From Wikipedia, the free encyclopedia   (Redirected from GPS) It has been suggested that Introduction to the Global Positioning System be merged into this article or section. (Discuss) "GPS" redirects here. For other uses, see GPS (disambiguation). For a generally accessible and less technical introduction to the topic, see Introduction to the Global Positioning System. Artists conception of GPS Block II-F satellite in orbit Civilian GPS receiver ("GPS navigation device") in a marine application. Automotive navigation system in a taxicab. GPS receivers are now integrated in many mobile phones.

The Global Positioning System (GPS) is a space-based global navigation satellite system that provides reliable location and time information in all weather and at all times and anywhere on or near the Earth when and where there is an unobstructed line of sight to four or more GPS satellites. It is maintained by the United States government and is freely accessible by anyone with a GPS receiver. In addition to GPS other systems are in use or under development. The Russian GLObal NAvigation Satellite System (GLONASS) is for use by the Russian military. There are also the planned Chinese Compass navigation system and Galileo positioning system of the European Union (EU). GPS was created and realized by the U.S. Department of Defense (DOD) and was originally run with 24 satellites. It was established in 1973 to overcome the limitations of previous navigation systems.[1]

Contents

• 1 Structure
• 2 Applications
  • 2.1 Civilian
    • 2.1.1 Restrictions on civilian use
  • 2.2 Military
• 3 History
  • 3.1 Timeline and modernization
  • 3.2 Awards
• 4 Basic concept of GPS
  • 4.1 Position calculation introduction
  • 4.2 Correcting a GPS receivers clock
• 5 System segmentation
  • 5.1 Space segment
  • 5.2 Control segment
  • 5.3 User segment
• 6 Communication
  • 6.1 Message format
  • 6.2 Satellite frequencies
    • 6.2.1 Demodulation and decoding
• 7 Navigation equations
• 8 Methods of solution of navigation equations
  • 8.1 Multidimensional Newton-Raphson for GPS
• 9 Error sources and analysis
  • 9.1 Signal arrival time measurement
  • 9.2 Atmospheric effects
  • 9.3 Multipath effects
  • 9.4 Ephemeris and clock errors
  • 9.5 Geometric dilution of precision computation (GDOP)
    • 9.5.1 Derivation of DOP equations
  • 9.6 Selective availability
    • 9.6.1 Antispoofing
  • 9.7 Relativity
    • 9.7.1 Special and general relativity
    • 9.7.2 Sagnac distortion
  • 9.8 Natural sources of interference
  • 9.9 Artificial sources of interference
• 10 Accuracy enhancement and surveying
  • 10.1 Augmentation
  • 10.2 Precise monitoring
  • 10.3 Timekeeping
  • 10.4 Carrier phase tracking (surveying)
• 11 Other systems
• 12 See also
• 13 Notes
• 14 References
• 15 Further reading
• 16 External links

//

Structure

Ground monitor station used from 1984 to 2007, on display at the Air Force Space & Missile Museum

GPS consists of three parts: the space segment, the control segment, and the user segment. The U.S. Air Force develops, maintains, and operates the space and control segments. GPS satellites broadcast signals from space, which each GPS receiver uses to calculate its three-dimensional location (latitude, longitude, and altitude) plus the current time.[2]

The space segment is composed of 24 to 32 satellites in medium Earth orbit and also includes the boosters required to launch them into orbit. The control segment is composed of a master control station, an alternate master control station, and a host of dedicated and shared ground antennas and monitor stations. The user segment 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 (see GPS navigation devices).

Applications

While originally a military project, GPS is considered a dual-use technology, meaning it has significant military and civilian applications.

GPS has become a widely used and a useful tool for commerce, scientific uses, tracking and surveillance. GPSs accurate timing facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids. Farmers, surveyors, geologists and countless others perform their work more efficiently, safely, economically, and accurately.[2]

Civilian

See also: GNSS applications and GPS navigation device This antenna is mounted on the roof of a hut containing a scientific experiment needing precise timing.

Many civilian applications use one or more of GPSs three basic components: absolute location, relative movement, and time transfer.

• Surveying: Surveyors use absolute locations to make maps and determine property boundaries
• Map-making: Both civilian and military cartographers use GPS extensively.
• Navigation: Navigators value digitally precise velocity and orientation measurements.
• 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 mobile emergency calls and other applications. The first handsets with integrated GPS launched in the late 1990s. The U.S. Federal Communications Commission (FCC) mandated the feature 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 in 2006, and Verizon soon thereafter.
• Tectonics: GPS enables direct fault motion measurement in earthquakes.
• Disaster relief/emergency services: Depend upon GPS for location and timing capabilities
• GPS tours: Location determines which content to display; for instance, information about an approaching point of interest is displayed.
• Geofencing: Vehicle tracking systems, person tracking systems, and pet tracking systems use GPS to locate a vehicle, person, or pet. These devices attach to the vehicle, person, or the pet collar. The application provides 24/7 tracking and mobile or Internet updates should the trackee leave a designated area.[3]
• Recreation: For example, geocaching, geodashing, GPS drawing and waymarking
• GPS Aircraft Tracking
• Geotagging: Applying location coordinates to digital objects such as photographs and other documents for purposes such as creating map overlays.

Restrictions on civilian use

The U.S. Government controls the export of some civilian receivers. All GPS receivers capable of functioning above 18 kilometers (11 mi) altitude and 515 metres per second (1,001 kn)[4] are classified as munitions (weapons) for which U.S. State Department export licenses are required. These limits attempt to prevent use of a receiver in a ballistic missile. They would not prevent use in a cruise missile since their altitudes and speeds are similar to those of ordinary aircraft.

This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A code and cannot correct for SA, etc.

Disabling operation above these limits exempts the receiver from classification as a munition. Vendor interpretations differ. The rule targets operation given the combination of altitude and speed, while some receivers stop operating even when stationary. This has caused problems with some amateur radio balloon launches, which regularly reach 30 kilometers (19 mi).

Military

As of 2009, military applications of GPS include:

• Navigation: GPS allows soldiers to find objectives, even in the dark or in unfamiliar territory, and to coordinate troop and supply movement. In the US armed forces, commanders use the Commanders Digital Assistant and lower ranks use the Soldier Digital Assistant.[5][6][7][8]
• Target tracking: Various military weapons systems use GPS to track potential ground and air targets before flagging them as hostile.[citation needed] 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 (for example, gun camera video from AH-1 Cobras in Iraq show GPS co-ordinates that can be viewed with special software.
• Missile and projectile guidance: GPS allows accurate targeting of various military weapons including ICBMs, cruise missiles and precision-guided munitions. Artillery projectiles. Embedded GPS receivers able to withstand accelerations of 12,000 g or about 118 km/s2 have been developed for use in 155 millimeters (6.1 in) howitzers.[9]
• Search and Rescue: Downed pilots can be located faster if their position is known.
• Reconnaissance: Patrol movement can be managed more closely.
• GPS satellites carry a set of nuclear detonation detectors consisting of an optical sensor (Y-sensor), an X-ray sensor, a dosimeter, and an electromagnetic pulse (EMP) sensor (W-sensor), which form a major portion of the United States Nuclear Detonation Detection System.[10][11]

History

Summary of satellites[21] Block Launch
Period Satellite launches Currently in orbit
and healthy Suc-
cess Fail-
ure In prep-
aration Plan-
ned I 1978–1985 10 1 0 0 0 II 1989–1990 9 0 0 0 0 IIA 1990–1997 19 0 0 0 10 of 19 launched IIR 1997–2004 12 1 0 0 12 of 13 launched IIR-M 2005–2009 8 0 0 0 7 of 8 launched IIF 2010–2011 1 0 11 0 1 of 1 launched IIIA 2014–? 0 0 0 12 0 IIIB 0 0 0 8 0 IIIC 0 0 0 16 0 Total 59 2 11 36 30 (Last update: 24 May 2010)

PRN 01 from Block IIR-M is unhealthy
PRN 25 from Block IIA is unhealthy
PRN 32 from Block IIA is unhealthy
[22] For a more complete list, see list of GPS satellite launches

• In 1972, the U.S. Air Force Central Inertial Guidance Test Facility (Holloman AFB), conducted developmental flight tests of two prototype GPS receivers 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 KAL 007 that strayed into prohibited airspace due to 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.[23][24]
• By 1985, ten more experimental Block-I satellites had been launched to validate the concept.
• On February 14, 1989, the first modern Block-II satellite was launched.
• The Gulf War from 1990 to 1992, was the first conflict where GPS was widely used.[25]
• In 1992, the 2nd Space Wing, which originally managed the system, was de-activated and replaced by the 50th Space Wing.
• By December 1993, GPS achieved initial operational capability.[citation needed]
• By January 17, 1994 a complete constellation of 24 satellites was in orbit.
• Full Operational Capability was declared by NAVSTAR in April 1995.
• In 1996, recognizing the importance of GPS to civilian users as well as military users, U.S. President Bill Clinton issued a policy directive[26] declaring GPS to be a dual-use system and establishing an Interagency GPS Executive Board to manage it as a national asset.
• In 1998, U.S. Vice President Al Gore 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 U.S. Congress authorized the effort, referring to it as GPS III.
• In 1998, GPS technology was inducted into the Space Foundation Space Technology Hall of Fame.
• On May 2, 2000 "Selective Availability" was discontinued as a result of the 1996 executive order, allowing 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 Europes planned Galileo system.
• In 2004, U.S. 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.[27]
• November 2004, QUALCOMM announced successful tests of assisted GPS for mobile phones.[28]
• 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 Control System was transferred to the new Architecture Evolution Plan.[29]
• The most recent launch was on May 28, 2010.[30] The oldest GPS satellite still in operation was launched on November 26, 1990, and became operational on December 10, 1990.[31]
• On May 19, 2009, the U. S. Government Accountability Office issued a report warning that some GPS satellites could fail as soon as 2010.[32]
• On May 21, 2009, the Air Force Space Command allayed fears of GPS failure saying "Theres only a small risk we will not continue to exceed our performance standard."[33]
• On January 11, 2010, an update of ground control systems caused a software incompatibility with 8000 to 10000 military receivers manufactured by a division of Trimble Navigation Limited of Sunnyvale, Calif.[34]

Awards

Two GPS developers received the National Academy of Engineering Charles Stark Draper Prize for 2003:

• Ivan Getting, emeritus president of The Aerospace Corporation and engineer at the Massachusetts Institute of Technology, established the basis for GPS, improving on the World War II land-based radio system called LORAN (Long-range Radio Aid to Navigation).
• 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.[35]

On February 10, 1993, the National Aeronautic Association selected the GPS Team as winners of the 1992 Robert J. Collier Trophy, the nations most prestigious aviation award. This team combines researchers from the Naval Research Laboratory, the U.S. Air Force, 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."

Basic concept of GPS

A GPS receiver calculates its position by precisely timing the signals sent by GPS satellites high above the Earth. Each satellite continually transmits messages that include

• the time the message was transmitted
• precise orbital information (the ephemeris)
• the general system health and rough orbits of all GPS satellites (the almanac).

The receiver utilizes the messages it receives to determine the transit time of each message and computes the distances to each satellite. These distances along with the satellites locations are used with the possible aid of trilateration, depending on which algorithm is used, to compute the position of the receiver. This position is then displayed, perhaps with a moving map display or latitude and longitude; elevation information may be included. Many GPS units show derived information such as direction and speed, calculated from position changes.

Three satellites might seem enough to solve for position, since space has three dimensions and a position near the Earths surface can be assumed. However, even a very small clock error multiplied by the very large speed of light[36] — the speed at which satellite signals propagate — results in a large positional error. Therefore receivers use four or more satellites to solve for the receivers location and time. The very accurately computed time is effectively hidden by most GPS applications, which use only the location. A few specialized GPS applications do however use the time; these include time transfer, traffic signal timing, and synchronization of cell phone base stations.

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 plane may have known elevation.) Some GPS receivers may use additional clues or assumptions (such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer) to give a less accurate (degraded) position when fewer than four satellites are visible.[37][38][39]

Position calculation introduction

To provide an introductory description of how a GPS receiver works, errors will be ignored in this section. Using messages received from a minimum of four visible satellites, a GPS receiver is able to determine the times sent and then the satellite positions corresponding to these times sent. The x, y, and z components of position, and the time sent, are designated as Two sphere surfaces intersecting in a circle

The intersection of a third spherical surface with the first two will be its intersection with that circle; in most cases of practical interest, this means they intersect at two points.[40] Another figure, Surface of Sphere Intersecting a Circle (not a solid disk) at Two Points, illustrates the intersection. The two intersections are marked with dots. Again the article trilateration clearly shows this mathematically.

Surface of sphere Intersecting a circle (not a solid disk) at two points

For automobiles and other near-earth-vehicles, the correct position of the GPS receiver is the intersection closest to the Earths surface.[41] For space vehicles, the intersection farthest from Earth may be the correct one.

The correct position for the GPS receiver is also the intersection closest to the surface of the sphere corresponding to the fourth satellite.

Correcting a GPS receivers clock

The method of calculating position for the case of no errors has been explained. One of the most significant error sources is the GPS receivers clock. Because of the very large value of the speed of light, c, the estimated distances from the GPS receiver to the satellites, the pseudoranges, are very sensitive to errors in the GPS receiver clock. This suggests that an extremely accurate and expensive clock is required for the GPS receiver to work. On the other hand, manufacturers prefer to build inexpensive GPS receivers for mass markets. The solution for this dilemma is based on the way sphere surfaces intersect in the GPS problem.

Diagram depicting satellite 4, sphere, p4, r4, and da

It is likely that the surfaces of the three spheres intersect, since the circle of intersection of the first two spheres is normally quite large, and thus the third sphere surface is likely to intersect this large circle. It is very unlikely that the surface of the sphere corresponding to the fourth satellite will intersect either of the two points of intersection of the first three, since any clock error could cause it to miss intersecting a point. However, the distance from the valid estimate of GPS receiver position to the surface of the sphere corresponding to the fourth satellite can be used to compute a clock correction. Let Unlaunched GPS satellite on display at the San Diego Air & Space Museum

The current GPS consists of three major segments. These are the space segment (SS), a control segment (CS), and a user segment (US).[42]

Space segment See also: GPS satellite and List of GPS satellite launches A visual example of the GPS constellation in motion with the Earth rotating. Notice how the number of satellites in view from a given point on the Earths surface, in this example at 45°N, changes with time.

The space segment (SS) is composed of the orbiting GPS satellites, or Space Vehicles (SV) in GPS parlance. The GPS design originally called for 24 SVs, eight each in three circular orbital planes,[43] but this was modified to six planes with four satellites each.[44] The orbital planes are centered on the Earth, not rotating with respect to the distant stars.[45] The six planes have approximately 55° inclination (tilt relative to Earths equator) and are separated by 60° right ascension of the ascending node (angle along the equator from a reference point to the orbits intersection).[46] The orbits are arranged so that at least six satellites are always within line of sight from almost everywhere on Earths surface.[47]

Orbiting at an altitude of approximately 20,200 kilometers (about 12,550 miles or 10,900 nautical miles; orbital radius of approximately 26,600 km (about 16,500 mi or 14,400 NM)), each SV makes two complete orbits each sidereal day, repeating the same ground track each day.[48] This was very helpful during development, since even with just 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.

As of March 2008[update],[49] there are 31 actively broadcasting satellites in the GPS constellation, and two older, retired from active service satellites kept in the constellation as orbital 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 reliability and availability of the system, relative to a uniform system, when multiple satellites fail.[50] About eight satellites are visible from any point on the ground at any one time (see animation at right).

Control segment

The control segment is composed of

a master control station (MCS),

an alternate master control station,

four dedicated ground antennas and

six dedicated monitor stations.

The MCS can also access U.S. Air Force Satellite Control Network (AFSCN) ground antennas (for additional command and control capability) and NGA (National Geospatial-Intelligence Agency) monitor stations. The flight paths of the satellites are tracked by dedicated U.S. Air Force monitoring stations in Hawaii, Kwajalein, Ascension Island, Diego Garcia, Colorado Springs, Colorado and Cape Canaveral, along with shared NGA monitor stations operated in England, Argentina, Ecuador, Bahrain, Australia and Washington DC.[51] The tracking information is sent to the Air Force Space Commands MCS at Schriever Air Force Base 25 km (16 miles) ESE of Colorado Springs, which is operated by the 2nd Space Operations Squadron (2 SOPS) of the United States Air Force (USAF). Then 2 SOPS contacts each GPS satellite regularly with a navigational update using dedicated or shared (AFSCN) ground antennas (GPS dedicated ground antennas are located at Kwajalein, Ascension Island, Diego Garcia, and Cape Canaveral). These updates synchronize the atomic clocks on board the satellites to within a few nanoseconds of each other, and adjust the ephemeris of each satellites internal orbital model. The updates are created by a Kalman filter, which uses inputs from the ground monitoring stations, space weather information, and various other inputs.[52]

Satellite maneuvers are not precise by GPS standards. So to change the orbit of a satellite, the satellite must be marked unhealthy, so receivers will not use it in their calculation. Then the maneuver can be carried out, and the resulting orbit tracked from the ground. Then the new ephemeris is uploaded and the satellite marked healthy again.

User segment GPS receivers come in a variety of formats, from devices integrated into cars, phones, and watches, to dedicated devices such as those shown here from manufacturers Trimble, Garmin and Leica (left to right).

The user segment 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, as of 2007[update], receivers typically have between 12 and 20 channels.[53]

A typical OEM GPS receiver module measuring 15×17 mm.

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. As of 2006[update], even low-cost units commonly include Wide Area Augmentation System (WAAS) receivers.

A typical GPS receiver with integrated antenna.

Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol, or the newer and less widely used NMEA 2000.[54] Although these protocols are officially defined by the National Marine Electronics Association (NMEA),[55] references to these protocols 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 MTK protocols. Receivers can interface with other devices using methods including a serial connection, USB, or Bluetooth.

Further information: GPS navigation device

Communication

Main article: GPS signals

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

GPS message format Subframes Description 1 Satellite clock,
GPS time relationship 2–3 Ephemeris
(precise satellite orbit) 4–5 Almanac component
(satellite network synopsys,
error correction)

Each GPS satellite continuously broadcasts a navigation message at a rate of 50 bits per second (see bitrate). Each complete message is composed of 30-second frames, distinct groupings of 1,500 bits of information. Each frame is further subdivided into 5 subframes of length 6 seconds and with 300 bits each. Each subframe contains 10 words of 30 bits with length 0.6 seconds each. Each 30 second frame begins precisely on the minute or half minute as indicated by the atomic clock on each satellite.[56]

The first part of the message encodes the week number and the time within the week,[57] as well as the data about the health of the satellite. The second part of the message, the ephemeris, provides the precise orbit for the satellite. The last part of the message, the almanac, contains coarse orbit and status information for all satellites in the network as well as data related to error correction.[58]

All satellites broadcast at the same frequencies. Signals are encoded using code division multiple access (CDMA) allowing messages from individual satellites to be distinguished from each other based on unique encodings for each satellite (which the receiver must be aware of). Two distinct types of CDMA encodings are used: the coarse/acquisition (C/A) code, which is accessible by the general public, and the precise (P) code, that is encrypted so that only the U.S. military can access it.

The ephemeris is updated every 2 hours and is generally valid 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 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 chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code.[59] The P code can be encrypted as a so-called P(Y) code which 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.

Demodulation and decoding Demodulating and Decoding GPS Satellite Signals using the Coarse/Acquisition Gold code.

Since all of the satellite signals are modulated onto the same L1 carrier frequency, there is a need to separate the signals 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.[60][61]

If the almanac information has previously been acquired, the receiver picks which 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 satellites 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 Demodulation and Decoding, Advanced.

Navigation equations

The receiver uses messages received from four satellites to determine the satellite positions and time sent. The x, y, and z components of position and the time sent are designated as Two sphere surfaces intersecting in a circle

This can be seen more clearly by considering a side view of the intersecting spheres. This view would match the figure because of the symmetry of the spheres. A view from any horizontal direction would look exactly the same. Therefore the diameter as seen from all directions is the same and thus the surfaces actually do intersect in a circle. The article trilateration algebraically confirms this geometric argument that the two sphere surfaces intersect in a circle.

Having found that two sphere surfaces intersect in a circle, we now consider how the intersection of the first two sphere surfaces, the circle, intersect with the third sphere. A circle and sphere surface intersect at zero, one or two points. For the GPS problem we are concerned with the case of two points of intersection. Another figure, Surface of Sphere Intersecting a Circle (not a solid disk) at Two Points, is shown below to aid in visualizing this intersection. Trilateration algebraically confirms this geometric observation. The ambiguity of two points of intersection of three sphere surfaces can be resolved by noting which point is closest to the fourth sphere surface.

Surface of a sphere intersecting a circle (i.e., the edge of a disk) at two points

Having provided a discussion of how sphere surfaces intersect, we now formulate the equations for the case when errors are present.

Let Main article: Error analysis for the Global Positioning System Sources of User Equivalent Range Errors (UERE) Source Effect (m) Signal arrival C/A ±3 Signal arrival P(Y) ±0.3 Ionospheric effects ±5 Ephemeris errors ±2.5 Satellite clock errors ±2 Multipath distortion ±1 Tropospheric effects ±0.5 σR C/A ±6.7 σR P(Y) ±6.0 Geometric Error Diagram Showing Typical Relation of Indicated Receiver Position, Intersection of Sphere Surfaces, and True Receiver Position in Terms of Pseudorange Errors, PDOP, and Numerical Errors

The term user equivalent range error (UERE) refers to the error of a component in the distance from receiver to a satellite. User equivalent range errors (UERE) are shown in the table. There is also a numerical error with an estimated value, σnum, of about 1 meter. The standard deviations, σR, for the coarse/acquisition 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 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 RSSed 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 (49 ft). These effects also reduce the more precise P(Y) codes accuracy. However, the advancement of technology means that today, civilian GPS fixes under a clear view of the sky are on average accurate to about 5 meters (16 ft) horizontally.

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, σrc, is computed by multiplying PDOP (Position Dilution Of Precision) by σR, the standard deviation of the user equivalent range errors. σR 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).

σR for the C/A code is given by:

The first three elements of each row of A are the components of a unit vector from the receiver to the indicated satellite. The elements in the fourth column are c where c denotes the speed of light. Formulate the matrix, Q, as

The Greek letter σ is used quite often where we have used d. However the elements of the Q matrix do not represent variances and covariances as they are defined in probability and statistics. Instead they are strictly geometric terms. Therefore d as in dilution of precision is used. PDOP, TDOP and GDOP are given by

Derivation of DOP equations

Consider the position error vector,

where .

Transposing both sides:

.

Post multiplying the matrices on both sides of equation (2) by the corresponding matrices in equation (3), there results

.

Taking the expected value of both sides and taking the non-random matrices outside the expectation operator, E, there results:

Assuming the pseudorange errors are uncorrelated and have the same variance, the covariance matrix on the right side can be expressed as a scalar times the identity matrix. Thus

since

From equation (7), it follows that the variances of indicated receiver position and time are

Antispoofing

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 is so much better than originally expected (especially with DGPS) 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

Satellite clocks are slowed by their orbital speed but sped up by their distance out of the Earths gravitational well.

GPS positioning is one of the few everyday events in which relativistic effects must be accounted for.[81] For example, satellite clocks are tuned to 10.22999999543 MHz before launch, to compensate for the effects of gravitational time dilation and achieve a frequency of precisely 10.23 MHz once in orbit.[82] Some other relativistic effects (such as gravitational time delays, frequency shifts of clocks in satellites due to earths quadrupole potential, and space curvature) are too small to affect the system at current accuracy levels.[83]

Special and general relativity

According to the theory of relativity, due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial reference frame, satellite clocks are affected by their speed. Special relativity predicts that the frequency of atomic clocks moving at orbital speeds tick more slowly than stationary ground clocks by a factor of Sagnac distortion

GPS must also compensate for the Sagnac effect. The GPS time scale is defined in an inertial system but observations are processed in an Earth-centered, Earth-fixed (ECEF) co-rotating system, a system in which simultaneity is not uniquely defined. A Lorentz transformation converts from the inertial system to the ECEF system. The resulting correction has opposite algebraic signs for satellites in the Eastern and Western celestial hemispheres. Ignoring this effect produces an east-west error on the order of hundreds of nanoseconds, or tens of meters in position.[88]

Natural sources of interference

Since terrestrial GPS signals tend to be relatively weak, natural radio signals or scattering can desensitize the receiver, making acquiring and tracking satellite signals difficult or impossible.

Space weather degrades GPS operation in two ways, direct interference by solar radio burst noise in the same frequency band[89] or by scattering of the GPS radio signal in ionospheric irregularities referred to as scintillation.[90] Both forms of degradation follow the 11 year solar cycle and peak at sunspot maximum although they can occur anytime. Solar radio bursts are associated with solar flares and coronal mass ejections (CMEs)[91] and their impact can affect reception over the half of the Earth facing the sun. Scintillation occurs most frequently at tropical latitudes at night. It occurs less frequently at high latitudes or mid-latitudes where magnetic storms can lead to scintillation.[92] In addition to scintillation, magnetic storms can produce strong ionospheric gradients that degrade SBAS accuracy.[93]

Artificial sources of interference

In automotive GPS receivers, metallic features in windshields,[94] such as defrosters or car window tinting films,[95] can act as a Faraday cage, degrading reception inside the car.

Man-made electromagnetic interference (EMI) can also disrupt or jam GPS signals. In one well-documented case it was impossible to receive GPS signals in the entire harbor of Moss Landing, California due to unintentional jamming caused by malfunctioning TV antenna preamplifiers.[96][97] 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.[98]

The U.S. government believes that such jammers were used occasionally during the 2001 war in Afghanistan, and the U.S. military claims to have destroyed six GPS jammers during the Iraq War, including one that was destroyed with a GPS-guided bomb.[99] A GPS jammer is relatively easy to detect and locate, making it an attractive target for anti-radiation missiles. The UK Ministry of Defence tested a jamming system in the UKs West Country on 7 and 8 June 2007.[100]

Some countries allow GPS repeaters, to facilitate the reception of GPS signals indoors and in obscured locations; however, under European Union and U.K. laws, these are prohibited because the signals can interfere with other GPS receivers that receive data from both satellites and the repeater.

Various techniques can address interference. One is to not rely on GPS as a sole source. According to John Ruley, "IFR pilots should have a fallback plan in case of a GPS malfunction".[101] Receiver Autonomous Integrity Monitoring (RAIM) is included in some receivers, to warn 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 (DAGR).[102] DAGR detects jamming and maintains its lock on encrypted GPS signals during interference.

Accuracy enhancement and surveying

Main article: GPS augmentation

Augmentation

Main article: GNSS 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, Inertial Navigation Systems (INS) and Assisted GPS.

Precise monitoring

Accuracy can be improved through precise monitoring and measurement of existing GPS signals in additional or alternate ways.

The largest remaining error is usually the unpredictable delay through the ionosphere. The spacecraft broadcast ionospheric model parameters, but 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. However, 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 (see GPS modernization). Then all users will 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 PRN is not instantaneous, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. CPGPS utilizes the L1 carrier wave, which has a period of

Triple differencing[105] subtracts the receiver difference from time 1 from that of time 2. This eliminates the ambiguity associated with the integral number of wave lengths 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:

Main article: Global Navigation Satellite System

Other satellite navigation systems in use or various states of development include:

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  Notes

  References

  • "NAVSTAR GPS User Equipment Introduction" (PDF). US Coast Guard. September 1996. http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf. 

  Further reading

  • Parkinson; Spilker (1996). The global positioning system. American Institute of Aeronautics and Astronautics. ISBN 9781563471063. http://books.google.com/?id=lvI1a5J_4ewC. 

  External links

  Wikimedia Commons has media related to: Global Positioning System
  • Global Positioning System at the Open Directory Project
  • GPS.gov—General public education website created by the U.S. Government
  • National Space-Based PNT Executive Committee—Established in 2004 to oversee management of GPS and GPS augmentations at a national level.
  • USCG Navigation Center—Status of the GPS constellation, government policy, and links to other references. Also includes satellite almanac data.
  • Air Force Space Command GPS Operations Center homepage
  • The GPS Program Office (GPS Wing)—Responsible for designing and acquiring the system on behalf of the US Government.
  • U.S. Army Corps of Engineers manual: NAVSTAR HTML and PDF (22.6 MB, 328 pages)
  • FAA GPS FAQ
  • National Geodetic Survey Orbits for the Global Positioning System satellites in the Global Navigation Satellite System
  • GPS SPS Performance Standard—The official Standard Positioning Service specification (2008 version).
  • GPS SPS Performance Standard—The official Standard Positioning Service specification (2001 version).
  • GPS PPS Performance Standard—The official Precise Positioning Service specification.
  • Satellite Navigation: GPS & Galileo (PDF)—16-page paper about the history and working of GPS, touching on the upcoming Galileo
  • Average Latitude & Longitude of Countries
  • "Sources of Errors in GPS"
  • GPS and GLONASS Simulation(Java applet) Simulation and graphical depiction of space vehicle motion including computation of dilution of precision (DOP)
  • University of New South Wales: Carrier Phase Measurement
  • University of New South Wales: Carrier Beat Phase
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