The Global Positioning System (GPS) is a space-based global navigation satellite system (GNSS) that provides location and time information in all weather, anywhere on or near the Earth, 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 with some technical limitations which are only removed for military users.
The GPS project was developed in 1973 to overcome the limitations of previous navigation systems, integrating ideas from several predecessors, including a number of classified engineering design studies from the 1960s. GPS was created and realized by the U.S. Department of Defense (USDOD) and was originally run with 24 satellites. It became fully operational in 1994.
In addition to GPS, other systems are in use or under development. The Russian GLObal NAvigation Satellite System (GLONASS) was in use by only the Russian military, until it was made fully available to civilians in 2007. There are also the planned Chinese Compass navigation system and the European Union's Galileo positioning system.
While there were wide needs for accurate navigation in military and civilian sectors, almost none of those were seen as justification for the billions of dollars it would cost in research, development, deployment, and operation for a constellation of navigation satellites. During the Cold War arms race, the nuclear threat to the existence of the United States was the one need that did justify this cost in the view of the United States Congress. This deterrent effect is why GPS was funded. The nuclear triad consisted of the United States Navy's submarine-launched ballistic missiles (SLBMs) along with United States Air Force (USAF) strategic bombers and intercontinental ballistic missiles (ICBMs). Considered vital to the nuclear deterrence posture, accurate determination of the SLBM launch position was a force multiplier.
Precise navigation would enable United States submarines to get an accurate fix of their positions prior to launching their SLBMs. The USAF with two-thirds of the nuclear triad also had requirements for a more accurate and reliable navigation system. The Navy and Air Force were developing their own technologies in parallel to solve what was essentially the same problem. To increase the survivability of ICBMs, there was a proposal to use mobile launch platforms (such as Russian SS-24 and SS-25) and so the need to fix the launch position had similarity to the SLBM situation.
In 1960, the Air Force proposed a radio-navigation system called MOSAIC (MObile System for Accurate ICBM Control) that was essentially a 3-D LORAN. A follow-on study called Project 57 was worked in 1963 and it was "in this study that the GPS concept was born." That same year the concept was pursued as Project 621B, which had "many of the attributes that you now see in GPS" and promised increased accuracy for Air Force bombers as well as ICBMs. Updates from the Navy Transit system were too slow for the high speeds of Air Force operation. The Navy Research Laboratory continued advancements with their Timation (Time Navigation) satellites, first launched in 1967, and with the third one in 1974 carrying the first atomic clock into orbit.
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.
During Labor Day weekend in 1973, a meeting of about 12 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''. 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'', which was later shortened simply to GPS.
After Korean Air Lines Flight 007, 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 satellite was launched in 1989, and the 24th satellite was launched in 1994.
Initially, the highest quality signal was reserved for military use, and the signal available for civilian use was intentionally degraded ("Selective Availability", SA). This changed with President Bill Clinton ordering Selective Availability to be turned off at midnight May 1, 2000, improving the precision of civilian GPS from 100 meters (about 300 feet) to 20 meters (about 65 feet). The executive order signed in 1996 to turn off Selective Availability in 2000 was proposed by the US Secretary of Defense, William Perry, because of the widespread growth of differential GPS services to improve civilian accuracy and eliminate the US military advantage. Moreover, the US military was actively developing technologies to deny GPS service to potential adversaries on a regional basis.
GPS is owned and operated by the United States Government as a national resource. Department of Defense (USDOD) is the steward of GPS. ''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.
USDOD 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."
+ Summary of satellites< | rowspan="2">Block | Launch < | Period | colspan="4">Satellite launchesCurrently 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 | |
IIR | 1997–2004 | 12 | 1| | 0 | 0 | 12 | |
IIR-M | 2005–2009 | 8 | 0| | 0 | 0 | 7 | |
GPS Block IIF | IIF | 2010– | 2 | 0| | 10 | 0 | 2 |
IIIA | 2014– | 0 | 0| | 0 | 12 | 0 | |
IIIB | Theoretical | 0 | 0| | 0 | 8 | 0 | |
IIIC | Theoretical | 0 | 0| | 0 | 16 | 0 | |
colspan="2">Total | 60 | 2 | 10| | 36 | 31 | ||
PRN 01 from Block IIR-M is unhealthy | PRN 25 from Block IIA is unhealthy | PRN 32 from Block IIA is unhealthy | For a more complete list, see ''list of GPS satellite launches'' |
Two GPS developers received the National Academy of Engineering Charles Stark Draper Prize for 2003:
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.
The receiver uses the messages it receives to determine the transit time of each message and computes the distance 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 Earth's surface can be assumed. However, even a very small clock error multiplied by the very large speed of light — the speed at which satellite signals propagate — results in a large positional error. Therefore receivers use four or more satellites to solve for the receiver's 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 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, or including information from the vehicle computer) to give a less accurate (degraded) position when fewer than four satellites are visible.
A satellite's position and pseudorange define a sphere, centered on the satellite, with radius equal to the pseudorange. The position of the receiver is somewhere on the surface of this sphere. Thus with four satellites, the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. In the ideal case of no errors, the GPS receiver would be at a precise intersection of the four surfaces.
If the surfaces of two spheres intersect at more than one point, they intersect in a circle. The article trilateration shows this mathematically. A figure, ''Two Sphere Surfaces Intersecting in a Circle'', is shown below. Two points where the surfaces of the spheres intersect are clearly shown in the figure. The distance between these two points is the diameter of the circle of intersection. 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. 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.
and other near-earth vehicles, the correct position of the GPS receiver is the intersection closest to the Earth's surface. 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.
It is likely that the surfaces of the three spheres intersect, because 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, because 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 denote the distance from the valid estimate of GPS receiver position to the fourth satellite and let denote the pseudorange of the fourth satellite. Let . is the distance from the computed GPS receiver position to the surface of the sphere corresponding to the fourth satellite. Thus the quotient, , provides an estimate of
: (correct time) – (time indicated by the receiver's on-board clock), and the GPS receiver clock can be advanced if is positive or delayed if is negative.
However, it should be kept in mind that a less simple function of may be needed to estimate the time error in an iterative algorithm as discussed in the Navigation equations section.
The space segment is composed of 24 to 32 satellites in medium Earth orbit and also includes the payload adapters to 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).
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 approximately circular orbits, but this was modified to six orbital planes with four satellites each. The orbits are centered on the Earth, not rotating with the Earth, but instead fixed with respect to the distant stars. The six orbit planes have approximately 55° inclination (tilt relative to Earth's equator) and are separated by 60° right ascension of the ascending node (angle along the equator from a reference point to the orbit's intersection). The orbits are arranged so that at least six satellites are always within line of sight from almost everywhere on Earth's surface. The result of this objective is that the four satellites are not evenly spaced (90 degrees) apart within each orbit. In general terms, the angular difference between satellites in each orbit is 30, 105, 120, and 105 degrees apart which, of course, sum to 360 degrees.
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 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. About nine satellites are visible from any point on the ground at any one time (see animation at right).
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. The tracking information is sent to the Air Force Space Command's 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 U.S. Air Force. 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 satellite's internal orbital model. The updates are created by a Kalman filter that uses inputs from the ground monitoring stations, space weather information, and various other inputs.
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.
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, , receivers typically have between 12 and 20 channels.
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 MTK protocols. Receivers can interface with other devices using methods including a serial connection, USB, or Bluetooth.
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.
Clock synchronization: The accuracy of GPS time signals (±10 ns) is second only to the atomic clocks upon which they are based.
This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A (Coarse/Acquisition) code and cannot correct for Selective Availability (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 that regularly reach .
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.
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.
The first part of the message encodes the week number and the time within the week, 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.
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 (that 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.
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. 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 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 would provide this signal is set to be launched in 2009. 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."
A waiver has recently been 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 sometime in late 2010. 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 will 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.
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 Demodulation and Decoding, Advanced.
Let ''b'' denote the clock error or bias, the amount that the receiver's clock is off. The receiver has four unknowns, the three components of GPS receiver position and the clock bias [''x, y, z, b'']. The equations of the sphere surfaces are given by: : or in terms of ''pseudoranges'', , as : .
These navigation equations can be solved by algebraic or numerical methods.
Finally, results from other positioning systems such as GLONASS or the upcoming Galileo can be incorporated or used to check the result. (By design, these systems use the same frequency bands, so much of the receiver circuitry can be shared, though the decoding is different.)
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.
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 uses the L1 carrier wave, which has a period of , which is about one-thousandth of the C/A Gold code bit period of , 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 positioning, RTK).
The GPS navigation message includes the difference between GPS time and UTC, which as of 2011 is 15 seconds because of the leap second added to UTC December 31, 2008. Receivers add this offset to GPS time to calculate UTC and specific timezone 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) that, given the current period of the Earth's rotation (with one leap second introduced approximately every 18 months), should be sufficient to last until approximately the year 2300.
However, 2 millimeter accuracy requires measuring the total phase—the number of waves times the wavelength plus the fractional wavelength, which requires specially equipped receivers. This method has many surveying applications.
Triple differencing followed by numerical root finding, and a mathematical technique called least squares 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 denote the phase of the carrier of satellite ''j'' measured by receiver ''i'' at time . 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 and to balance readability and conciseness, let be a concise abbreviation. Also we define three functions, :, 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 is a function of the three integer arguments, ''i, j,'' and ''k'' then it is a valid argument for the functions, :, with the values defined as
:, :, and : .
Also if are valid arguments for the three functions and ''a'' and ''b'' are constants then is a valid argument with values defined as
:, :, and : .
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
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: :
Triple differencing 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: :
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 quite possibly will be sufficient to solve for receiver 2's three position components. This may require the use of a numerical procedure. 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 which best fits the observed triple difference results for receiver 2 positions under the criterion of minimizing the sum of the squares.
Category:Aerospace engineering Category:Articles with separate introductions Category:Avionics Category:Command and control Category:Geodesy Category:Geographical technology Category:Hiking equipment Category:Missile guidance Category:Navigation Category:Navigational equipment Category:Nuclear command and control Category:Outdoor locating games Category:Radio navigation Category:Surveying Category:Technology systems Category:Weapon guidance Category:Wireless locating Category:American inventions Category:Satellite navigation systems
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Coordinates | 13 °31 ′30 ″N71 °58 ′20 ″N |
---|---|
name | Global Deejays |
background | group_or_band |
origin | Austria |
genre | HouseElectro house |
years active | 2004 - present |
website | www.global-deejays.com |
current members | DJ Taylor (Konrad Schreyvogl)DJ Mikkel (Mikkel Christensen)FLOw (Florian Schreyvogl) |
notable instruments | }} |
The group's track "The Sound of San Francisco" partially samples the 1967 (The Summer of Love) song "San Francisco (Be Sure to Wear Flowers in Your Hair)" sung by Scott McKenzie. The video includes scenes of the band in a decorated school bus driving through popular destinations.
In 2005 the Global Deejays won both the Russian MTV Energy Award and the Polish ESKA Award.
January 26 of 2009 saw the remixed version of the group's Everybody's Free (To Feel Good) debut on the Australian ARIA Charts at number 33. This popularity was the result of the track featuring in television commercials for the Australian version of So You Think You Can Dance that summer.
April 2010 saw the Global Deejays release "My Friend" with the vocal talents of Danish singer Ida Corr.
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Category:Eurodance groups Category:House music groups Category:Austrian musical groups Category:Austrian pop music groups Category:Musical groups established in 2004
de:Global Deejays es:Global Deejays fr:Global Deejays is:Global Deejays it:Global Deejays pl:Global Deejays pt:Global Deejays ru:Global Deejays sv:Global DeeJays
This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
Coordinates | 13 °31 ′30 ″N71 °58 ′20 ″N |
---|---|
name | Rob Wells |
background | non_vocal_instrumentalist |
origin | Peterborough, Ontario, Canada |
instrument | Piano & Drums |
genre | Rock, Pop, R&B; |
occupation | Record Producer, Songwriter & Musician |
website | |
notable instruments | }} |
Wells has worked with Justin Bieber, Selena Gomez, Adam Lambert, Nick Lachey, Miranda Cosgrove, Mika, Backstreet Boys, Paloma Faith, Cyndi Lauper, Olivia Newton John, Daisy Dares You, Boyzone, Matt Dusk, Marie-Mai, Shiloh, RyanDan, Ry Cuming & many others.
Rob's work has been featured on ''So You Think You Can Dance'', ''Dancing With The Stars'', ''One Tree Hill'', ''The View'', ''Late Show with David Letterman'', ''Laguna Beach'', ''House Of Carters'', ''Degrassi: The Next Generation'', ''Instant Star'', & 20th Century Fox's ''Flicka''.
In 2005, Wells (along with Christopher Ward) placed first in the International Songwriting Competition's Top40/Pop Category with the song "There's Us", which was later recorded by Backstreet Boys and Alexz Johnson.
Wells received a SOCAN #1 award for Matt Dusk's "All About Me", having reached the top of the Canadian AC Radio Charts in August 2006.
In the summer and fall of 2008, Rob appeared on YTV's "The Next Star" as a music producer. He was also on an episode of E!'s "House Of Carters".
In the winter of 2011, his co-written song "Comme Avant" with Marie-Mai spent 11 weeks at #1 in Quebec.
He is the younger brother of writer/producer Greg Wells.
This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
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