Global Positioning System
The Global Positioning System ( GPS ; German Global Positioning System ), officially NAVSTAR GPS is a global navigation satellite system for positioning . It was developed by the US Department of Defense since the 1970s and replaced the old NNSS ( Transit ) satellite navigation system of the US Navy from around 1985 , as did the Vela satellites for locating nuclear weapon explosions . GPS has been fully functional since the mid-1990s and, since the artificial signal degradation ( selective availability ) was switched off on May 2, 2000, it has also enabled civil users to achieve an accuracy of often better than 10 meters. The accuracy can be increased to values in the centimeter range or better using differential methods ( differential GPS / DGPS ) in the vicinity of a reference receiver. With the satellite-based improvement systems ( SBAS ), which distribute correction data via geostationary satellites that cannot be received in the polar regions and also belong to the class of DGPS systems, accuracies of one meter are achieved across the continent. GPS has established itself as the world's most important positioning method and is widely used in navigation systems.
The official name is " Nav igational S atellite T IMing a nd R was concerned - G lobal P ositioning S ystem" (NAVSTAR GPS). NAVSTAR is sometimes referred to as an abbreviation for " Nav igation S ystem using T IMing a nd R was concerned" (without GPS used). The system was officially put into operation on July 17, 1995 .
The abbreviation GPS has become so well established that it is used colloquially, sometimes even in technical terms, as a generic term or pars pro toto for all satellite navigation systems. The latter are however under the symbol GNSS ( G lobal N avigation (al) S atellite S ystem) are summarized.
Areas of application
GPS was originally intended for position determination and navigation in the military sector (in weapon systems , warships , aircraft , etc.). One advantage is that GPS devices only receive signals and do not send them. This means that you can navigate without third parties receiving information about your own location. Today it is also used in the civil sector: in seafaring , aviation , through navigation systems in the car , for position determination and tracking in the rescue and fire service as well as in public transport , for orientation in the outdoor area etc. DGPS procedures have in Germany according to the Establishment of the satellite positioning service of the German national surveying service (SAPOS) is of particular importance in geodesy , since measurements can be carried out nationwide with centimeters accuracy. In agriculture , it is used in precision farming to determine the position of machines in the field. GPS is also used in competitive sports. The Assisted Global Positioning System (A-GPS) was specially developed for use in mobile phones .
Structure and functionality of the location function
GPS is based on satellites that continuously broadcast their current position and the exact time with coded radio signals. Special receivers (GNSS) can calculate their own position and speed from the signal propagation times . Theoretically, the signals from three satellites are sufficient, which must be above their switch-off angle, since the exact position and altitude can be determined from them. In practice, GPS receivers do not have a clock that is accurate enough to correctly measure the transit times. Therefore, the signal from a fourth satellite is required, with which the exact time can be determined in the receiver. For the minimum number of satellites required, see article GPS technology .
The GPS signals can be used to determine not only the position, but also the speed of the receiver. This is generally done by measuring the Doppler effect or the numerical differentiation of the location according to time. The direction of movement of the receiver can also be determined and used as an artificial compass or to align electronic maps. The compass function is also based on the Doppler effect. This means that it is not possible to take a compass measurement when the receiver is stationary. If the receiver starts moving, a compass measurement is only available after a short delay.
A satellite constellation is defined so that a GPS receiver can have contact with at least four satellites. For GPS, this includes six orbital planes that are inclined 55 ° to the equator and cover almost the whole world. GPS devices cannot be used in the polar regions, but other satellite navigation systems whose satellites run in suitable orbits to cover the polar region can.
In each of these six orbital levels, according to the GPS basic configuration, at least four satellites should orbit the earth twice at an altitude of 20,200 km on each sidereal day. A satellite of the IIR version is designed for a service life of 7.5 years. The actual operating time can be reduced due to a technical defect, the operating conditions can result in a longer or shorter operating time. Additional satellites are available to maintain the constellation. Some of these are placed in extended slots of the constellation and play an active role there. Further replacement satellites are waiting in orbit in a sleep state for their use. A resulting gap in the constellation leads, e.g. B. if an immediately adjacent extended slot is occupied, there is no restriction of the GPS signal availability. To fill a gap, a new satellite can be launched, a sleeping satellite that is already orbiting can be reactivated, or an active satellite can be maneuvered to a different position. All of these measures are time consuming. It takes months to get a satellite into the position it needs to be deployed. With the weak engines of the satellites, it is impossible to order a satellite into another orbit. Repositioning can be achieved in the path level by a sequence of braking and acceleration maneuvers. Of course, this also consumes the precious fuel supply, which is usually only used to maintain the exact position.
- On the L1 frequency (1575.42 MHz) , the C / A code ("Coarse / Acquisition") for civil use, and the not publicly known P / Y code ("Precision / encrypted" ) used for military use. The transmitted data signal is identical for both code sequences and represents the 1500- bit navigation message. It contains all important information about the satellite, date, identification number, corrections, orbits, but also the status, and it takes half a minute to transmit. GPS receivers normally store this data temporarily. To initialize the devices, the so-called almanac data are transmitted, which contain the rough orbit data of all satellites and which take twelve minutes to transmit.
- The second frequency, L2 frequency (1227.60 MHz) , only transmits the P / Y code. The C / A code can optionally be transmitted on the second frequency. By transmitting on two frequencies, ionospheric effects that lead to an increase in the transit time can be calculated out, which increases the accuracy. As part of the GPS modernization, a new civil C code (L2C) with an optimized data structure has also been transmitted since 2005 (satellites of type IIR-M and IIF).
- The third L5 frequency (1176.45 MHz) is currently under construction. It is intended to further improve the robustness of reception and is primarily intended for aviation and rescue service applications. The L5-capable IIF satellites have been in use since 2010, since April 28, 2014 the L5 signals contain usable navigation data and since December 31, 2014 these have been updated daily. L5 uses the same modernized data structure as the L2C signal.
Each satellite has a receiver for a data connection in the S-band (1783.74 MHz for receiving, 2227.5 MHz for transmitting).
C / A code
The C / A code used for modulating the data signal in the civil sector is a pseudo-random code sequence with a length of 1023 bits. The transmission bits of a code sequence are referred to as so-called “chips” in “spread spectrum” modulations and do not carry any user data information, but are only used for demodulation by means of correlation with the code sequence itself. This 1023 chip long sequence has a period length of 1 ms, and the chips -Rate is 1.023 Mcps. The two code generators for the Gold sequence each consist of 10-bit long shift registers and are comparable to shift registers with linear feedback , although individually they do not result in the maximum sequence. The generator polynomials G 1 and G 2 used in the C / A code are:
The final Gold sequence (C / A code sequence) is achieved by a code phase shift between the two generators. The phase shift is selected differently for each GPS satellite so that the resulting transmission sequences (chip signal sequences) are orthogonal to one another - this enables independent reception of the individual satellite signals, although all GPS satellites are on the same nominal frequencies L 1 and L 2 send (so-called code division multiplex , CDMA method).
In contrast to the pseudo-random noise sequences from linear feedback shift registers ( LFSR ), the also pseudo-random noise sequences from Gold code generators have significantly better cross-correlation properties if the underlying generator polynomials are selected accordingly. This means that different Gold sequences set by the code phase shift with the same generator polynomials are almost orthogonal to one another in the code space and therefore hardly influence one another. The LFSR generator polynomials G1 and G2 used for the C / A code allow a maximum of 1023 code phase shifts, of which approximately 25% have a sufficiently small cross-correlation for CDMA reception in GPS applications. This means that in addition to the maximum of 32 GPS satellites and their navigation signals, another 200 or so satellites can also transmit data on the same transmission frequency to the GPS receivers - this fact is used, for example, as part of EGNOS for the transmission of atmospheric correction data, weather data and data for civil aviation exploited.
Since the data rate of the user data transmitted is 50 bit / s and a user data bit is exactly 20 ms long, a single user data bit is always transmitted by repeating a Gold sequence exactly 20 times.
The selectable artificial error Selective Availability , which has not been used since the year 2000, was achieved with the C / A code by subjecting the timing (clock signal) of the chips to a slight temporal fluctuation ( jitter ). The regional interference of GPS signals is achieved by the US military through GPS jammers and thus does not make GPS a reliable means of orientation in every case, since it is not possible to reliably determine whether and how far GPS signals are from the actual UTM / MGRS -Coordinates differ.
P (Y) code
The longer P code, which is mostly used by the military, uses so-called JPL sequences as a code generator . It is divided into the publicly documented P-code and the secret Y-code used for encryption on the radio interface, which can be switched on or off as required. The combination of these is known as the P / Y code. Encryption with the Y-code is intended to enable operation that is as tamper-proof as possible ( anti- spoofing or AS mode ). The AS mode has been permanently activated since January 31, 1994, and the publicly known P-code is no longer transmitted directly.
The P-code is formed from four linear shift registers ( LFSR ) of length 10. Two of them form the so-called X1 code, the other two the X2 code. The X1 code is combined with the X2 code using XOR links so that a total of 37 different phase shifts result in 27 different week segments of the P code. The lengths of this code are much longer than those of the C / A code. The X1 code generator provides a length of 15,345,000 chips and X2 a code sequence that is exactly 37 chips longer. The time it takes for the P code to repeat itself is 266 days (38 weeks). The P / Y code is sent at a chip rate of 10.23 Mcps, which is ten times the chip rate of the C / A code. It therefore requires a wider frequency spectrum than the C / A code.
To differentiate between the individual GPS satellites in the P / Y code, the very long code sequence of around 38 weeks is divided into individual weekly segments. Each GPS satellite has a code section that lasts exactly one week , and at the beginning of each week (Sunday 00:00) all P code generators are reset to the starting value. This means that the P / Y code is repeated once a week for each GPS satellite. The ground stations require five weekly segments of the 38-week long P-code for control tasks, 32 weekly segments are provided to differentiate between the individual GPS satellites.
The C / A code is used to switch - so-called hand over - to the P / Y code. Since the P-code sequence per GPS satellite lasts for a week, it would be practically impossible to synchronize simple receivers directly to the P-code sequence without knowing the exact GPS time. Simple GPS receivers that use the P / Y code first synchronize with the C / A code, obtain the necessary switching information such as time, day of the week and other information from the transmitted data, and use them to set their P code generators accordingly then switch to receiving the P / Y code.
Modern military GPS receivers are now equipped with a much larger number of correlators , similar to the SiRFstar III chipset used in the civil sector , which makes it possible to evaluate the P / Y code directly. These receivers are called “direct Y-code” receivers by the manufacturers. This generation of receivers makes it possible to disrupt the C / A code in order to prevent the use of civilian GPS receivers by opposing forces, for example for measuring firing positions . Since the bandwidth of the military signal is approx. 20 MHz, the 1–2 MHz bandwidth of the C / A code, which is used for civil purposes, can be disrupted without significantly affecting military receivers. This and the assumption that today's conflicts are regionally limited led to the decision to switch off the artificial deterioration permanently.
The exact parameters for the Y-encryption of the P-code are not publicly known. The parameters of the navigation data (user data, frame structure, bit rate) that are transmitted using the P / Y code are, however, exactly identical to the data that are transmitted using the publicly known C / A code sequence. The main difference is that the clock rate of the P / Y code sequence in the satellite is not subject to any artificial clock errors and the P code has 10 times the clock rate of the C / A code. This enables P / Y receivers to obtain the information about the transmission times that is essential for determining the position more precisely.
There are strict controls on the transfer of P-code data to countries outside of NATO. Such users such. B. the Swiss Air Force receive the current P-code, which is changed weekly by the NSA, and upload it to the navigation hardware in their combat aircraft. Without this update, the aiming accuracy of the on-board weapons drops drastically.
Propagation properties of the signal
In the frequency ranges used, the electromagnetic radiation spreads almost in a straight line, similar to visible light, but is hardly influenced by cloud cover or precipitation. However, due to the low transmission power of the GPS satellites, a direct line of sight to the satellite is necessary for the best reception of the signals. In buildings , a GPS receiver was not possible until recently. New receiver technology enables applications in buildings under favorable conditions. Multiple reflected signals ( multipath effect ) can lead to inaccuracies between tall buildings . In addition, z. Sometimes large inaccuracies in the case of unfavorable satellite constellations, for example if only three satellites standing close together are available from one direction for position calculation. For an exact determination of the position, it should be possible to receive four satellite signals from different directions.
The technical implementation including its mathematical basics is described in the article GPS technology .
Each GPS satellite is equipped with one or more atomic time clocks. The atomic time thus generated, together with the exact position of the satellite, is a prerequisite for determining the position of the GPS receiver. At the same time, a globally standardized time system is made available. The time received by a GPS receiver is initially GPS time , an atomic time scale without a leap second . The GPS time is therefore 18 seconds ahead of Coordinated Universal Time (UTC) since 1980 (as of January 2017). The satellite message contains the current difference between GPS time and UTC. This allows the exact UTC to be calculated in the receiver. If the transit time of the satellite signal is precisely determined, the GPS system guarantees a deviation from UTC of a maximum of one microsecond.
Nuclear Detection System
The GPS satellites are part of the US Nuclear Detection System (NDS) program, formerly known as the Integrated Operational Nuclear Detection System (IONDS), and integrated into the DSP ( Defense Support Program ). They have optical and X-ray sensors and also detectors for EMP . They are supposed to register atomic bomb explosions and launches of ICBMs with a spatial resolution of 100 m. The GPS has replaced the Vela system.
In addition to ground-based radio navigation systems such as the Decca Navigation System , which was developed during the Second World War and which later served primarily for maritime navigation and was only available locally due to its principle, the US Navy developed the first Transit satellite navigation system from 1958 onwards. Initially under the name Navy Navigation Satellite System (NNSS) , it was used militarily from 1964 for the guidance of ballistic missiles on submarines and aircraft carriers of the US Navy and from 1967 also civilly. Its transmission frequencies were between 150 and 400 MHz, and it achieved an accuracy between 500 and 15 m. It has been out of service since December 31, 1996.
The GPS program was started with the establishment of the JPO ( Joint Program Office ) in 1973. Bradford W. Parkinson is considered to be a co-inventor of the global positioning system used by the military. Together with the Americans Roger L. Easton and Ivan A. Getting , who are primarily to be named as inventors for the civil use of GPS, he developed GPS. The first GPS satellite was launched in 1978 from the Vandenberg launch site SLC-3E with an Atlas F rocket into orbit at an altitude of 20,200 km and an orbit inclination of 63 ° .
As a result of the downing of Korean Air Lines Flight 007 , US President Reagan announced on September 16, 1983 that GPS would be released for civilian use. In 1985, the last first-generation satellite was launched from the Vandenberg SLC-3W launch pad with an Atlas-E rocket.
With the introduction of the GPS II series (1989), the company moved to Cape Canaveral and launched from the LC-17 launch pad with Delta 6925 missiles . The GPS IIA to GPS IIR-M series followed with Delta 7925 missiles . The inclination was reduced to 55 ° when taking off from Cape Canaveral while maintaining the orbit height. In December 1993 the initial operational capability was determined. At that time, 24 satellites were in use. The full operational capability was achieved in April 1995 and announced on July 17, 1995. The GPS-IIF series, whose first satellite GPS IIF-1 was launched in 2010, no longer has a solid-state apogee motor , but is launched by its Delta-IV or Atlas-V launchers directly in GPS orbit instead of on a transfer orbit, such as it was common up to GPS-IIR-M series.
In order to exclude unauthorized users - potential military opponents - from an exact position determination, the accuracy for users who do not have a key was artificially deteriorated (selective availability = SA, with an error of greater than 100 m). SA had to be implemented in the Block II satellites because the C / A service was significantly better than originally expected. There were almost always a few satellites in which SA was not activated, so that precise time transmissions were possible. On May 2, 2000, this artificial inaccuracy of the satellites was switched off, and from approx. Since then, the system can also be used for precise positioning outside of the previously exclusive application area. Among other things, this led to the boom in navigation systems in vehicles and outdoors, as the measurement error is now less than 10 m in at least 90% of the measurements.
On September 25, 2005, a Delta II rocket launched the first GPS satellite of the GPS 2R-M ( m odernized) series into space. The antenna was improved and the transmission spectrum was expanded to include a second civilian frequency and two new military signals. In use since December 2005, the new satellite expanded the fleet of fully functional satellites to 28. In June 2008, 32 satellites were active. On August 17, 2009, GPS 2R-M8, the last GPS satellite in this series, successfully launched into its transfer orbit with a Delta II rocket.
The Pentagon authorized the United States Air Force on May 9, 2008 to order the first eight third-series satellites. US $ 2 billion was made available for development and construction. The third generation will consist of a total of 32 satellites and will replace the GPS II system from 2014. They differ in their increased signal strength and other measures to make signal disruption more difficult. Lockheed Martin and Boeing competed for the contract, which would automatically link the delivery of the next 24 satellites. On May 15, 2008, Lockheed Martin won the contract to build the first two GPS IIIA satellites. The order is now said to have been increased to eight satellites.
The GPS satellites are numbered in several ways:
- Sequential Navstar number of the satellite: This is the name of the satellite in international registers.
- The position on the six main orbits A to F.
- USA number: this has been used to number US military satellites since 1984.
- consecutive SVN number (space vehicle number) for GPS satellites.
- PRN number which identifies the signal coding (not the satellite) and is displayed on the GPS receiver. If one satellite fails, another can send out its signal with the PRN code.
The constellation originally planned by GPS, now referred to as the 24-slot basic configuration, comprises six evenly distributed orbital planes, each inclined 55 ° to the equator. These levels of circulation are marked with the letters A - F. In the basic configuration, four satellites are in orbit in each of these levels, but they are not evenly distributed! The individual positions in a circulation level are defined and numbered 1 - 4.
The current configuration includes up to six additional satellites.
The information on this can be found in the performance standard document. The text in section 3.0 states that the additional satellites are located in planes B, D and F. The actual constellation does not seem to adhere to this restriction. The unevenly distributed occupancy of a level with satellites is shown using level B as an example. The slot B1 expanded to B1F = B5, B1A = B6 is shown here in red. The occupancy in the other levels is similar in each case, but offset by an angle in order to ensure optimal basic coverage for the GPS clients on the ground.
The constellation includes satellites of generation IIR, IIF and III. Some operational satellites are not part of the constellation, but can be integrated should another satellite fail due to a technical defect or due to age, this happened temporarily with Navstar 35. All satellites of the generation require annual downtime of <1 day each to correct their position or to carry out maintenance work perform.
( AFSC )
|NAVSTAR 43 (USA 132)||F6||July 23, 1997||43||13||24876||1997-035A||IIR|
|NAVSTAR 46 (USA 145)||D5||October 7, 1999||46||11||25933||1999-055A||IIR|
|NAVSTAR 47 (USA 150)||E4||May 11, 2000||51||20th||26360||2000-025A||IIR|
|NAVSTAR 48 (USA 151)||B3||July 16, 2000||44||28||26407||2000-040A||IIR|
|NAVSTAR 49 (USA 154)||F5||November 10, 2000||41||14th||26605||2000-071A||IIR|
|NAVSTAR 51 (USA 166)||B1||January 29, 2003||56||16||27663||2003-005A||IIR|
|NAVSTAR 52 (USA 168)||D3||March 31, 2003||45||21st||27704||2003-010A||IIR|
|NAVSTAR 53 (USA 175)||E6||December 21, 2003||47||22nd||28129||2003-058A||IIR|
|NAVSTAR 54 (USA 177)||C5||March 20, 2004||59||19th||28190||2004-009A||IIR|
|NAVSTAR 56 (USA 180)||D1||November 6, 2004||61||02||28474||2004-045A||IIR|
|NAVSTAR 57 (USA 183)||C4||September 26, 2005||53||17th||28874||2005-038A||IIR-M|
|NAVSTAR 58 (USA 190)||A2||September 25, 2006||52||31||29486||2006-042A||IIR-M|
|NAVSTAR 59 (USA 192)||B4||November 17, 2006||58||12||29601||2006-052A||IIR-M|
|NAVSTAR 60 (USA 196)||F2||October 17, 2007||55||15th||32260||2007-047A||IIR-M|
|NAVSTAR 61 (US 199)||C1||December 20, 2007||57||29||32384||2007-062A||IIR-M|
|NAVSTAR 62 (USA 201)||A4||March 15, 2008||48||07||32711||2008-012A||IIR-M|
|NAVSTAR 64 (USA 206)||E3||17th August 2009||50||05||35752||2009-043A||IIR-M|
|NAVSTAR 65 (USA 213)||B2||May 28, 2010||62||25th||36585||2010-022A||IIF|
|NAVSTAR 66 (USA 232)||D2||July 16, 2011||63||01||37753||2011-036A||IIF|
|NAVSTAR 67 (USA 239)||A1||4th October 2012||65||24||38833||2012-053A||IIF|
|NAVSTAR 68 (USA 242)||C2||May 15, 2013||66||27||39166||2013-023A||IIF|
|NAVSTAR 69 (USA 248)||A3||February 21, 2014||64||30th||39533||2014-008A||IIF|
|NAVSTAR 70 (USA 251)||D4||17th May 2014||67||06||39741||2014-026A||IIF|
|NAVSTAR 71 (USA 256)||F3||2nd August 2014||68||09||40105||2014-045A||IIF|
|NAVSTAR 72 (USA 258)||E1||October 29, 2014||69||03||40294||2014-068A||IIF|
|NAVSTAR 73 (USA 260)||B5||March 25, 2015||71||26th||40534||2015-013A||IIF|
|NAVSTAR 74 (USA 262)||C3||15th July 2015||72||08||40730||2015-033A||IIF|
|NAVSTAR 75 (USA 265)||E2||October 31, 2015||73||10||41019||2015-062A||IIF|
|NAVSTAR 76 (USA 266)||F1||5th February 2016||70||32||41328||2016-007A||IIF|
|NAVSTAR 77 (USA 289)||A6||23 December 2018||74||04||43873||2018-109A||III|
|NAVSTAR 78 (USA 293)||D6||22nd August 2019||75||18th||44506||2019-056A||III|
Satellites not yet active
The following GPS satellites have been started, but are still being transferred or tested. (As of June 30, 2020)
( AFSC )
|NAVSTAR 79 (USA 304)||E4||June 30, 2020||76||45854||2020-041A||III|
Overview of the GPS satellite models
- No satellite of this series is active anymore.
- Manufacturer: Rockwell
- Orbits: circular at 20,200 km altitude with 63 ° inclination .
GPS II / IIA
- Manufacturer: Rockwell
- Orbits: circular at 20,200 km altitude with 55 ° inclination.
- Mass: 2032 kg
- Dimensions: 152 cm × 193 cm × 191 cm
- Electrical power: 1.136 kW
- Estimated service life: designed for 6 to 7.5 years, average actual service life: 10 years, longest service life: 16 years.
- Transponder: 2 × L-band , 1 × S-band
- Cost: $ 40 million
- Manufacturer: Lockheed Martin
- Payload: 2 Cs atomic clocks, 2 Rb atomic clocks
- Distribution: 21 manufactured, 13 started, 11 are in use, the remaining 8 have been converted to GPS IIR-M.
- Based on: Lockheed-Martins AS 4000 satellite bus
- Orbits: circular at 20,200 km altitude with 55 ° inclination.
- Launch of Navstar 57 (other names: USA 183, GPS IIR-M1, GPS IIR-14M): Sept 25, 2005
- Last start: August 17th, 2009
- Mass: 2060 kg
- Estimated service life: 13 years
- Cost: 60 million euros
- Manufacturer: Lockheed Martin
- Distribution: 8 converted from GPS IIR, all 8 started
- Signal: L2C (second civil signal on L2); L2M (another military signal, from 2008). Probably L5 test signal from 2008
- Payload: 3 Rb atomic clocks; Transmitting power adjustable.
- Based on: Lockheed-Martins AS 4000 satellite bus
- Orbits: circular at 20,200 km altitude with 55 ° inclination.
- Start: first start initially planned for 2002, then 2007, through 2009, finally on May 28, 2010.
- Signal: L5 (third civil signal)
- Cost: 121 million US dollars
- Payload: 2 Cs atomic clocks, 1 Rb atomic clock;
- Manufacturer: Boeing
- Distribution: 12
- Orbits: circular at 20,200 km altitude with 55 ° inclination.
- Manufacturer: Lockheed Martin
- First launch: December 23, 2018 with Falcon 9 , commissioning expected in 2020
- Second start: August 22, 2019 with the last Delta IV Medium
- Distribution (planned): 10 satellites
- Orbits: circular at 20,200 km altitude with 55 ° inclination.
- Manufacturer: Lockheed Martin
- First launch (planned): 2026
- Distribution (planned): 22 satellites
There are two classes of service:
Standard Positioning Service (SPS) is available to anyone and reached a precision (Engl. Accuracy ) of about 15 m horizontally (in 95% of measurements). After constant improvements, especially through the successive replacement of older satellites with successor models, an accuracy of 7.8 m (in 95% of the measurements) or 4 m RMS ( root mean square, standard deviation ) is currently guaranteed . However, this accuracy only applies to the emitted signal in space and does not describe any 2D or 3D errors. In addition, there are receiver and environmental errors such as receiver noise, tropospheric errors, software errors, multipath signals, etc.
In May 2000, an artificial inaccuracy was switched off by the US military; before that the accuracy was 100 m. With the fourth expansion stage, an artificial deterioration (selective availability) is to be achieved in crisis or war zones by local interference with reception.
- Precise Positioning Service (PPS) is reserved for military use and is designed for an accuracy of the signal in space of 5.9 m (in 95% of the measurements) or 3 m RMS. These signals are transmitted in encrypted form.
The accuracy (0.01–5 m) can be increased by using DGPS ( differential GPS ).
GPS uses its own continuous atomic time scale , which coincided with UTC when GPS was introduced in 1980 , but does not take leap seconds into account. Since the introduction of the last leap second in December 2016, the difference between the two times has been 18 seconds (UTC + 18 seconds = GPS time). The current value of this difference is transmitted in the system's user data signal.
There are two ways to get a position using GPS:
- Code: This procedure enables a fairly robust position determination with an accuracy of less than 10 m. All inexpensive recipients use this procedure. Accuracies of less than one meter are possible using DGPS.
- Code + carrier phase: Under good reception conditions and with precise receivers, an accuracy of less than 5 m is possible with this method. The increase in accuracy is due not only to the lower noise of the carrier phase measurement, but also to the use of the second frequency for the ionosphere measurement . If the millimeter range is to be achieved, this has so far only been possible in DGPS operation, because the local effects of the troposphere have to be taken into account.
In vehicles, odometry data such as speed and acceleration as well as direction data (e.g. differential odometer, yaw rate sensor ) can be used to determine the position more precisely or even in dead spots such as B. tunneling to determine a position. Since this data can only be measured by the sensors implemented in the vehicle electronics and transmitted to the navigation system, this higher level of precision can currently only be achieved with permanently installed navigation systems.
The time shown by the atomic clocks on the GPS satellites is subject to the effects of relativistic time dilation . According to the general theory of relativity, the speed of a clock depends on the location in the gravitational field and, according to the special theory, also on its speed. The lower gravitational potential in the satellite orbit makes time pass faster, the orbital movement of the satellites relative to a stationary observer on earth delays it. At an altitude of approx. 3,000 km both effects cancel each other out, in the GPS satellite orbit the gravitational effect outweighs more than six times. Time passes faster on the satellite than it does on a clock on the ground. The relative time difference (Δ t / t ) to a terrestrial clock is only 4.4 · 10 −10 , but it is significantly greater than the relative precision of cesium atomic clocks, which are better than 10 −13 .
In the graphic, the reference altitude is in the center of the earth, the surface of the earth is accordingly at 6370 km. The ordinate is the time dilation based on an earth second. The upper curve provides information on how many seconds time passes faster at high altitude and under low gravity. The time delay caused by the orbital movement of a satellite follows from the lower curve. The sum of both effects leads to the middle curve.
Due to the relative movement between the receiver (rotation of the earth) and the satellite (orbital movement), the signals are subject to the relativistic Doppler effect . At a carrier frequency of 1.5 GHz, the signal varies by ± 5 kHz. The time and frequency accuracy of the satellite atomic clocks of better than 10 −12 is sufficient to recognize movements of the receiver in the order of magnitude of 1 m / s. It is often erroneously pointed out that these path differences would lead to a positioning error of several kilometers per day if they were not corrected. Such an error would only occur if the position was determined by determining the distances between the GPS receiver and three satellites using a clock comparison with a clock in the receiver. In this case, each of these distance determinations would accumulate an error of approximately 12 km per day. Ordinary GPS receivers are not equipped with an atomic clock; instead, the precise time at the receiving location is also determined from the C / A code of the received satellites. For this reason, at least four satellites are required for a 3D position determination (four transit time signals for determining four parameters, namely three spatial parameters and the time). Because all satellites are exposed to the same relativistic effects, this results in a negligible error in determining the position, because this error only affects the time difference.
So that the satellite signals of the GPS can also be used as a time standard in addition to determining the position, the relativistic path difference of the clocks is compensated. For this purpose, the oscillation frequency of the satellite clocks is detuned to 10.229999995453 MHz, so that, despite the relativistic effects, a synchronous rate with an earthly clock with 10.23 MHz is guaranteed. Other relativistic effects, such as the Sagnac effect , are so small that they do not have to be taken into account separately for stationary recipients.
Under Selective Availability ( SA ) to dt. About "selectable Availability" is the addition of pseudo-random noise understood to the signals for the position determination. Before this accuracy-falsifying measure was switched off on May 2, 2000, it was intended to prevent guided weapon systems that were to be used outside the US military from being equipped with a freely available GPS receiver for guidance. Before the cut-off date, the accuracy of civilian GPS devices was around 100 meters or worse, after that it was 10 to 15 meters.
Differential GPS (DGPS, also dGPS) is a collective term for processes that use correction data in addition to the GPS signal in order to increase accuracy. The correction data are i. d. Usually from another GPS receiver, the reference station , whose exact position is known. The errors in the position determination of nearby receivers that occur at a certain point in time are almost identical, so that they fall out of the difference .
The standard format for GPS data is the RINEX format, a standard and format definition that is intended to enable the free exchange of raw GPS data. The RTCM format is important for the exchange of GPS data in real-time applications .
In addition to these basic formats, the GPS devices from different manufacturers often save the GPS results ( routes , track logs and waypoints ) in their own proprietary file formats. The gpx format and Google Earth's own kml format are available as general exchange formats . The free software GPSBabel enables conversion between different formats .
To disrupt the system, there is the possibility of jamming (jammer = English for jamming transmitter ), see GPS jammer and GPS spoofing . However, for political reasons, the US could distort the GPS signal or switch off the signal for an indefinite period in some areas of the world.
GPS and data protection
The location of the wearer of a GPS receiver cannot be tracked because receivers work passively and do not send any signals. A combination of a passive GPS receiver with an active transmitter is required for GPS monitoring, e.g. B. a cellular module that forwards the determined position data to third parties. Such combination devices are often incorrectly referred to as GPS transmitters .
GPS is used by the German police for investigations. It is used to monitor certain vehicles and drivers. In April 2005 the Federal Constitutional Court ruled that the use of the satellite-based system for surveillance in criminal investigations does not violate the Basic Law. The Second Senate rejected by this judgment a constitutional challenge of an ex-member of the Anti-imperialist cell (AIZ) back, which had objected to a two and a half month long monitoring of his vehicle and its various users had intervened in an exaggerated manner in fundamental rights under surveillance.
On June 4, 2013, the Federal Court of Justice ruled that the covert surveillance of a vehicle by means of a GPS receiver by a private detective agency is to be regarded as a criminal offense against the BDSG . An exception to this principle can only be considered if there is a strong legitimate interest in this data collection, for example in situations similar to self-defense.
GPS in practice
The use of GPS devices has increased considerably in recent years due to the inexpensive technology. A widespread area of application is the fleet management of transport companies and the transport system on land and on water / sea. If the vehicles are equipped with GPS and a transponder , the control center has an overview of the location of the vehicles at all times.
Commercially available civil GPS devices are suitable for use in cars and in the "outdoor" area. Commercially available GPS receivers ( GPS mice ) mostly use the NMEA 0183 data format to output position data.
Most devices can be set to various output formats such as UTM , MGRS , geographical coordinates in degrees, minutes, seconds and others. For the transmission of numerical coordinates on and for determining of topographic maps a is schedule pointer to the same scale as the map required.
In 2006, Alessandro Cerruti from Cornell University in America discovered that GPS can be disrupted by solar flares . In the past few years these - and the associated geomagnetic storms - were not very pronounced.
The GPS reception can also be disturbed by heavy snowfalls. Other weather conditions, such as rain and fog, do not normally affect reception - however, reception under rain-soaked leaves in the forest is significantly worse than in dry weather.
In scientific use
GPS technology is used in science to measure the surface of the earth. For example, a study by Michael Bevis and colleagues in 2019 caused a stir , in which it was shown that the Greenland ice sheet is melting faster and thus contributing to a more rapid rise in sea levels than previous calculations had shown; the authors attributed this in particular to the overheating of the earth's climate system , which is causing the surface mass of Greenland to melt towards the southwest - an effect that has hardly been taken into account in previous calculations. A complete melting of the Greenland ice would raise the sea level by about seven meters. Without the use of GPS technology, the speed of the ice melt was still significantly underestimated.
In business, security and medical use
Possible uses in the business, security and medical environment are, for example:
- Trace and tracking to determine and save routes and their time as for an electronic logbook.
- Localization of the locations of employees, products or persons in need of protection such as children, the sick and the elderly.
- Geofencing for tracking locations and events in real time, as well as for personal and vehicle protection when transporting valuables.
- automatic control, monitoring and recording of agricultural implements when cultivating large areas, with many combine harvesters and similar vehicles being equipped with this technology today.
- The modern versions of the electronic ankle cuffs are also equipped with GPS.
For sports competitions , GPS control of every competitor (similar to the ChampionChip system based on transponder technology ) is basically technically possible, but widespread use in classic competition formats ( mass sports event ) is still a long way off. On May 1, 2010, the Dresden 100km Duathlon was the first popular sports event to be recorded completely and system-identical with GPS. In the case of exotic sports such as geocaching , kite surfing , paragliding and gliding, on the other hand, GPS monitoring is already carried out nowadays.
GPS-based competition monitoring offers advantages such as:
- Control function: route conformity (do the athletes shorten the specified competition route?) This advantage is particularly relevant for the organizer of the competition.
- Experience value : Traceability of the competition in detail, creates added value for the sports event.
- Live transmission : The prerequisite for this is the direct transmission of the geodata and the presentation of the competition. This z. B. can be reached via the Internet to a broad public.
Hiking, ski touring and mountaineering
In contrast to compasses, GPS devices enable you to determine your position even when the visibility conditions are poor and the terrain has no distinctive features. However, they are problematic when mountaineering and on ski tours , because good visibility is often indispensable for assessing and mastering a pathless, technically difficult terrain. The characteristics of the terrain are only roughly entered on the maps - whether on paper or on the GPS device. For example, crevasses , bergschrunds and ravines on the edge of a glacier change year after year, so even GPS tracks from previous tours do not provide reliable assistance in choosing a route. For this reason, you can only be out and about at night, in fog, in heavy rain or snowfall when there are no threats or when orientation is otherwise guaranteed, e.g. B. through a continuous, clearly visible path.
The greatest beneficiary of GPS is civil aviation. All modern navigation systems are GPS-supported, but systems in the form of VOR or NDB receivers and inertial navigation are still common , especially in commercial aviation ; GPS generally only has a supporting function here.
Theoretically, subject to approval, the accuracies (P / Y signal) even allow automatic landings, provided that the runway center lines have been precisely measured beforehand, i.e. H. the coordinates are known and DGPS is also used. Some unmanned aerial vehicles , such as EuroHawk, use this method. It is currently (end of 2008) partially approved in commercial aviation. Whether an approach is only permitted with GPS as a navigation system depends on the visibility conditions, the system used (GPS, DGPS) and the equipment of the aircraft and runway. The United States is playing a pioneering role here, but GPS-based approaches are also spreading more and more in Europe.
GPS receivers are particularly popular in small aircraft such as gliders or microlight aircraft that do not have radio navigation receivers. Since the navigational support enables the pilot to concentrate more on guiding the aircraft, this also increases safety. Navigation using GPS alone is not permitted, however, so that a failure of the system does not lead to dangerous situations such as lack of fuel due to loss of orientation or entry into cleared airspaces .
As with the use in motor vehicles, there are both permanently installed systems and retrofitted devices. In particular, the use of PDAs with connected GPS mice is increasing sharply in the leisure sector, since a high-performance navigation system is available with little effort and expense.
In the car
Here is GPS devices with extensive maps - and map - software feature. They usually allow acoustic directions to the driver who, for example, only indicate the destination such as the destination at the beginning of the journey. B. Enter street name and place. In the case of fixed installations ex works (see infotainment system ), a distinction is made between systems that combine voice output with directional information on an LCD (usually in the car radio slot), as well as voice output with colored map display, in which the driver can better see where he is on the road.
Recently, PDA , smartphone , and mobile navigation systems have grown rapidly. They can be used quickly and flexibly in different vehicles. Usually the route guidance is shown graphically on a color screen with touchscreen .
With most of the fixed installations ex works as well as the latest PDA and PNA solutions, traffic reports from the TMC system , according to which the driver should be automatically directed past traffic jams or obstructions, are taken into account.
Fixed systems are usually considerably more expensive than mobile devices in the form of e.g. B. PDAs, however, have the advantage that they are coupled with the vehicle electronics and also use odometry data such as speed and acceleration to determine the position more precisely and also in dead spots such as B. tunneling to determine a position.
The advantage of the rapidly increasing navigation in cars is that the driver can concentrate fully on the traffic. In theory, fuel consumption can be reduced by 1–3% if all drivers choose the optimal route.
GPS can be used to prevent theft . For this purpose, the GPS system z. B. the vehicle combined with a GSM module . In the event of a vehicle theft, the device then sends the exact coordinates to a service provider. In connection with a PC z. B. The corresponding street and location can be read immediately via the Internet and the police can be alerted.
However, the big difference in comparable systems today is less the technology than the respective navigation program and the data it uses . There are currently still differences in the routing from program to program.
GPS devices are suitable for use on bicycles , when hiking (for example as a compact device on the wrist) or on the plane . The range of functions of the commercially available devices depends on the area of application and price. Even simple devices can now not only the lengths - and latitudes show, but also make directional information, calculate distances and the current speed state. The display can be set to output a direction symbol that points in the direction specified by the user by entering the destination coordinates ( waypoint ). GPS devices represent a further development of the classic navigation with compass and map. This function is required for geocaching . High-quality, modern devices can save waypoints, routes and track logs as well as digital maps and thus display the current location on a map. For the outside area, topographic maps are available for various countries on a scale of 1: 25,000 for use with the GPS.
Although the outdoor -GPS devices are not intended for primary, even small bracelet devices in cars or on the train (window seat, possibly in interchange ) can be used; however, indoor reception is usually not possible with these devices.
GPS receivers are used in photography, similar to devices for outdoor use . When recording, the current coordinates ( geo-imaging , geotagging, georeferencing) are incorporated into the Exif data of the image and saved with the image.
Some GPS receivers support the determination and storage of the orientation (direction of view of the camera at the time of recording). However, this does not always make sense, as it is possible to mount the GPS receiver on the camera's lanyard instead of on the hot shoe, for example if this is used for the flash. This means that there is no reliable indication of the direction.
Impairments to GPS reception when the view of the sky is not sufficiently clear, place considerable limits on the accuracy of GPS in photography, depending on buildings, trees, etc. The fact that many GPS receivers continue to use the last known position in case of doubt means that you must be aware of these boundary conditions and, if necessary, correct the EXIF data on your PC afterwards.
A wide range of GPS devices is tailored to the special requirements of navigation in seafaring. Today, GPS is part of the basic equipment of a ship, mostly as a chart plotter , in which the ship's location determined via GPS is displayed in real time on an electronic nautical chart . Mobile GPS receivers have been around since the 1980s. A navigation program and a GPS mouse can be used to navigate on a PC, notebook or PDA ; Most cell phones today are GPS enabled. Integrated electronic information, navigation and ship control systems ( ECDIS ) are used in large shipping . The devices intended for sea navigation usually have a map display ("moving map") with special, electronic nautical charts in encrypted formats. OpenSeaMap uses a free format. Many of the devices are built waterproof; More sophisticated ones allow the combined display of the nautical charts with other data such as weather maps or radar displays. With the automatic identification system (AIS), the GPS serves not only to determine the position, but also as a time base for coordinating the transmission sequence.
In buildings, GPS reception is generally reduced or even impossible. In a specific case, it depends on the building materials used in the building and their damping behavior on the location within a building. In the vicinity of a window or in rooms with large windows and a clear view of the sky, location determination with reduced accuracy may still be possible, depending on the current satellite position. GPS reception is practically always impossible in shaded rooms such as basements.
With newer receiver chipsets from SiRF ( e.g. SiRF Star III) or u-blox (e.g. u-blox-5), GPS reception is possible in some situations, such as in buildings, using correlation receivers that are massively parallelized in hardware . Instead of trying out the correlations of the code sequences ( CDMA ) one after the other as with conventional GPS receivers and only being able to specify one reception path, 204,800 correlation receivers (SiRF Star III) are used in parallel with these chipsets and evaluated at the same time. This means that multipath reception can be reduced, and in combination with an increased input sensitivity of the HF input part, the GPS radio signals reflected on walls or floors can, under certain circumstances, still be evaluated inside buildings or narrow streets in densely built-up areas. However, the indirect reception of GPS signals via reflections is associated with a reduction in accuracy, since the signal then has a longer transit time and the exact time references no longer match. The additional error about multipath reception can be several tens of meters.
In investigations against suspected criminals
The use of GPS in criminal investigations in Germany is legal. On September 2, 2010, the European Court of Human Rights (ECHR) dismissed the action brought by a former member of the left-wing extremist “ anti-imperialist cells ” (AIZ). The ECHR has thus confirmed the assessment of the Federal Constitutional Court, which ruled on April 12, 2005 (2 BvR 581/01) and rejected Bernhard Uzun's complaint .
In its judgment, the ECHR indicated that the surveillance should prevent further bomb attacks. "It served the interests of national and public security , the prevention of crimes and the protection of the rights of the victims."
In vehicle tracking, hidden GPS tracking devices are used by both authorities and private investigators. These tracking devices are very small and are magnetically attached to the underbody of the vehicle in a few seconds. They work for weeks without an external power source. The location data is either transmitted live by radio or recorded.
- GLONASS , Russia
- Galileo , European Union
- Beidou , China (in operation for the Asian area since 2004, a worldwide network is being set up)
- Indian Regional Navigation Satellite System , India (under construction; covers India only)
- Quasi-Zenit satellite system , Japan (under construction for regional coverage)
- Automatic Packet Reporting System (APRS) - u. a. GPS position data transmission in the amateur radio service
- Geodetic datum - underlying ellipsoidal models of the earth, for example WGS84
- GPS leveling - geoid determination by combining GPS and classic leveling
- GpsDrive - free navigation software under Linux
- Navit - free navigation software for a number of different operating systems
- List of navigation satellites
- Live tracking
- Receiver Autonomous Integrity Monitoring (RAIM) - a technology for checking the integrity of GPS
- Elliott D. Kaplan (Ed.): Understanding GPS. Principles and Applications. Artech House, Boston 1996, ISBN 0-89006-793-7 .
- Günter Seeber: Satellite Geodesy. 2nd Edition. De Gruyter, Berlin 2003, ISBN 3-11-017549-5 .
- Guochang Xu: GPS. Theory, Algorithms and Applications. Springer, Berlin 2003, ISBN 3-540-67812-3 .
- Rainer Höh: GPS outdoor navigation. Reise-Know-How-Verlag Rump, Bielefeld 2005, ISBN 3-8317-1116-X .
- Ralf Schönfeld: The GPS manual. Monsenstein and Vannerdat, 2005, ISBN 3-86582-234-7 (two volumes, volume 1: basics, basic functions, navigation and orientation, maps. )
- Jean-Marie Zogg: GPS and GNSS: Basics of positioning and navigation with satellites. u-blox, Thalwil 2009 (online publication, PDF, 8 MB)
- Uli Benker: GPS. Practical book and guide for GPS navigation on outdoor tours. Bruckmann, Munich 2009, ISBN 978-3-7654-5110-2 .
- Manfred Bauer: Surveying and positioning with satellites. 6th edition. Wichmann, Berlin 2011, ISBN 978-3-87907-482-2 .
- Martin Asbeck, Stefan Drüppel, Klaus Skindelies, Markus Stein: Surveying and Geoinformation . Specialist book for surveyors and geomatists. Ed .: Michael Gärtner. Gärtner, Solingen 2012, ISBN 978-3-00-038273-4 , p. 111-123 .
- GPS Standard Positioning Service Performance Standard. (PDF; 2.05 MB) Department of Defense (USA), October 15, 2001, accessed on May 1, 2011 .
- GPS Standard Positioning Service Performance Standard. (PDF; 1.63 MB) Department of Defense (USA), October 1, 2008, accessed on May 1, 2011 (English).
- GPS General Information US Coast Guard. (English)
- Example data sets, C code (English)
- GPS navigation system. Gunter's Space Page (English)
- Spiegel article with a concise description of the simple interference with GPS
- Global Positioning System fully operational. In: uscg.gov , material from United States Air Force . July 17, 1995, accessed July 16, 2019 .
- Carina Homrighausen: The GPS system. A theoretical approach and approaches for application in physics lessons. (PDF, 4MB) 2008, p. 27 , accessed on August 6, 2019 (Master's thesis at Bielefeld University).
- defense.gov DOD Announces Start of Civil Navigation Message Broadcasting April 25, 2014 ( Memento from April 27, 2014 in the Internet Archive )
- IS-GPS-200 Official website of the GPS PUBLIC INTERFACE CONTROL WORKING GROUP with the reference documentation IS-GPS-200 in the current version.
- Totally dependent. In: aargauerzeitung.ch. August 13, 2015, accessed August 13, 2015 .
- Global Positioning System. In: decodesystems.com. Decode Systems, accessed January 13, 2017.
- GPS history from 1973 In: kowoma.de.
- Ron White, Tim Downs: How Global Positioning Systems Work. In: pcmag.com. July 8, 2008, accessed January 13, 2017.
- Gunter Krebs: GPS-2A (Navstar-2A). In: skyrocket.de. Gunter's Space Page, March 8, 2012, accessed December 28, 2012 .
- Gunter Krebs: GPS-2F (Navstar-2F). In: skyrocket.de. Gunter's Space Page, December 10, 2012, accessed December 28, 2012 .
- Data From the First Week Without Selective Availability. National Coordination Office for Space-Based Positioning, Navigation, and Timing, February 17, 2012, accessed December 28, 2012 .
- Justin Ray: First-of-its-kind satellite for GPS launched into space. Spaceflight Now, May 28, 2010, accessed May 28, 2010 .
- Jane's Defense Weekly , May 21, 2008, p. 10.
- US Air Force Awards Lockheed Martin Team $ 1.4 Billion Contract To Build GPS III Space System. (No longer available online.) Lockheed Martin, May 15, 2008, archived from the original on January 17, 2012 ; accessed on December 28, 2012 (English).
- Gunter Krebs: GPS-3 (Navstar-3). In: skyrocket.de. Gunter's Space Page, April 22, 2012, accessed December 28, 2012 .
- PLC Performance Standard. Retrieved January 8, 2019 .
- US Naval Observatory: GPS CONSTELLATION STATUS. Retrieved December 30, 2018 .
- US Naval Observatory: BLOCK II SATELLITE INFORMATION. Retrieved December 30, 2018 .
- US Coast Guard: GPS CONSTELLATION STATUS. Retrieved July 7, 2020 .
- Gunter Krebs: GPS-2R (Navstar-2R). In: skyrocket.de. Gunter's Space Page, April 22, 2012, accessed December 28, 2012 .
- Justin Ray: Bittersweet launch ends several chapters of history. Spaceflight Now, August 17, 2009, accessed December 28, 2012 .
- Gunter Krebs: GPS-2RM (Navstar-2RM). In: skyrocket.de. Gunter's Space Page, April 22, 2012, accessed December 28, 2012 .
- SpaceX closes out year with successful GPS satellite launch. December 23, 2018, accessed December 28, 2018 .
- GPS-3 (Navstar-3) on Gunter's Space Page
- AF Announces selection of GPS III follow-on contract . Secretary of the Air Force Public Affairs, Sept. 14, 2018.
- GPS SPS Performance DOD 09/2008, p. 22 (PDF; 1.7 MB).
- GPS PPS Performance DOD 02/2007, p. 22 (PDF; 1.9 MB).
- J.-F. Pascual-Sánches: Introducing relativity in global navigation satellite systems . In: Annals of Physics . tape 16 , no. 4 . Wiley-VCH, 2007, ISSN 0003-3804 , p. 258–273 , doi : 10.1002 / andp.200610229 (English).
- Martin Asbeck, Stefan Drüppel, Klaus Skindelies, Markus Stein: Surveying and Geoinformation . Specialist book for surveyors and geomatists. Ed .: Michael Gärtner. Gärtner, Solingen 2012, ISBN 978-3-00-038273-4 , p. 114-115 .
- Selective Availability. In: GPS.gov. Retrieved January 13, 2017.
- Federal Court of Justice: Monitoring people using GPS receivers attached to vehicles is generally a criminal offense. Press release of the Federal Court of Justice No. 96/13. In: juris.bundesgerichtshof.de. The Federal Court of Justice, June 4, 2013, accessed on June 4, 2013 .
- Bevis, M. et al. (2019). Accelerating changes in ice mass within Greenland, and the ice sheet's sensitivity to atmospheric forcing. Proceedings of the National Academy of Sciences . https://doi.org/10.1073/pnas.1806562116
- GPS-RaceMap 2010. (No longer available online.) In: 100km-duathlon.de. Association for Endurance Sports Dresden e. V., archived from the original on April 18, 2012 ; Retrieved December 28, 2012 .
- Electronic cow bells in Tyrol and Bavaria in the orf.at test , July 14, 2018, accessed on July 14, 2018.
- commons: Commons: Georeferencing There are also georeferenced photos on Wikimedia Commons.
- Principles on the judgment of the Second Senate of April 12, 2005 - 2 BvR 581/01 - ( Memento of January 12, 2012 in the Internet Archive )
- European judges approve secret GPS surveillance. In: spiegel.de. Spiegel Online, September 2, 2010, accessed December 28, 2012 .