TheInfoList

The Global Positioning System (GPS), originally Navstar GPS, Announcements from Vice President
Al Gore Albert Arnold Gore Jr. (born March 31, 1948) is an American politician and environmentalist who served as the 45th vice president of the United States from 1993 to 2001. Gore was Bill Clinton's running mate in their Bill Clinton presidential ...

and the
Clinton Administration The presidency of Bill Clinton began at noon Eastern Time Zone, EST (17:00 UTC) on January 20, 1993, when Bill Clinton was First inauguration of Bill Clinton, inaugurated as the List of presidents of the United States, 42nd president of the Uni ...

in 1998 initiated these changes, which were authorized by the U.S. Congress in 2000. During the 1990s, GPS quality was degraded by the United States government in a program called "Selective Availability"; this was discontinued on May 1, 2000 by a law signed by President
Bill Clinton William Jefferson Clinton (''Birth name, né'' Blythe III; born August 19, 1946) is an American politician and attorney who served as the 42nd president of the United States from 1993 to 2001. Prior to his Presidency of Bill Clinton, presid ...

. The GPS service is provided by the United States government, which can selectively deny access to the system, as happened to the Indian military in 1999 during the , or degrade the service at any time. As a result, several countries have developed or are in the process of setting up other global or regional satellite navigation systems. The Russian Global Navigation Satellite System () was developed contemporaneously with GPS, but suffered from incomplete coverage of the globe until the mid-2000s. GLONASS can be added to GPS devices, making more satellites available and enabling positions to be fixed more quickly and accurately, to within . China's BeiDou Navigation Satellite System began global services in 2018, and finished its full deployment in 2020. There are also the European Union Galileo positioning system, and India's NavIC. Japan's Quasi-Zenith Satellite System (QZSS) is a GPS satellite-based augmentation system to enhance GPS's accuracy in Asia-Oceania, with satellite navigation independent of GPS scheduled for 2023. When selective availability was lifted in 2000, GPS had about a accuracy. The latest stage of accuracy enhancement uses the L5 band and is now fully deployed. GPS receivers released in 2018 that use the L5 band can have much higher accuracy, pinpointing to within .

# History

The GPS project was launched in the United States in 1973 to overcome the limitations of previous navigation systems, integrating ideas from several predecessors, including classified engineering design studies from the 1960s. The U.S. Department of Defense developed the system, which originally used 24 satellites. It was initially developed for use by the United States military and became fully operational in 1995. Civilian use was allowed from the 1980s. Roger L. Easton of the , Ivan A. Getting of The Aerospace Corporation, and Bradford Parkinson of the Applied Physics Laboratory are credited with inventing it. The work of Gladys West is credited as instrumental in the development of computational techniques for detecting satellite positions with the precision needed for GPS. The design of GPS is based partly on similar ground-based radio-navigation systems, such as LORAN and the Decca Navigator System, Decca Navigator, developed in the early 1940s. In 1955, Friedwardt Winterberg proposed a test of general relativity – detecting time slowing in a strong gravitational field using accurate atomic clocks placed in orbit inside artificial satellites. Special and general relativity predict that the clocks on the GPS satellites would be seen by the Earth's observers to run 38 microseconds faster per day than the clocks on the Earth. The GPS calculated positions would quickly drift into error, accumulating to . This was corrected for in the design of GPS.

## Development

With these parallel developments in the 1960s, it was realized that a superior system could be developed by synthesizing the best technologies from 621B, Transit, Timation, and SECOR in a multi-service program. Satellite orbital position errors, induced by variations in the gravity field and radar refraction among others, had to be resolved. A team led by Harold L Jury of Pan Am Aerospace Division in Florida from 1970–1973, used real-time data assimilation and recursive estimation to do so, reducing systematic and residual errors to a manageable level to permit accurate navigation. During Labor Day weekend in 1973, a meeting of about twelve military officers at the Pentagon discussed the creation of a ''Defense Navigation Satellite System (DNSS)''. It was at this meeting that the real synthesis that became GPS was created. Later that year, the DNSS program was named ''Navstar.'' Navstar is often erroneously considered an acronym for "NAVigation System Using Timing and Ranging" but was never considered as such by the GPS Joint Program Office (TRW may have once advocated for a different navigational system that used that acronym). With the individual satellites being associated with the name Navstar (as with the predecessors Transit and Timation), a more fully encompassing name was used to identify the constellation of Navstar satellites, ''Navstar-GPS''. Ten "GPS Block I, Block I" prototype satellites were launched between 1978 and 1985 (an additional unit was destroyed in a launch failure). The effect of the ionosphere on radio transmission was investigated in a geophysics laboratory of Air Force Cambridge Research Laboratory, renamed to Air Force Geophysical Research Lab (AFGRL) in 1974. AFGRL developed the Klobuchar model for computing ionosphere, ionospheric corrections to GPS location. Of note is work done by Australian space scientist Elizabeth Essex-Cohen at AFGRL in 1974. She was concerned with the curving of the paths of radio waves (atmospheric refraction) traversing the ionosphere from NavSTAR satellites. After Korean Air Lines Flight 007, a Boeing 747 carrying 269 people, was shot down in 1983 after straying into the USSR's prohibited airspace, in the vicinity of Sakhalin and Moneron Islands, President Ronald Reagan issued a directive making GPS freely available for civilian use, once it was sufficiently developed, as a common good. The first Block II satellite was launched on February 14, 1989, and the 24th satellite was launched in 1994. The GPS program cost at this point, not including the cost of the user equipment but including the costs of the satellite launches, has been estimated at US\$5 billion (then-year dollars). Initially, the highest-quality signal was reserved for military use, and the signal available for civilian use was intentionally degraded, in a policy known as Selective Availability. This changed with President
Bill Clinton William Jefferson Clinton (''Birth name, né'' Blythe III; born August 19, 1946) is an American politician and attorney who served as the 42nd president of the United States from 1993 to 2001. Prior to his Presidency of Bill Clinton, presid ...

signing on May 1, 2000 a policy directive to turn off Selective Availability to provide the same accuracy to civilians that was afforded to the military. The directive was proposed by the U.S. Secretary of Defense, William Perry, in view of the widespread growth of differential GPS services by private industry to improve civilian accuracy. Moreover, the U.S. military was actively developing technologies to deny GPS service to potential adversaries on a regional basis. Since its deployment, the U.S. has implemented several improvements to the GPS service, including new signals for civil use and increased accuracy and integrity for all users, all the while maintaining compatibility with existing GPS equipment. Modernization of the satellite system has been an ongoing initiative by the U.S. Department of Defense through a series of GPS Block IIIA, satellite acquisitions to meet the growing needs of the military, civilians, and the commercial market. As of early 2015, high-quality, Federal Aviation Administration, FAA grade, Standard Positioning Service (SPS) GPS receivers provided horizontal accuracy of better than , although many factors such as receiver quality and atmospheric issues can affect this accuracy. GPS is owned and operated by the United States government as a national resource. The Department of Defense is the steward of GPS. The ''Interagency GPS Executive Board (IGEB)'' oversaw GPS policy matters from 1996 to 2004. After that, the National Space-Based Positioning, Navigation and Timing Executive Committee was established by presidential directive in 2004 to advise and coordinate federal departments and agencies on matters concerning the GPS and related systems. The executive committee is chaired jointly by the Deputy Secretaries of Defense and Transportation. Its membership includes equivalent-level officials from the Departments of State, Commerce, and Homeland Security, the Joint Chiefs of Staff and NASA. Components of the executive office of the president participate as observers to the executive committee, and the FCC chairman participates as a liaison. The U.S. Department of Defense is required by law to "maintain a Standard Positioning Service (as defined in the federal radio navigation plan and the standard positioning service signal specification) that will be available on a continuous, worldwide basis," and "develop measures to prevent hostile use of GPS and its augmentations without unduly disrupting or degrading civilian uses."

## Timeline and modernization

* In 1972, the USAF Central Inertial Guidance Test Facility (Holloman AFB) conducted developmental flight tests of four prototype GPS receivers in a Y configuration over White Sands Missile Range, using ground-based pseudo-satellites. * In 1978, the first experimental Block-I GPS satellite was launched. * In 1983, after Soviet interceptor aircraft shot down the civilian airliner Korean Air Flight 007, KAL 007 that strayed into prohibited airspace because of navigational errors, killing all 269 people on board, U.S. President Ronald Reagan announced that GPS would be made available for civilian uses once it was completed, although it had been previously published [in Navigation magazine], and that the CA code (Coarse/Acquisition code) would be available to civilian users. * By 1985, ten more experimental Block-I satellites had been launched to validate the concept. * Beginning in 1988, command and control of these satellites was moved from Onizuka AFS, California to the 2nd Satellite Control Squadron (2SCS) located at Falcon Air Force Station in Colorado Springs, Colorado. * On February 14, 1989, the first modern Block-II satellite was launched. * The Gulf War from 1990 to 1991 was the first conflict in which the military widely used GPS. * In 1991, a project to create a miniature GPS receiver successfully ended, replacing the previous military receivers with a handheld receiver. * In 1992, the 2nd Space Wing, which originally managed the system, was inactivated and replaced by the 50th Space Wing. * By December 1993, GPS achieved initial operational capability (IOC), with a full constellation (24 satellites) available and providing the Standard Positioning Service (SPS). * Full Operational Capability (FOC) was declared by Air Force Space Command (AFSPC) in April 1995, signifying full availability of the military's secure Precise Positioning Service (PPS). * In 1996, recognizing the importance of GPS to civilian users as well as military users, U.S. President
Bill Clinton William Jefferson Clinton (''Birth name, né'' Blythe III; born August 19, 1946) is an American politician and attorney who served as the 42nd president of the United States from 1993 to 2001. Prior to his Presidency of Bill Clinton, presid ...

issued a policy directive declaring GPS a dual-use system and establishing an Interagency GPS Executive Board to manage it as a national asset. * In 1998, United States Vice President
Al Gore Albert Arnold Gore Jr. (born March 31, 1948) is an American politician and environmentalist who served as the 45th vice president of the United States from 1993 to 2001. Gore was Bill Clinton's running mate in their Bill Clinton presidential ...

announced plans to upgrade GPS with two new civilian signals for enhanced user accuracy and reliability, particularly with respect to aviation safety, and in 2000 the United States Congress authorized the effort, referring to it as ''GPS III''. * On May 2, 2000 "Selective Availability" was discontinued as a result of the 1996 executive order, allowing civilian users to receive a non-degraded signal globally. * In 2004, the United States government signed an agreement with the European Community establishing cooperation related to GPS and Europe's Galileo (satellite navigation), Galileo system. * In 2004, United States President George W. Bush updated the national policy and replaced the executive board with the National Executive Committee for Space-Based Positioning, Navigation, and Timing. * November 2004, Qualcomm announced successful tests of assisted GPS for mobile phones. * In 2005, the first modernized GPS satellite was launched and began transmitting a second civilian signal (L2C) for enhanced user performance. * On September 14, 2007, the aging mainframe-based Ground segment, Ground Segment Control System was transferred to the new Architecture Evolution Plan. * On May 19, 2009, the United States Government Accountability Office issued a report warning that some GPS satellites could fail as soon as 2010. * On May 21, 2009, the Air Force Space Command allayed fears of GPS failure, saying "There's only a small risk we will not continue to exceed our performance standard." * On January 11, 2010, an update of ground control systems caused a software incompatibility with 8,000 to 10,000 military receivers manufactured by a division of Trimble Navigation Limited of Sunnyvale, Calif. * On February 25, 2010, the U.S. Air Force awarded the contract to develop the GPS Next Generation Operational Control System (OCX) to improve accuracy and availability of GPS navigation signals, and serve as a critical part of GPS modernization.

## Awards

On February 10, 1993, the National Aeronautic Association selected the GPS Team as winners of the 1992 Collier Trophy, Robert J. Collier Trophy, the US's most prestigious aviation award. This team combines researchers from the Naval Research Laboratory, the USAF, the Aerospace Corporation, Rockwell International Corporation, and IBM Federal Systems Company. The citation honors them "for the most significant development for safe and efficient navigation and surveillance of air and spacecraft since the introduction of radio navigation 50 years ago." Two GPS developers received the United States National Academy of Engineering, National Academy of Engineering Charles Stark Draper Prize for 2003: * Ivan Getting, emeritus president of The Aerospace Corporation and an engineer at Massachusetts Institute of Technology, MIT, established the basis for GPS, improving on the World War II land-based radio system called LORAN (''Lo''ng-range ''R''adio ''A''id to ''N''avigation). * Bradford Parkinson, professor of aeronautics and astronautics at Stanford University, conceived the present satellite-based system in the early 1960s and developed it in conjunction with the U.S. Air Force. Parkinson served twenty-one years in the Air Force, from 1957 to 1978, and retired with the rank of colonel. GPS developer Roger L. Easton received the National Medal of Technology on February 13, 2006. Francis X. Kane (Col. USAF, ret.) was inducted into the U.S. Air Force Space and Missile Pioneers Hall of Fame at Lackland A.F.B., San Antonio, Texas, March 2, 2010 for his role in space technology development and the engineering design concept of GPS conducted as part of Project 621B. In 1998, GPS technology was inducted into the Space Foundation Space Technology Hall of Fame. On October 4, 2011, the International Astronautical Federation (IAF) awarded the Global Positioning System (GPS) its 60th Anniversary Award, nominated by IAF member, the American Institute for Aeronautics and Astronautics (AIAA). The IAF Honors and Awards Committee recognized the uniqueness of the GPS program and the exemplary role it has played in building international collaboration for the benefit of humanity. Gladys West was inducted into the Air Force Space and Missile Pioneers Hall of Fame in 2018 for recognition of her computational work which led to breakthroughs for GPS technology. On February 12, 2019, four founding members of the project were awarded the Queen Elizabeth Prize for Engineering with the chair of the awarding board stating "Engineering is the foundation of civilisation; there is no other foundation; it makes things happen. And that's exactly what today's Laureates have done - they've made things happen. They've re-written, in a major way, the infrastructure of our world."

# Basic concept

## Fundamentals

The GPS receiver calculates its own position and time based on data received from multiple GPS satellites. Each satellite carries an accurate record of its position and time, and transmits that data to the receiver. The satellites carry very stable atomic clocks that are synchronized with one another and with ground clocks. Any drift from time maintained on the ground is corrected daily. In the same manner, the satellite locations are known with great precision. GPS receivers have clocks as well, but they are less stable and less precise. Since the speed of radio waves is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the receiver receives it is proportional to the distance from the satellite to the receiver. At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).

## More detailed description

Each GPS satellite continually broadcasts a signal (carrier wave with modulation) that includes: * A Pseudorandom binary sequence, pseudorandom code (sequence of ones and zeros) that is known to the receiver. By time-aligning a receiver-generated version and the receiver-measured version of the code, the time of arrival (TOA) of a defined point in the code sequence, called an epoch, can be found in the receiver clock time scale * A message that includes the time of transmission (TOT) of the code epoch (in GPS time scale) and the satellite position at that time Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. From the TOAs and the TOTs, the receiver forms four time of flight (TOF) values, which are (given the speed of light) approximately equivalent to receiver-satellite ranges plus time difference between the receiver and GPS satellites multiplied by speed of light, which are called as pseudo-ranges. The receiver then computes its three-dimensional position and clock deviation from the four TOFs. In practice the receiver position (in three dimensional Cartesian coordinate system, Cartesian coordinates with origin at the Earth's center) and the offset of the receiver clock relative to the GPS time are computed simultaneously, using the #Navigation equations, navigation equations to process the TOFs. The receiver's Earth-centered solution location is usually converted to latitude, longitude and height relative to an ellipsoidal Earth model. The height may then be further converted to height relative to the geoid, which is essentially mean sea level. These coordinates may be displayed, such as on a moving map display, or recorded or used by some other system, such as a vehicle guidance system.

## User-satellite geometry

Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry. Each TDOA corresponds to a hyperboloid of revolution (see Multilateration). The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect. It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is the case only if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are marked performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If it were an essential part of the GPS concept that all users needed to carry a synchronized clock, a smaller number of satellites could be deployed, but the cost and complexity of the user equipment would increase.

The description above is representative of a receiver start-up situation. Most receivers have a track algorithm, sometimes called a ''tracker'', that combines sets of satellite measurements collected at different times—in effect, taking advantage of the fact that successive receiver positions are usually close to each other. After a set of measurements are processed, the tracker predicts the receiver location corresponding to the next set of satellite measurements. When the new measurements are collected, the receiver uses a weighting scheme to combine the new measurements with the tracker prediction. In general, a tracker can (a) improve receiver position and time accuracy, (b) reject bad measurements, and (c) estimate receiver speed and direction. The disadvantage of a tracker is that changes in speed or direction can be computed only with a delay, and that derived direction becomes inaccurate when the distance traveled between two position measurements drops below or near the random error of position measurement. GPS units can use measurements of the Doppler shift of the signals received to compute velocity accurately. More advanced navigation systems use additional sensors like a compass or an inertial navigation system to complement GPS.

GPS requires four or more satellites to be visible for accurate navigation. The solution of the #Navigation equations, navigation equations gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a more precise and possibly impractical receiver based clock. Applications for GPS such as time transfer, traffic signal timing, and IS-95#Physical layer, synchronization of cell phone base stations, #Timekeeping, make use of this cheap and highly accurate timing. Some GPS applications use this time for display, or, other than for the basic position calculations, do not use it at all. Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation. Some GPS receivers may use additional clues or assumptions such as reusing the last known altitude, dead reckoning, inertial navigation system, inertial navigation, or including information from the vehicle computer, to give a (possibly degraded) position when fewer than four satellites are visible. Chapter 7

# Structure

The current GPS consists of three major segments. These are the space segment, a control segment, and a user segment. The U.S. Space Force develops, maintains, and operates the space and control segments. GPS satellites broadcast signals from space, and each GPS receiver uses these signals to calculate its three-dimensional location (latitude, longitude, and altitude) and the current time.

## Space segment

The space segment (SS) is composed of 24 to 32 satellites, or Space Vehicles (SV), in medium Earth orbit, and also includes the payload adapters to the boosters required to launch them into orbit. The GPS design originally called for 24 SVs, eight each in three approximately circular orbital plane (astronomy), orbits, but this was modified to six orbital planes with four satellites each. The six orbit planes have approximately 55° inclination (tilt relative to the Earth's equator) and are separated by 60° right ascension of the orbital node, ascending node (angle along the equator from a reference point to the orbit's intersection).GPS Overview from the NAVSTAR Joint Program Office
. Retrieved December 15, 2006.
The orbital period is one-half a sidereal day, i.e., 11 hours and 58 minutes so that the satellites pass over the same locations or almost the same locations. Retrieved October 27, 2011 every day. The orbits are arranged so that at least six satellites are always within Line-of-sight propagation, line of sight from everywhere on the Earth's surface (see animation at right). The result of this objective is that the four satellites are not evenly spaced (90°) apart within each orbit. In general terms, the angular difference between satellites in each orbit is 30°, 105°, 120°, and 105° apart, which sum to 360°. Orbiting at an altitude of approximately ; orbital radius of approximately , each SV makes two complete orbits each sidereal day, repeating the same ground track each day. This was very helpful during development because even with only four satellites, correct alignment means all four are visible from one spot for a few hours each day. For military operations, the ground track repeat can be used to ensure good coverage in combat zones. , there are 31 satellites in the GPS satellite constellation, constellation, 27 of which are in use at a given time with the rest allocated as stand-bys. A 32nd was launched in 2018, but as of July 2019 is still in evaluation. More decommissioned satellites are in orbit and available as spares. The additional satellites improve the precision of GPS receiver calculations by providing redundant measurements. With the increased number of satellites, the constellation was changed to a nonuniform arrangement. Such an arrangement was shown to improve accuracy but also improves reliability and availability of the system, relative to a uniform system, when multiple satellites fail. With the expanded constellation, nine satellites are usually visible from any point on the ground at any time, ensuring considerable redundancy over the minimum four satellites needed for a position.

## User segment

The user segment (US) is composed of hundreds of thousands of U.S. and allied military users of the secure GPS Precise Positioning Service, and tens of millions of civil, commercial and scientific users of the Standard Positioning Service. In general, GPS receivers are composed of an antenna, tuned to the frequencies transmitted by the satellites, receiver-processors, and a highly stable clock (often a crystal oscillator). They may also include a display for providing location and speed information to the user. A receiver is often described by its number of channels: this signifies how many satellites it can monitor simultaneously. Originally limited to four or five, this has progressively increased over the years so that, , receivers typically have between 12 and 20 channels. Though there are many receiver manufacturers, they almost all use one of the chipsets produced for this purpose. GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. This is typically in the form of an RS-232 port at 4,800 bit/s speed. Data is actually sent at a much lower rate, which limits the accuracy of the signal sent using RTCM. Receivers with internal DGPS receivers can outperform those using external RTCM data. , even low-cost units commonly include Wide Area Augmentation System (WAAS) receivers. Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol. Although this protocol is officially defined by the National Marine Electronics Association (NMEA), references to this protocol have been compiled from public records, allowing open source tools like gpsd to read the protocol without violating intellectual property laws. Other proprietary protocols exist as well, such as the SiRF and MediaTek, MTK protocols. Receivers can interface with other devices using methods including a serial connection, Universal Serial Bus, USB, or Bluetooth.

# Applications

While originally a military project, GPS is considered a dual-use technology, meaning it has significant civilian applications as well. GPS has become a widely deployed and useful tool for commerce, scientific uses, tracking, and surveillance. GPS's accurate time facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids by allowing well synchronized hand-off switching.

## Civilian

Many civilian applications use one or more of GPS's three basic components: absolute location, relative movement, and time transfer. * Atmosphere: studying the troposphere delays (recovery of the water varpour content) and ionosphere delays (recovery of the number of free electrons). Recovery of Earth surface displacements due to the atmospheric pressure loading. * Astronomy: both positional and clock synchronization data is used in astrometry and celestial mechanics and precise orbit determination. GPS is also used in both amateur astronomy with GoTo (telescopes), small telescopes as well as by professional observatories for finding extrasolar planets. * Automated vehicle: applying location and routes for cars and trucks to function without a human driver. * Cartography: both civilian and military cartographers use GPS extensively. * Cellular telephony: clock synchronization enables time transfer, which is critical for synchronizing its spreading codes with other base stations to facilitate inter-cell handoff and support hybrid GPS/cellular position detection for E911#Wireless enhanced 911, mobile emergency calls and other applications. The first Mobile GPS navigation, handsets with integrated GPS launched in the late 1990s. The U.S. Federal Communications Commission (FCC) mandated the feature in either the handset or in the towers (for use in triangulation) in 2002 so emergency services could locate 911 callers. Third-party software developers later gained access to GPS APIs from Nextel upon launch, followed by Sprint Nextel, Sprint in 2006, and Verizon soon thereafter. * Clock synchronization: the accuracy of GPS time signals (±10 ns) is second only to the atomic clocks they are based on, and is used in applications such as GPS disciplined oscillators. * Disaster relief/emergency services: many emergency services depend upon GPS for location and timing capabilities. * GPS-equipped radiosondes and dropsondes: measure and calculate the atmospheric pressure, wind speed and direction up to from the Earth's surface. * Radio occultation for weather and atmospheric science applications. * Fleet tracking: used to identify, locate and maintain contact reports with one or more fleet vehicle, fleet vehicles in real-time. * Geodesy: determination of Earth orientation parameters including the daily and sub-daily polar motion, and length-of-day variabilities, Earth's center-of-mass - geocenter motion, and low-degree gravity field parameters. * Geofence, Geofencing: vehicle tracking systems, Handheld tracker, person tracking systems, and Tracking collar, pet tracking systems use GPS to locate devices that are attached to or carried by a person, vehicle, or pet. The application can provide continuous tracking and send notifications if the target leaves a designated (or "fenced-in") area. * Geotagging: applies location coordinates to digital objects such as photographs (in Exif data) and other documents for purposes such as creating map overlays with devices like Nikon GP-1 * GPS aircraft tracking * GPS for mining: the use of RTK GPS has significantly improved several mining operations such as drilling, shoveling, vehicle tracking, and surveying. RTK GPS provides centimeter-level positioning accuracy. * GPS data mining: It is possible to aggregate GPS data from multiple users to understand movement patterns, common trajectories and interesting locations. * GPS tours: location determines what content to display; for instance, information about an approaching point of interest. * Navigation: navigators value digitally precise velocity and orientation measurements, as well as precise positions in real-time with a support of orbit and clock corrections. * Orbit determination of low-orbiting satellites with GPS receiver installed onboard, such as GOCE, GRACE and GRACE-FO, GRACE, Jason-1, Jason-2, TerraSAR-X, TanDEM-X, CHAMP (satellite), CHAMP, Sentinel-3, and some cubesats, e.g., CubETH. * Phasor measurement unit, Phasor measurements: GPS enables highly accurate timestamping of power system measurements, making it possible to compute Phasor measurement unit, phasors. * Recreation: for example, Geocaching, Geodashing, GPS drawing, waymarking, and other kinds of Location-based game, location based mobile games such as Pokémon Go. * Reference frames: realization and densification of the terrestrial reference frames in the framework of Global Geodetic Observing System. Co-location in space between Satellite laser ranging and microwave observations for deriving global geodetic parameters. * Robotics: self-navigating, autonomous robots using a GPS sensors, which calculate latitude, longitude, time, speed, and heading. * Sport: used in football and rugby for the control and analysis of the training load. * Surveying: surveyors use absolute locations to make maps and determine property boundaries. * Tectonics: GPS enables direct fault motion measurement of earthquakes. Between earthquakes GPS can be used to measure Crust (geology), crustal motion and deformation to estimate seismic strain buildup for creating seismic hazard maps. * Telematics: GPS technology integrated with computers and mobile communications technology in automotive navigation systems.

### Restrictions on civilian use

The U.S. government controls the export of some civilian receivers. All GPS receivers capable of functioning above above sea level and , or designed or modified for use with unmanned missiles and aircraft, are classified as United States Munitions List, munitions (weapons)—which means they require United States Department of State, State Department export licenses. This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A (Coarse/Acquisition) code. Disabling operation above these limits exempts the receiver from classification as a munition. Vendor interpretations differ. The rule refers to operation at both the target altitude and speed, but some receivers stop operating even when stationary. This has caused problems with some amateur radio balloon launches that regularly reach . These limits only apply to units or components exported from the United States. A growing trade in various components exists, including GPS units from other countries. These are expressly sold as International Traffic in Arms Regulations, ITAR-free.

## Military

File:XM982 Excalibur inert.jpg, upM982 Excalibur GPS-guided artillery shell. As of 2009, military GPS applications include: * Navigation: Soldiers use GPS to find objectives, even in the dark or in unfamiliar territory, and to coordinate troop and supply movement. In the United States armed forces, commanders use the ''Commander's Digital Assistant'' and lower ranks use the ''Soldier Digital Assistant''. * Target tracking: Various military weapons systems use GPS to track potential ground and air targets before flagging them as hostile. These weapon systems pass target coordinates to precision-guided munitions to allow them to engage targets accurately. Military aircraft, particularly in air-to-ground roles, use GPS to find targets. * Missile and projectile guidance: GPS allows accurate targeting of various military weapons including ICBMs, cruise missiles, precision-guided munitions and artillery shells. Embedded GPS receivers able to withstand accelerations of 12,000 ''g-force, g'' or about have been developed for use in howitzer shells. * Search and rescue. * Reconnaissance: Patrol movement can be managed more closely. * GPS satellites carry a set of nuclear detonation detectors consisting of an optical sensor called a bhangmeter, an X-ray sensor, a dosimeter, and an electromagnetic pulse (EMP) sensor (W-sensor), that form a major portion of the United States Nuclear Detonation Detection System. General William Shelton has stated that future satellites may drop this feature to save money. GPS type navigation was first used in war in the Gulf War, 1991 Persian Gulf War, before GPS was fully developed in 1995, to assist Coalition of the Gulf War, Coalition Forces to navigate and perform maneuvers in the war. The war also demonstrated the vulnerability of GPS to being radio jamming, jammed, when Iraqi forces installed jamming devices on likely targets that emitted radio noise, disrupting reception of the weak GPS signal. GPS's vulnerability to jamming is a threat that continues to grow as jamming equipment and experience grows. GPS signals have been reported to have been jammed many times over the years for military purposes. Russia seems to have several objectives for this behavior, such as intimidating neighbors while undermining confidence in their reliance on American systems, promoting their GLONASS alternative, disrupting Western military exercises, and protecting assets from drones. China uses jamming to discourage US surveillance aircraft near the contested Spratly Islands. North Korea has mounted several major jamming operations near its border with South Korea and offshore, disrupting flights, shipping and fishing operations.

## Timekeeping

### Leap seconds

While most clocks derive their time from Coordinated Universal Time (UTC), the atomic clocks on the satellites are set to "GPS time". The difference is that GPS time is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections that are periodically added to UTC. GPS time was set to match UTC in 1980, but has since diverged. The lack of corrections means that GPS time remains at a constant offset with International Atomic Time (TAI) (TAI - GPS = 19 seconds). Periodic corrections are performed to the on-board clocks to keep them synchronized with ground clocks. The GPS navigation message includes the difference between GPS time and UTC. GPS time is 18 seconds ahead of UTC because of the leap second added to UTC on December 31, 2016. Receivers subtract this offset from GPS time to calculate UTC and specific time zone values. New GPS units may not show the correct UTC time until after receiving the UTC offset message. The GPS-UTC offset field can accommodate 255 leap seconds (eight bits).

### Accuracy

GPS time is theoretically accurate to about 14 nanoseconds, due to the clock drift that atomic clocks experience in GPS transmitters, relative to International Atomic Time. Most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds.

### Format

As opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number and a seconds-into-week number. The week number is transmitted as a ten-bit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1,024 weeks (19.6 years). GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6, 1980, and the week number became zero again for the first time at 23:59:47 UTC on August 21, 1999 (00:00:19 TAI on August 22, 1999). It happened the second time at 23:59:42 UTC on April 6, 2019. To determine the current Gregorian date, a GPS receiver must be provided with the approximate date (to within 3,584 days) to correctly translate the GPS date signal. To address this concern in the future the modernized GPS civil navigation (CNAV) message will use a 13-bit field that only repeats every 8,192 weeks (157 years), thus lasting until 2137 (157 years after GPS week zero).

# Communication

The navigational signals transmitted by GPS satellites encode a variety of information including satellite positions, the state of the internal clocks, and the health of the network. These signals are transmitted on two separate carrier frequencies that are common to all satellites in the network. Two different encodings are used: a public encoding that enables lower resolution navigation, and an encrypted encoding used by the U.S. military.

## Message format

: Each GPS satellite continuously broadcasts a ''navigation message'' on L1 (C/A and P/Y) and L2 (P/Y) frequencies at a rate of 50 bits per second (see bitrate). Each complete message takes 750 seconds ( minutes) to complete. The message structure has a basic format of a 1500-bit-long frame made up of five subframes, each subframe being 300 bits (6 seconds) long. Subframes 4 and 5 are commutation (telemetry), subcommutated 25 times each, so that a complete data message requires the transmission of 25 full frames. Each subframe consists of ten words, each 30 bits long. Thus, with 300 bits in a subframe times 5 subframes in a frame times 25 frames in a message, each message is 37,500 bits long. At a transmission rate of 50-bit/s, this gives 750 seconds to transmit an entire GPS Almanac, almanac message (GPS). Each 30-second frame begins precisely on the minute or half-minute as indicated by the atomic clock on each satellite. The first subframe of each frame encodes the week number and the time within the week, as well as the data about the health of the satellite. The second and the third subframes contain the ''ephemeris'' – the precise orbit for the satellite. The fourth and fifth subframes contain the ''almanac'', which contains coarse orbit and status information for up to 32 satellites in the constellation as well as data related to error correction. Thus, to obtain an accurate satellite location from this transmitted message, the receiver must demodulate the message from each satellite it includes in its solution for 18 to 30 seconds. To collect all transmitted almanacs, the receiver must demodulate the message for 732 to 750 seconds or minutes. All satellites broadcast at the same frequencies, encoding signals using unique code division multiple access (CDMA) so receivers can distinguish individual satellites from each other. The system uses two distinct CDMA encoding types: the coarse/acquisition (C/A) code, which is accessible by the general public, and the precise (P(Y)) code, which is encrypted so that only the U.S. military and other NATO nations who have been given access to the encryption code can access it. The ephemeris is updated every 2 hours and is sufficiently stable for 4 hours, with provisions for updates every 6 hours or longer in non-nominal conditions. The almanac is updated typically every 24 hours. Additionally, data for a few weeks following is uploaded in case of transmission updates that delay data upload.

## Satellite frequencies

: All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal). The satellite network uses a CDMA spread-spectrum technique where the low-bitrate message data is encoded with a high-rate pseudorandom number generator, pseudo-random (PRN) sequence that is different for each satellite. The receiver must be aware of the PRN codes for each satellite to reconstruct the actual message data. The C/A code, for civilian use, transmits data at 1.023 million chip (CDMA), chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The actual internal reference of the satellites is 10.22999999543 MHz to compensate for Theory of relativity, relativistic effects that make observers on the Earth perceive a different time reference with respect to the transmitters in orbit. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code. The P code can be encrypted as a so-called P(Y) code that is only available to military equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user. The L3 signal at a frequency of 1.38105 GHz is used to transmit data from the satellites to ground stations. This data is used by the United States Nuclear Detonation (NUDET) Detection System (USNDS) to detect, locate, and report nuclear detonations (NUDETs) in the Earth's atmosphere and near space. One usage is the enforcement of nuclear test ban treaties. The L4 band at 1.379913 GHz is being studied for additional ionospheric correction. The L5 frequency band at 1.17645 GHz was added in the process of GPS modernization. This frequency falls into an internationally protected range for aeronautical navigation, promising little or no interference under all circumstances. The first Block IIF satellite that provides this signal was launched in May 2010. On February 5th 2016, the 12th and final Block IIF satellite was launched. The L5 consists of two carrier components that are in phase quadrature with each other. Each carrier component is bi-phase shift key (BPSK) modulated by a separate bit train. "L5, the third civil GPS signal, will eventually support safety-of-life applications for aviation and provide improved availability and accuracy." In 2011, a conditional waiver was granted to LightSquared to operate a terrestrial broadband service near the L1 band. Although LightSquared had applied for a license to operate in the 1525 to 1559 band as early as 2003 and it was put out for public comment, the FCC asked LightSquared to form a study group with the GPS community to test GPS receivers and identify issue that might arise due to the larger signal power from the LightSquared terrestrial network. The GPS community had not objected to the LightSquared (formerly MSV and SkyTerra) applications until November 2010, when LightSquared applied for a modification to its Ancillary Terrestrial Component (ATC) authorization. This filing (SAT-MOD-20101118-00239) amounted to a request to run several orders of magnitude more power in the same frequency band for terrestrial base stations, essentially repurposing what was supposed to be a "quiet neighborhood" for signals from space as the equivalent of a cellular network. Testing in the first half of 2011 has demonstrated that the impact of the lower 10 MHz of spectrum is minimal to GPS devices (less than 1% of the total GPS devices are affected). The upper 10 MHz intended for use by LightSquared may have some impact on GPS devices. There is some concern that this may seriously degrade the GPS signal for many consumer uses. ''Aviation Week'' magazine reports that the latest testing (June 2011) confirms "significant jamming" of GPS by LightSquared's system.

## Demodulation and decoding

Because all of the satellite signals are modulated onto the same L1 carrier frequency, the signals must be separated after demodulation. This is done by assigning each satellite a unique binary sequence known as a Gold code. The signals are decoded after demodulation using addition of the Gold codes corresponding to the satellites monitored by the receiver. If the almanac information has previously been acquired, the receiver picks the satellites to listen for by their PRNs, unique numbers in the range 1 through 32. If the almanac information is not in memory, the receiver enters a search mode until a lock is obtained on one of the satellites. To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then acquire the almanac and determine the satellites it should listen for. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern. There can be a delay of up to 30 seconds before the first estimate of position because of the need to read the ephemeris data. Processing of the navigation message enables the determination of the time of transmission and the satellite position at this time. For more information see GPS signals#Demodulation and decoding, Demodulation and Decoding, Advanced.

## Problem description

The receiver uses messages received from satellites to determine the satellite positions and time sent. The ''x, y,'' and ''z'' components of satellite position and the time sent (''s'') are designated as [''xi, yi, zi, si''] where the subscript ''i'' denotes the satellite and has the value 1, 2, ..., ''n'', where ''n'' ≥ 4. When the time of message reception indicated by the on-board receiver clock is ''t̃i'', the true reception time is , where ''b'' is the receiver's clock bias from the much more accurate GPS clocks employed by the satellites. The receiver clock bias is the same for all received satellite signals (assuming the satellite clocks are all perfectly synchronized). The message's transit time is , where ''si'' is the satellite time. Assuming the message traveled at Speed of light, the speed of light, ''c'', the distance traveled is . For n satellites, the equations to satisfy are: :$d_i = \left\left( \tilde_i - b - s_i \right\right)c, \; i=1,2,\dots,n$ where ''di'' is the geometric distance or range between receiver and satellite ''i'' (the values without subscripts are the ''x, y,'' and ''z'' components of receiver position): :$d_i = \sqrt$ Defining ''pseudoranges'' as $p_i = \left \left( \tilde_i - s_i \right \right)c$, we see they are biased versions of the true range: :$p_i = d_i + bc, \;i=1,2,...,n$ .section 4 beginning on page 1
Geoffery Blewitt: Basics of the GPS Techique
Since the equations have four unknowns [''x, y, z, b'']—the three components of GPS receiver position and the clock bias—signals from at least four satellites are necessary to attempt solving these equations. They can be solved by algebraic or numerical methods. Existence and uniqueness of GPS solutions are discussed by Abell and Chaffee. When ''n'' is greater than four, this system is Overdetermined system, overdetermined and a Mean, fitting method must be used. The amount of error in the results varies with the received satellites' locations in the sky, since certain configurations (when the received satellites are close together in the sky) cause larger errors. Receivers usually calculate a running estimate of the error in the calculated position. This is done by multiplying the basic resolution of the receiver by quantities called the Dilution of precision (navigation), geometric dilution of position (GDOP) factors, calculated from the relative sky directions of the satellites used. The receiver location is expressed in a specific coordinate system, such as latitude and longitude using the WGS 84 datum (geodesy), geodetic datum or a country-specific system.

## Geometric interpretation

The GPS equations can be solved by numerical and analytical methods. Geometrical interpretations can enhance the understanding of these solution methods.

### Spheres

The measured ranges, called pseudoranges, contain clock errors. In a simplified idealization in which the ranges are synchronized, these true ranges represent the radii of spheres, each centered on one of the transmitting satellites. The solution for the position of the receiver is then at the intersection of the surfaces of these spheres; see trilateration (more generally, true-range multilateration). Signals from at minimum three satellites are required, and their three spheres would typically intersect at two points. One of the points is the location of the receiver, and the other moves rapidly in successive measurements and would not usually be on Earth's surface. In practice, there are many sources of inaccuracy besides clock bias, including random errors as well as the potential for precision loss from subtracting numbers close to each other if the centers of the spheres are relatively close together. This means that the position calculated from three satellites alone is unlikely to be accurate enough. Data from more satellites can help because of the tendency for random errors to cancel out and also by giving a larger spread between the sphere centers. But at the same time, more spheres will not generally intersect at one point. Therefore, a near intersection gets computed, typically via least squares. The more signals available, the better the approximation is likely to be.

### Hyperboloids

If the pseudorange between the receiver and satellite ''i'' and the pseudorange between the receiver and satellite ''j'' are subtracted, , the common receiver clock bias (''b'') cancels out, resulting in a difference of distances . The locus of points having a constant difference in distance to two points (here, two satellites) is a hyperbola on a plane and a hyperboloid of revolution (more specifically, a two-sheeted hyperboloid) in 3D space (see Multilateration). Thus, from four pseudorange measurements, the receiver can be placed at the intersection of the surfaces of three hyperboloids each with Focus (geometry), foci at a pair of satellites. With additional satellites, the multiple intersections are not necessarily unique, and a best-fitting solution is sought instead.

### Inscribed sphere

The receiver position can be interpreted as the center of an inscribed sphere (insphere) of radius ''bc'', given by the receiver clock bias ''b'' (scaled by the speed of light ''c''). The insphere location is such that it touches other spheres. The Circumscribed sphere, circumscribing spheres are centered at the GPS satellites, whose radii equal the measured pseudoranges ''p''i. This configuration is distinct from the one described above, in which the spheres' radii were the unbiased or geometric ranges ''d''i.

### Hypercones

The clock in the receiver is usually not of the same quality as the ones in the satellites and will not be accurately synchronized to them. This produces pseudoranges with large differences compared to the true distances to the satellites. Therefore, in practice, the time difference between the receiver clock and the satellite time is defined as an unknown clock bias ''b''. The equations are then solved simultaneously for the receiver position and the clock bias. The solution space [''x, y, z, b''] can be seen as a four-dimensional spacetime, and signals from at minimum four satellites are needed. In that case each of the equations describes a hypercone (or spherical cone), with the cusp located at the satellite, and the base a sphere around the satellite. The receiver is at the intersection of four or more of such hypercones.

## Solution methods

### Least squares

When more than four satellites are available, the calculation can use the four best, or more than four simultaneously (up to all visible satellites), depending on the number of receiver channels, processing capability, and Dilution of precision (GPS), geometric dilution of precision (GDOP). Using more than four involves an over-determined system of equations with no unique solution; such a system can be solved by a least-squares or weighted least squares method. :$\left\left( \hat,\hat,\hat,\hat \right\right) = \underset \sum_i \left\left( \sqrt + bc - p_i \right\right)^2$

### Iterative

Both the equations for four satellites, or the least squares equations for more than four, are non-linear and need special solution methods. A common approach is by iteration on a linearized form of the equations, such as the Gauss–Newton algorithm. The GPS was initially developed assuming use of a numerical least-squares solution method—i.e., before closed-form solutions were found.

### Closed-form

One closed-form solution to the above set of equations was developed by S. Bancroft. Its properties are well known;Chaffee, J. and Abel, J., "On the Exact Solutions of Pseudorange Equations", ''IEEE Transactions on Aerospace and Electronic Systems'', vol:30, no:4, pp: 1021–1030, 1994 in particular, proponents claim it is superior in low-geometric dilution of precision, GDOP situations, compared to iterative least squares methods. Bancroft's method is algebraic, as opposed to numerical, and can be used for four or more satellites. When four satellites are used, the key steps are inversion of a 4x4 matrix and solution of a single-variable quadratic equation. Bancroft's method provides one or two solutions for the unknown quantities. When there are two (usually the case), only one is a near-Earth sensible solution. When a receiver uses more than four satellites for a solution, Bancroft uses the generalized inverse (i.e., the pseudoinverse) to find a solution. A case has been made that iterative methods, such as the Gauss–Newton algorithm approach for solving over-determined non-linear least squares (NLLS) problems, generally provide more accurate solutions. Leick et al. (2015) states that "Bancroft's (1985) solution is a very early, if not the first, closed-form solution." Other closed-form solutions were published afterwards,Alfred Kleusberg, "Analytical GPS Navigation Solution", ''University of Stuttgart Research Compendium'',1994Oszczak, B., "New Algorithm for GNSS Positioning Using System of Linear Equations," ''Proceedings of the 26th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013)'', Nashville, TN, September 2013, pp. 3560–3563. although their adoption in practice is unclear.

# Error sources and analysis

GPS error analysis examines error sources in GPS results and the expected size of those errors. GPS makes corrections for receiver clock errors and other effects, but some residual errors remain uncorrected. Error sources include signal arrival time measurements, numerical calculations, atmospheric effects (ionospheric/tropospheric delays), ephemeris and clock data, multipath signals, and natural and artificial interference. Magnitude of residual errors from these sources depends on geometric dilution of precision. Artificial errors may result from jamming devices and threaten ships and aircraft or from intentional signal degradation through selective availability, which limited accuracy to ≈ , but has been switched off since May 1, 2000.

# Accuracy enhancement and surveying

## Augmentation

Integrating external information into the calculation process can materially improve accuracy. Such augmentation systems are generally named or described based on how the information arrives. Some systems transmit additional error information (such as clock drift, ephemera, or ionospheric delay), others characterize prior errors, while a third group provides additional navigational or vehicle information. Examples of augmentation systems include the Wide Area Augmentation System (WAAS), European Geostationary Navigation Overlay Service (EGNOS), Differential GPS (DGPS), inertial navigation systems (INS) and Assisted GPS. The standard accuracy of about can be augmented to with DGPS, and to about with WAAS.

## Precise monitoring

Accuracy can be improved through precise monitoring and measurement of existing GPS signals in additional or alternative ways. The largest remaining error is usually the unpredictable delay through the ionosphere. The spacecraft broadcast ionospheric model parameters, but some errors remain. This is one reason GPS spacecraft transmit on at least two frequencies, L1 and L2. Ionospheric delay is a well-defined function of frequency and the total electron content (TEC) along the path, so measuring the arrival time difference between the frequencies determines TEC and thus the precise ionospheric delay at each frequency. Military receivers can decode the P(Y) code transmitted on both L1 and L2. Without decryption keys, it is still possible to use a ''codeless'' technique to compare the P(Y) codes on L1 and L2 to gain much of the same error information. This technique is slow, so it is currently available only on specialized surveying equipment. In the future, additional civilian codes are expected to be transmitted on the L2 and L5 frequencies. All users will then be able to perform dual-frequency measurements and directly compute ionospheric delay errors. A second form of precise monitoring is called ''Carrier-Phase Enhancement'' (CPGPS). This corrects the error that arises because the pulse transition of the pseudorandom noise, PRN is not instantaneous, and thus the cross-correlation, correlation (satellite–receiver sequence matching) operation is imperfect. CPGPS uses the L1 carrier wave, which has a frequency, period of $\frac = 0.63475\,\mathrm \approx 1\, \mathrm \$, which is about one-thousandth of the C/A Gold code bit period of $\frac = 977.5 \, \mathrm \approx 1000 \, \mathrm \$, to act as an additional clock signal and resolve the uncertainty. The phase difference error in the normal GPS amounts to of ambiguity. CPGPS working to within 1% of perfect transition reduces this error to of ambiguity. By eliminating this error source, CPGPS coupled with DGPS normally realizes between of absolute accuracy. ''Relative Kinematic Positioning'' (RKP) is a third alternative for a precise GPS-based positioning system. In this approach, determination of range signal can be resolved to a precision of less than . This is done by resolving the number of cycles that the signal is transmitted and received by the receiver by using a combination of differential GPS (DGPS) correction data, transmitting GPS signal phase information and ambiguity resolution techniques via statistical tests—possibly with processing in real-time (Real Time Kinematic, real-time kinematic positioning, RTK).

## Carrier phase tracking (surveying)

Another method that is used in surveying applications is carrier phase tracking. The period of the carrier frequency multiplied by the speed of light gives the wavelength, which is about for the L1 carrier. Accuracy within 1% of wavelength in detecting the leading edge reduces this component of pseudorange error to as little as . This compares to for the C/A code and for the P code. accuracy requires measuring the total phase—the number of waves multiplied by the wavelength plus the fractional wavelength, which requires specially equipped receivers. This method has many surveying applications. It is accurate enough for real-time tracking of the very slow motions of Plate tectonics, tectonic plates, typically per year. Triple differencing followed by numerical root finding, and the least squares technique can estimate the position of one receiver given the position of another. First, compute the difference between satellites, then between receivers, and finally between epochs. Other orders of taking differences are equally valid. Detailed discussion of the errors is omitted. The satellite carrier total phase can be measured with ambiguity as to the number of cycles. Let $\ \phi\left(r_i, s_j, t_k\right)$ denote the phase of the carrier of satellite ''j'' measured by receiver ''i'' at time $\ \ t_k$. This notation shows the meaning of the subscripts ''i, j,'' and ''k.'' The receiver (''r''), satellite (''s''), and time (''t'') come in alphabetical order as arguments of $\ \phi$ and to balance readability and conciseness, let $\ \phi_ = \phi\left(r_i, s_j, t_k\right)$ be a concise abbreviation. Also we define three functions, :$\ \Delta^r, \Delta^s, \Delta^t$, which return differences between receivers, satellites, and time points, respectively. Each function has variables with three subscripts as its arguments. These three functions are defined below. If $\ \alpha_$ is a function of the three integer arguments, ''i, j,'' and ''k'' then it is a valid argument for the functions, :$\ \Delta^r, \Delta^s, \Delta^t$, with the values defined as :$\ \Delta^r\left(\alpha_\right) = \alpha_ - \alpha_$, :$\ \Delta^s\left(\alpha_\right) = \alpha_ - \alpha_$, and :$\ \Delta^t\left(\alpha_\right) = \alpha_ - \alpha_$ . Also if $\ \alpha_\ and\ \beta_$ are valid arguments for the three functions and ''a'' and ''b'' are constants then $\ \left( a\ \alpha_ + b\ \beta_ \right)$ is a valid argument with values defined as :$\ \Delta^r\left(a\ \alpha_ + b\ \beta_\right) = a \ \Delta^r\left(\alpha_\right) + b \ \Delta^r\left(\beta_\right)$, :$\ \Delta^s\left(a\ \alpha_ + b\ \beta_ \right)= a \ \Delta^s\left(\alpha_\right) + b \ \Delta^s\left(\beta_\right)$, and :$\ \Delta^t\left(a\ \alpha_ + b\ \beta_ \right)= a \ \Delta^t\left(\alpha_\right) + b \ \Delta^t\left(\beta_\right)$ . Receiver clock errors can be approximately eliminated by differencing the phases measured from satellite 1 with that from satellite 2 at the same epoch. This difference is designated as $\ \Delta^s\left(\phi_\right) = \phi_ - \phi_$ Double differencing computes the difference of receiver 1's satellite difference from that of receiver 2. This approximately eliminates satellite clock errors. This double difference is: :$\begin \Delta^r\left(\Delta^s\left(\phi_\right)\right)\,&=\,\Delta^r\left(\phi_ - \phi_\right) &=\,\Delta^r\left(\phi_\right) - \Delta^r\left(\phi_\right) &=\,\left(\phi_ - \phi_\right) - \left(\phi_ - \phi_\right) \end$ Triple differencing subtracts the receiver difference from time 1 from that of time 2. This eliminates the ambiguity associated with the integral number of wavelengths in carrier phase provided this ambiguity does not change with time. Thus the triple difference result eliminates practically all clock bias errors and the integer ambiguity. Atmospheric delay and satellite ephemeris errors have been significantly reduced. This triple difference is: :$\ \Delta^t\left(\Delta^r\left(\Delta^s\left(\phi_\right)\right)\right)$ Triple difference results can be used to estimate unknown variables. For example, if the position of receiver 1 is known but the position of receiver 2 unknown, it may be possible to estimate the position of receiver 2 using numerical root finding and least squares. Triple difference results for three independent time pairs may be sufficient to solve for receiver 2's three position components. This may require a numerical procedure.chapter on root finding and nonlinear sets of equations An approximation of receiver 2's position is required to use such a numerical method. This initial value can probably be provided from the navigation message and the intersection of sphere surfaces. Such a reasonable estimate can be key to successful multidimensional root finding. Iterating from three time pairs and a fairly good initial value produces one observed triple difference result for receiver 2's position. Processing additional time pairs can improve accuracy, overdetermining the answer with multiple solutions. Least squares can estimate an overdetermined system. Least squares determines the position of receiver 2 that best fits the observed triple difference results for receiver 2 positions under the criterion of minimizing the sum of the squares.

# Regulatory spectrum issues concerning GPS receivers

To build public support of efforts to continue the 2004 FCC authorization of LightSquared's ancillary terrestrial component vs. a simple ground-based LTE service in the Mobile Satellite Service band, GPS receiver manufacturer Trimble Navigation Ltd. formed the "Coalition To Save Our GPS." The FCC and LightSquared have each made public commitments to solve the GPS interference issue before the network is allowed to operate. According to Chris Dancy of the Aircraft Owners and Pilots Association, airline pilots with the type of systems that would be affected "may go off course and not even realize it." The problems could also affect the Federal Aviation Administration upgrade to the air traffic control system, United States Defense Department guidance, and local emergency services including 9-1-1, 911. On February 14, 2012, the FCC moved to bar LightSquared's planned national broadband network after being informed by the National Telecommunications and Information Administration (NTIA), the federal agency that coordinates spectrum uses for the military and other federal government entities, that "there is no practical way to mitigate potential interference at this time".FCC press releas
"Spokesperson Statement on NTIA Letter – LightSquared and GPS"
. February 14, 2012. Accessed 2013-03-03.
LightSquared is challenging the FCC's action.

# Other systems

Other notable satellite navigation systems in use or various states of development include: * Beidou navigation system, Beidou – system deployed and operated by the China, People's Republic of China's, initiating global services in 2019. * Galileo (satellite navigation), Galileo – a global system being developed by the European Union and other partner countries, which began operation in 2016, and is expected to be fully deployed by 2020. * – Russia's global navigation system. Fully operational worldwide. *NavIC – A regional navigation system developed by the Indian Space Research Organisation. *Michibiki – A regional navigation system receivable in the Asia-Oceania regions, with a focus on Japan.

* GPS/INS * GPS navigation software * GPS spoofing * Indoor positioning system * List of GPS satellites * Local Area Augmentation System * Local positioning system * Military invention * Mobile phone tracking * Navigation paradox * Notice Advisory to Navstar Users * S-GPS