The position calculated by a GPS receiver relies on three accurate measurements: the current time, the position of the satellite, and the time delay for the signal. Errors in the clock signal can be reduced using the method above, meaning that the overall accuracy of the system is generally based on the accuracy of the position and delay.
The measurement of the delay requires the receiver to “lock onto” the same sequence of bits being sent from the satellite. This can be made relatively accurate by timing comparing the rising or trailing edges of the bits. Modern electronics can lock the two signals to about 1% of a bit time, or in this case about 1% of a microsecond. Since light travels at 299,792,458 m/s, this represents an error of about 3 meters (10 ft), the minimum error possible given the timing of the C/A signal.
This can be improved by using the higher-speed P(Y) signal, assuming the same 1% accuracy in locking the retrieved P-code to the internally generated version. In this case the same calculation results in an accuracy of about 30 centimeters (1 ft). Since the P-code repeats at 10.23 MHz, it has a “repeat range” of about 30 kilometers (20 mi). This explains the terminology; when using the P-code, it was first necessary to calculate a coarse position with the C/A code in order to determine how to line up the P-code with the internally generated copy.
However, several “real world” effects intrude and degrade the accuracy of the system. These are outlined in the table below, with descriptions following. When all of these effects are added up, GPS is typically accurate to about 15 meters (50 ft). These effects also overwhelm the P(Y) code’s added accuracy.
Sources of error
|Ionospheric effects||± 5 meter|
|Ephemeris errors||± 2.5 meter|
|Satellite clock errors||± 2 meter|
|Multipath distortion||± 1 meter|
|Tropospheric effects||± 0.5 meter|
|Numerical errors||± 1 meter or less|
One of the biggest problems for GPS accuracy is that changing atmospheric conditions change the speed of the GPS signals unpredictably as they pass through the ionosphere. The effect is minimized when the satellite is directly overhead and becomes greater toward the horizon, since the satellite signals must travel through the greater “thickness” of the ionosphere as the angle increases. Once the receiver’s rough location is known, an internal mathematical model can be used to estimate and correct for the error.
Because ionospheric delay affects the speed of radio waves differently based on their frequencies, the second frequency band (L2) can be used to help eliminate this type of error. Some military and expensive survey-grade civilian receivers can compare the difference between the P(Y) signal carried in the L1 and L2 frequencies to measure atmospheric delay and apply precise corrections. This correction can be applied even without decrypting the P(Y) signal, as long as the encryption key is the same on both channels. In order to make this easier, the military is considering broadcasting the C/A signal on L2 starting with the Block III-R satellites. This would allow a direct comparison of the L1 and L2 signals using the same circuitry that already decodes the C/A on L1.
The effects of the ionosphere are generally slow-moving and can easily be tracked. The effects for any particular geographical area can be easily calculated by comparing the GPS-measured position to a known surveyed location. This correction, say, “10 meters to the east” is also valid for other receivers in the same general location. Several systems send this information over radio or other links to the receivers, allowing them to make better corrections that a comparison of L1 and L2 alone could.
The amount of humidity in the air also has a delaying effect on the signal, resulting in errors similar to those generated in the ionosphere but located much closer to the ground in the troposphere. The areas affected by these problems tend to be smaller in area and faster moving than the billows in the ionosphere, making accurate correction for these effects more difficult.
GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. This delay in reaching the receiver causes inaccuracy. A variety of receiver techniques, most notably narrow correlator spacing, have been developed to mitigate multipath errors. For long delay multipath, the receiver itself can recognize the wayward signal and discard it. To address shorter delay multipath from the signal reflecting off the ground, specialized antennas may be used. This form of multipath is harder to filter out since it is only slightly delayed as compared to the direct signal, causing effects almost indistinguishable from routine fluctuations in atmospheric delay.
Multipath effects are much less severe in dynamic applications such as cars and planes. When the GPS antenna is moving, the false solutions using reflected signals quickly fail to converge and only the direct signals result in stable solutions.
Ephemeris and clock errors
The navigation message from a satellite is sent out only every 12.5 minutes. In reality, the data contained in these messages tends to be “out of date” by an even larger amount. Consider the case when a GPS satellite is boosted back into a proper orbit; for some time following the maneuver, the receiver’s calculation of the satellite’s position will be incorrect until it receives another ephemeris update. Additionally, the amount of accuracy sent in the ephemeris is limited by the bandwidth; using the data from the satellites alone limits its accuracy.
Further, while it is true that the onboard clocks are extremely accurate, they do suffer from clock drift. This problem tends to be very small, but may add up to 2 meters (6 ft) of inaccuracy.
These sorts of errors are even more “stable” than ionospheric problems and tend to change on the order of days or weeks, as opposed to minutes. This makes correcting for these errors fairly simple by sending out a more accurate almanac on a separate channel.
Techniques to improve accuracy
The accuracy of GPS can be improved several ways:
Differential GPS (DGPS) can improve the normal GPS accuracy of 4-20 meters (13-65 ft) to 1-3 meters (3-10 ft). DGPS uses a network of stationary GPS receivers to calculate the difference between their actual known position and the position as calculated by their received GPS signal. The “difference” is broadcast as a local FM signal, allowing many civilian GPS receivers to “fix” the signal for greatly improved accuracy. The US Coast Guard maintains a similar system on marine longwave radio near ports and major waterways, supplemented by additional sites in Canada.
The Wide Area Augmentation System (WAAS). This system uses a series of ground reference stations to calculate GPS correction messages, which are uploaded to a series of additional satellites in geosynchronous orbit for transmission to GPS receivers, including information on ionospheric delays and individual satellite clock drift. Although only a few WAAS satellites are currently available as of 2004, it is hoped that eventually WAAS will provide sufficient reliability and accuracy that it can be used for critical applications such as GPS-based instrument approaches in aviation (landing an airplane in conditions of little or no visibility). The current WAAS only works for North America (where the reference stations are located), and because of the satellite location, the system is only generally usable in the eastern and western coastal regions. However, variants of the WAAS are being developed in Europe (EGNOS, the European Geostationary Navigation Overlay Service) and Japan (MSAS, the Multi-Functional Satellite Augmentation System), which are virtually identical to WAAS.
A Local Area Augmentation System (LAAS). This is similar to WAAS, in that similar correction data are used. But in this case, the correction data are transmitted from a local source, typically at an airport or another location where accurate positioning is needed. These correction data are typically useful for only about a thirty to fifty kilometer (20-50 mi) radius around the transmitter.
Exploitation of DGPS for Guidance Enhancement (EDGE) is an effort to integrate DGPS into precision guided munitions such as the Joint Direct Attack Munition (JDAM).
A Carrier-Phase Enhancement (CPGPS). This technique utilizes the 1.575 GHz L1 carrier wave to act as a sort of additional clock signal, resolving ambiguity caused by variations in the location of the pulse transition (logic 1-0 or 0-1) of the C/A PRN signal. The problem arises because the transition from 0-1 or 1-0 on the C/A signal is not instantaneous, it takes a non-zero amount of time, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. A successful correlation could be defined in a number of various places along the rising/falling edge of the pulse, which imparts timing errors. CPGPS solves this problem by using the L1 carrier, which has a period 1/1000 that of the C/A bit width, to define the transition point instead. The phase difference error in the normal GPS amounts to a 2-3 meter (6-10 ft) ambiguity. CPGPS working to within 1% of perfect transition matching can achieve 3 mm ambiguity; in reality, CPGPS coupled with DGPS normally realizes 20-30 centimeter (8-12 in) accuracy.
Wide Area GPS Enhancement (WAGE) is an attempt to improve GPS accuracy by providing more accurate satellite clock and ephemeris (orbital) data to specially-equipped receivers.
Relative Kinematic Positioning (RKP) is another approach for a precise GPS-based positioning system. In this approach, accurate determination of range signal can be resolved to an accuracy of less than 10 centimeters (4 in). This is done by resolving the number of cycles in which the signal is transmitted and received by the receiver. This can be accomplished 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).
- Many automobiles that use the GPS combine the GPS unit with a gyroscope and speedometer pickup, allowing the computer to maintain a continuous navigation solution by dead reckoning when buildings, terrain, or tunnels block the satellite signals. This is similar in principle to the combination of GPS and inertial navigation used in ships and aircraft, but less accurate and less expensive because it only fills in for short periods.
When it was first deployed, GPS included a feature called Selective Availability (SA) that introduced intentional errors of up to a hundred meters (300 ft) into the publicly available navigation signals, making it difficult to use for guiding long range missiles to precise targets. Additional accuracy was available in the signal, but in an encrypted form that was only available to the United States military, its allies and a few others, mostly government users.
SA typically added signal errors of up to about 10 meters (30 ft) horizontally and 30 meters (100 ft) vertically. The inaccuracy of the civilian signal was deliberately encoded so as not to change very quickly, for instance the entire eastern U.S. area might read 30 m off, but 30 m off everywhere and in the same direction. In order to improve the usefulness of GPS for civilian navigation, Differential GPS was used by many civilian GPS receivers to greatly improve accuracy.
During the Gulf War, the shortage of military GPS units and the wide availability of civilian ones among personnel resulted in a decision to disable Selective Availability. This was, perhaps, ironic, as SA had been introduced specifically for these situations, allowing friendly troops to use the signal for accurate navigation, while at the same time denying it to the enemy. But since SA was also denying the same accuracy to thousands of friendly troops, turning it off presented a clear benefit.
In the 1990s, the FAA started pressuring the military to turn off SA permanently. This would save the FAA millions of dollars every year in maintenance of their own radio navigation systems. The military resisted for most of the 1990s, but SA was eventually turned off in 2000 following an announcement by U.S. President Bill Clinton, allowing users access to an undegraded L1 signal.
The US military has developed the ability to locally deny GPS (and other navigation services) to hostile forces in a specific area of crisis without affecting the rest of the world or its own military systems. Such Navigation Warfare uses techniques such as local jamming to replace the blunt, world-wide degradation of civilian GPS service that SA represented.
Military (and selected civilian) users still enjoy some technical advantages which can give quicker satellite lock and increased accuracy. The increased accuracy comes mostly from being able to use both the L1 and L2 frequencies and thus better compensate for the varying signal delay in the ionosphere.
As of August 2006 the GPS system used a satellite constellation of 29 active Block II/IIA/IIR/IIR-M satellites (for the global coverage 24 is enough) in intermediate circular orbits. The constellation includes three spare satellites in orbit, in case of any failure. Each satellite circles the Earth twice each day at an altitude of 20,200 kilometers (12,600 miles). The orbits are aligned so at least four satellites are always within line of sight from almost any place on Earth. There are four active satellites in each of six orbital planes. Each orbit is inclined 55 degrees from the equatorial plane, and the right ascension of the ascending nodes is separated by sixty degrees.
The flight paths of the satellites are measured by five monitor stations around the world (Hawaii, Kwajalein, Ascension Island, Diego Garcia, Colorado Springs). The master control station, at Schriever Air Force Base, processes their combined observations and sends updates to the satellites through the stations at Ascension Island, Diego Garcia, and Kwajalein. The updates synchronize the atomic clocks on board each satellite to within one microsecond, and also adjust the ephemeris of the satellites’ internal orbital model to match the observations of the satellites from the ground.
Several frequencies make up the GPS electromagnetic spectrum:
L1 (1575.42 MHz):
Carries a publicly usable coarse-acquisition (C/A) code as well as an encrypted precision P(Y) code.
L2 (1227.60 MHz):
Usually carries only the P(Y) code, but will also carry a second C/A code on the Block III-R satellites.
- L3 (1381.05 MHz):
Carries the signal for the GPS constellation’s alternative role of detecting missile/rocket launches (supplementing Defense Support Program satellites), nuclear detonations, and other high-energy infrared events.
Two new signals are also being studied:
L4 (1841.40 MHz):
Being studied for additional ionospheric correction.
- L5 (1176.45 MHz):
Proposed for use as a civilian safety-of-life (SoL) signal. 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 2008.
A modern SiRF Star III chip based 20-channel GPS receiver with WAAS/EGNOS support.
GPS receivers vary widely in accuracy because of the expense of adding more radio receivers needed to tune in more satellites. For instance, early consumer-grade receivers typically included six to eight receivers for the L1 C/A signal. As the computer industry has improved the state of the art in chipmaking, the cost of implementing these receivers has fallen dramatically, and even low-cost hand held receivers typically have twelve receivers today. More expensive units, known as “dual-frequency receivers”, also tune in the L2 signals in order to correct for ionospheric delays.
Another major factor in the accuracy of a GPS fix is the amount of processing applied to the received signals. This is a function of the performance of the electronics and the required battery life. These factors have also been dramatically affected by improved chip making, allowing even low cost modern receivers to outperform much more expensive earlier models.
GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. This is typically in the form of a RS-232 port at 4,800 bps 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. The cost of implementing these receivers is also falling dramatically, and even low-cost units are commonly including WAAS receivers today.
Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol. NMEA 2000 is a newer and less widely adopted protocol. Both are proprietary and are controlled on a for-profit basis by the US-based National Marine Electronics Association. References to the NMEA protocols have been compiled from public records, allowing open source tools like gpsd to read the protocol without violating intellectual property laws. Other proprietary protocols exist as well, such as the SiRF protocol. Receivers can interface with external devices via a number of means, such as a serial connection, a USB connection or even a Bluetooth a wireless connection.
According to Einstein’s theory of relativity, because of their constant movement with respect to the Earth’s reference frame the clocks on the satellites are affected by both special and general relativity. According to the same theory, observing from the Earth’s reference frame, satellite clocks are perceived as running at a slightly faster rate than clocks on the Earth’s surface. This amounts to a discrepancy of around 38 microseconds per day, when observed from the Earth. To account for this, the frequency standard on-board the satellites runs slightly slower than its desired speed on Earth, at 10.22999999543 MHz instead of 10.23 MHz—a difference of 0.00457 Hz. This offset is claimed by relativity physicists to be a practical demonstration of the theory of relativity in a real-world system; they claim it to be exactly what has been predicted by the theory; however, even if true, this holds only within the limits of accuracy of measurements as affected by environmental effects.
Neil Ashby presented a controversial account of how these relativistic corrections are applied, and their orders of magnitude, in Physics Today (May 2002). Note that Einstein’s relativity is considered a mere correction to the Newtonian GPS theory. Namely, the relativistic corrections cancel out even in high-accuracy (millimetre) GPS positioning, which shows that they are an unnecessary mathematical complication altogether.
Thus in his book GPS Satellite Surveying, Alfred Leick writes (p.170): “In relative (mm) positioning, most of the relativistic effects cancel or become negligible.” This is because the relativity-predicted values, if real, would amount to less than one half of the normal environmental (insurmountable) geophysical noise. Therefore, geometrical differencing in precise positioning cancels out most of the relativistic effects; the GPS system can perform equally superb without SR or GR theories.
Two GPS developers have received the National Academy of Engineering Charles Stark Draper prize year 2003:
Ivan Getting, emeritus president of The Aerospace Corporation and engineer at the Massachusetts Institute of Technology, established the basis for GPS, improving on the World War II land-based radio system called LORAN (Long-range Radio Aid to Navigation).
- Bradford Parkinson, teacher of aeronautics and astronautics at Stanford University, developed the system.
One GPS developer, Roger L. Easton, received the National Medal of Technology on February 13, 2006 at the White House.
On February 10, 1993, the National Aeronautic Association selected the Global Positioning System Team as winners of the 1992 Robert J. Collier Trophy, the most prestigious aviation award in the United States. This team consists of researchers from the Naval Research Laboratory, the U.S. Air Force, the Aerospace Corporation, Rockwell International Corporation, and IBM Federal Systems Company. The citation accompanying the presentation of the trophy honors the GPS Team “for the most significant development for safe and efficient navigation and surveillance of air and spacecraft since the introduction of radio navigation 50 years ago.”
GPS Navigation System using TomTom software
A GPS tracking system uses GPS to determine the location of a vehicle, person, or pet and to record the position at regular intervals in order to create a track file or log of activities. The recorded data can be stored within the tracking unit, or it may be transmitted to a central location, or Internet-connected computer, using a cellular modem, 2-way radio, or satellite. This allows the data to be reported in real-time, using either web browser based tools or customized software.
Jamming of any radio navigation system, including satellite based navigation, is possible. The U.S. Air Force conducted GPS jamming exercises in 2003 and they also have GPS anti-spoofing capabilities. In 2002, a detailed description of how to build a short range GPS L1 C/A jammer was published in Phrack issue 60 by an anonymous author. There has also been at least one well-documented case of unintentional jamming, tracing back to a malfunctioning TV antenna preamplifier. If stronger signals were generated intentionally, they could potentially interfere with aviation GPS receivers within line of sight. According to John Ruley, of AVweb, “IFR pilots should have a fallback plan in case of a GPS malfunction”. Receiver Autonomous Integrity Monitoring (RAIM), a feature of some aviation and marine receivers, is designed to provide a warning to the user if jamming or another problem is detected. GPS signals can also be interfered with by natural geomagnetic storms, predominantly at high latitudes.
GPS jammers the size of a cigarette box are allegedly available from Russia; their effectiveness is in question following their use in the Iraq War. The U.S. government believes that such jammers were also used occasionally during the 2001 war in Afghanistan. Some officials believe that jammers could be used to attract the precision-guided munitions towards non-combatant infrastructure; other officials believe that the jammers are completely ineffective. In either case, the jammers may be attractive targets for anti-radiation missiles. Low power jammers would have limited military usefulness and high power jammers would be easy to locate and destroy. During the Iraq War, the U.S. military claimed to destroy a GPS jammer with a GPS-guided bomb.
Russia operates an independent system called GLONASS (GLObal NAvigation Satellite System), although with only twelve active satellites as of 2004, the system is of limited usefulness. Availability in Russia, Northern Europe and Canada is above 90%. Meaning that at least 4 satelites are visible 90% of time, which is not bad considering that GLONASS operate only 12 of 24 required satelites. There are plans to restore GLONASS to full operation by 2008 with India’s help. The European Union is developing Galileo as an alternative to USA owned operated GPS system. The People’s Republic of China, Israel, India, Morocco, Saudi Arabia and South Korea joined the EU in this project. It is planned to be in operation by 2010.