Department of Defense (DoD, USDOD or DOD) is an executive branch department of the federal government charged with coordinating and supervising all agencies and functions of the government directly related to national secu ...
announced that future
GPS III GPS Block III (previously Block IIIA) consists of the first ten GPS III satellites, which will be used to keep the Navstar Global Positioning System operational. Lockheed Martin designed, developed and manufactured the GPS III Non-Flight Sate ...
satellites will not be capable of implementing SA, eventually making the policy permanent.


Anti-spoofing

Another restriction on GPS, antispoofing, remains on. This encrypts the ''P-code'' so that it cannot be mimicked by a transmitter sending false information. Few civilian receivers have ever used the P-code, and the accuracy attainable with the public C/A code was much better than originally expected (especially with
DGPS Differential Global Positioning Systems (DGPSs) supplement and enhance the positional data available from global navigation satellite systems (GNSSs). A DGPS for GPS can increase accuracy by about a thousandfold, from approximately to . DGPSs c ...
), so much so that the antispoof policy has relatively little effect on most civilian users. Turning off antispoof would primarily benefit surveyors and some scientists who need extremely precise positions for experiments such as tracking tectonic plate motion.


Relativity

Special Relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
(SR) and
General Relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
(GR) are two separate and distinct theories under the title of the
Theory of Relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
. SR and GR make different (opposite) predictions when it comes to the clocks on-board GPS satellites. Note the opposite signs (plus and minus) below due to the different effects. A number of sources of error exist due to relativistic effects that would render the system useless if uncorrected. Three relativistic effects are time dilation, gravitational frequency shift, and eccentricity effects. Examples include the relativistic time ''slowing'' due to the speed of the satellite of about 1 part in 1010, the gravitational time dilation that makes a satellite run about 5 parts in 1010 ''faster'' than an Earth-based clock, and the
Sagnac effect The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer ...
due to rotation relative to receivers on Earth. These topics are examined below, one at a time.


Special Relativity (SR)

SR predicts that clocks slow down as velocity increases. That is the frequency of the atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by a factor of /\approx 10 ^ where the orbital velocity is v = 4 km/s and c = the speed of light. The result is an error of about -7.2 μs/day in the satellite. The SR effect is due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial
reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale are specified by a set of reference point ...
. In short, the clocks on the satellites are slowed down by the velocity of the satellite. This
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
effect has been measured and verified using the GPS.


General Relativity (GR)

GR has the opposite effect. GR predicts that clocks speed up as they get further away from a massive object (the Earth in this case). The effect of gravitational frequency shift on the GPS due to
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
is that a clock closer to a massive object will be slower than a clock farther away. Applied to the GPS, the receivers are much closer to Earth than the satellites, causing the GPS clocks in the satellites to be faster by a factor of 5×10−10, or about +45.8 μs/day. This gravitational frequency shift is measurable. During early development it was believed that GPS would not be affected by GR effects, but the
Hafele–Keating experiment The Hafele–Keating experiment was a test of the theory of relativity. In 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the ...
showed it would be.


Combined SR and GR

When combining SR and GR, the discrepancy is about +38 microseconds per day. This is a difference of 4.465 parts in 1010. Without correction, errors of roughly 11.4 km/day would accumulate in the position. This initial pseudorange error is corrected in the process of solving the 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 MHz instead of 10.23 MHz.The Global Positioning System by Robert A. Nelson Via Satellite
, November 1999
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. Placing atomic clocks on artificial satellites to test Einstein's general theory was proposed by
Friedwardt Winterberg Friedwardt Winterberg (born June 12, 1929) is a German-American theoretical physicist and was a research professor at the University of Nevada, Reno. He is known for his research in areas spanning general relativity, Planck scale physics, nucle ...
in 1955. The conclusion is that the GPS satellites must compensate for GR, the physics of
black holes A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
and extreme gravity.


Calculations

To calculate the amount of daily time dilation experienced by GPS satellites relative to Earth we need to separately determine the amounts due to
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
(velocity) and
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
(gravity) and add them together.


Special Relativity (SR)

The amount due to velocity will be determined using the
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
. This will be: : \frac = \sqrt For small values of ''v/c'', by using
binomial expansion In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the ...
this approximates to: : \frac \approx 1-\frac The GPS satellites move at relative to Earth's center. We thus determine: : \frac \approx 1-\frac \approx 1-8.349\times 10^ This difference below 1 of represents the fraction by which the satellites' clocks move slower than Earth's. It is then multiplied by the number of nanoseconds in a day: : -8.349\times 10^\times 60\times 60\times 24\times 10^9\approx -7214 \text That is the satellites' clocks lose 7214 nanoseconds a day due to SR effects. : Note that this speed of is measured relative to Earth's center rather than its surface where the GPS receivers (and users) are. This is because Earth's equipotential makes net time dilation equal across its geodesic surface. That is, the combination of Special and General effects make the net time dilation at the equator equal to that of the poles, which in turn are at rest relative to the center. Hence we use the center as a reference point to represent the entire surface.


General Relativity (GR)

The amount of dilation due to gravity will be determined using the
gravitational time dilation Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer t ...
equation: : \frac =\sqrt For small values of ''M/r'', by using
binomial expansion In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the ...
this approximates to: : \frac \approx 1-\frac We are again only interested in the fraction below 1, and in the difference between Earth and the satellites. To determine this difference we take: : \Delta \left(\frac\right) \approx \frac-\frac Earth has a radius of 6,357 km (at the poles) making ''Rearth'' = 6,357,000 m and the satellites have an altitude of 20,184 km making their orbit radius ''Rgps'' = 26,541,000 m. Substituting these in the above equation, with ''Mearth'' = , ''G'' = , and ''c'' = (all in SI units), gives: : \Delta \left(\frac\right) \approx 5.307\times 10^ This represents the fraction by which the satellites' clocks move faster than Earth's. It is then multiplied by the number of nanoseconds in a day: : 5.307\times 10^\times 60\times 60\times 24\times 10^9\approx 45850 \text That is the satellites' clocks gain 45850 nanoseconds a day due to GR effects.


Combined SR and GR

These effects are added together to give (rounded to 10 ns): : 45850 – 7210 = 38640 ns Hence the satellites' clocks gain approximately 38,640 nanoseconds a day or 38.6 μs per day due to relativity effects in total. In order to compensate for this gain, a GPS clock's frequency needs to be slowed by the fraction: : –   = This fraction is subtracted from 1 and multiplied by the pre-adjusted clock frequency of 10.23 MHz: : (1 –  ) × 10.23 = 10.22999999543 That is we need to slow the clocks down from 10.23 MHz to 10.22999999543 MHz in order to negate both the SR and GR effects of relativity.


Sagnac distortion

GPS observation processing must also compensate for the
Sagnac effect The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer ...
. The GPS time scale is defined in an
inertial In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
system but observations are processed in an Earth-centered, Earth-fixed (co-rotating) system, a system in which
simultaneity Simultaneity may refer to: * Relativity of simultaneity, a concept in special relativity. * Simultaneity (music), more than one complete musical texture occurring at the same time, rather than in succession * Simultaneity, a concept in Endogeneit ...
is not uniquely defined. A coordinate transformation is thus applied to convert from the inertial system to the ECEF system. The resulting signal run time correction has opposite algebraic signs for satellites in the Eastern and Western celestial hemispheres. Ignoring this effect will produce an east–west error on the order of hundreds of nanoseconds, or tens of meters in position.


Natural sources of interference

Since GPS signals at terrestrial receivers tend to be relatively weak, natural radio signals or scattering of the GPS signals can desensitize the receiver, making acquiring and tracking the satellite signals difficult or impossible.
Space weather Space weather is a branch of space physics and aeronomy, or heliophysics, concerned with the time varying conditions within the Solar System, including the solar wind, emphasizing the space surrounding the Earth, including conditions in the ma ...
degrades GPS operation in two ways, direct interference by solar radio burst noise in the same frequency band or by scattering of the GPS radio signal in ionospheric irregularities referred to as scintillation. Both forms of degradation follow the 11 year
solar cycle The solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a nearly periodic 11-year change in the Sun's activity measured in terms of variations in the number of observed sunspots on the Sun's surfa ...
and are a maximum at sunspot maximum although they can occur at any time. Solar radio bursts are associated with
solar flares A solar flare is an intense localized eruption of electromagnetic radiation in the Sun's atmosphere. Flares occur in active regions and are often, but not always, accompanied by coronal mass ejections, solar particle events, and other solar phe ...
and
coronal mass ejection A coronal mass ejection (CME) is a significant release of plasma and accompanying magnetic field from the Sun's corona into the heliosphere. CMEs are often associated with solar flares and other forms of solar activity, but a broadly accepted ...
s (CMEs) 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. In addition to producing scintillation, magnetic storms can produce strong ionospheric gradients that degrade the accuracy of SBAS systems.


Artificial sources of interference

In automotive GPS receivers, metallic features in windshields, such as defrosters, or car window tinting films can act as a
Faraday cage A Faraday cage or Faraday shield is an enclosure used to block electromagnetic fields. A Faraday shield may be formed by a continuous covering of conductive material, or in the case of a Faraday cage, by a mesh of such materials. Faraday cage ...
, degrading reception just inside the car. Man-made
EMI EMI Group Limited (originally an initialism for Electric and Musical Industries, also referred to as EMI Records Ltd. or simply EMI) was a British transnational conglomerate founded in March 1931 in London. At the time of its break-up in 201 ...
(electromagnetic interference) can also disrupt or
jam Jam is a type of fruit preserve. Jam or Jammed may also refer to: Other common meanings * A firearm malfunction * Block signals ** Radio jamming ** Radar jamming and deception ** Mobile phone jammer ** Echolocation jamming Arts and entertai ...
GPS signals. In one well-documented case it was impossible to receive GPS signals in the entire harbor of
Moss Landing, California Moss Landing, formerly Moss, is an unincorporated community and census-designated place (CDP) in Monterey County, California, United States. It is located north-northeast of Monterey, at an elevation of . It is on the shore of Monterey Bay, at the ...
due to unintentional jamming caused by malfunctioning TV antenna preamplifiers. Intentional jamming is also possible. Generally, stronger signals can interfere with GPS receivers when they are within radio range or line of sight. In 2002 a detailed description of how to build a short-range GPS L1 C/A jammer was published in the online magazine
Phrack ''Phrack'' is an e-zine written by and for hackers, first published November 17, 1985. Described by Fyodor as "the best, and by far the longest running hacker zine," the magazine is open for contributions by anyone who desires to publish remarkabl ...
. The U.S. government reported that such jammers were used occasionally during the
War in Afghanistan War in Afghanistan, Afghan war, or Afghan civil war may refer to: *Conquest of Afghanistan by Alexander the Great (330 BC – 327 BC) *Muslim conquests of Afghanistan (637–709) *Conquest of Afghanistan by the Mongol Empire (13th century), see als ...
, and the U.S. military destroyed six GPS jammers during the
Iraq War {{Infobox military conflict , conflict = Iraq War {{Nobold, {{lang, ar, حرب العراق (Arabic) {{Nobold, {{lang, ku, شەڕی عێراق (Kurdish languages, Kurdish) , partof = the Iraq conflict (2003–present), I ...
, including one that was destroyed with a GPS-guided bomb, noting the ineffectiveness of the jammers used in that situation. A GPS jammer is relatively easy to detect and locate, making it an attractive target for
anti-radiation missile An anti-radiation missile (ARM) is a missile designed to detect and home in on an enemy radio emission source. Typically, these are designed for use against an enemy radar, although jammers and even radios used for communications can also be ...
s. The UK Ministry of Defence tested a jamming system in the UK's West Country on 7 and 8 June 2007. Some countries allow the use of GPS repeaters to allow the reception of GPS signals indoors and in obscured locations; while in other countries these are prohibited as the retransmitted signals can cause multi-path interference to other GPS receivers that receive data from both GPS satellites and the repeater. In the UK Ofcom now permits the use of GPS/GNSS Repeaters under a 'light licensing' regime. Due to the potential for both natural and man-made noise, numerous techniques continue to be developed to deal with the interference. The first is to not rely on GPS as a sole source. According to John Ruley, "
IFR In aviation, instrument flight rules (IFR) is one of two sets of regulations governing all aspects of civil aviation aircraft operations; the other is visual flight rules (VFR). The U.S. Federal Aviation Administration's (FAA) ''Instrument Fly ...
pilots should have a fallback plan in case of a GPS malfunction". Receiver Autonomous Integrity Monitoring (RAIM) is a feature included in some receivers, designed to provide a warning to the user if jamming or another problem is detected. The U.S. military has also deployed since 2004 their Selective Availability / Anti-Spoofing Module (SAASM) in the
Defense Advanced GPS Receiver The AN/PSN-13 Defense Advanced GPS Receiver (DAGR; colloquially, "dagger") is a handheld GPS receiver used by the United States Department of Defense and select foreign military services. It is a military-grade, dual-frequency receiver, and has t ...
(DAGR).US Army DAGR page
In demonstration videos the DAGR was shown to detect jamming and maintain its lock on the encrypted GPS signals during interference which caused civilian receivers to lose lock.


See also

*
GPS augmentation Augmentation of a global navigation satellite system (GNSS) is a method of improving the navigation system's attributes, such as precision, reliability, and availability, through the integration of external information into the calculation process. ...


Notes


References

* * *


External links


GPS.gov
€”General public education website created by the U.S. Government
GPS SPS Performance Standard
€”The official Standard Positioning Service specification (2008 version).
GPS SPS Performance Standard
€”The official Standard Positioning Service specification (2001 version). {{Systems Global Positioning System