The Global Positioning System: A detailed analysis see the miracle of modern navigation
Global Positioning System (GPS) was originally designed jointly by the U.S. Navy and U.S. Air Force to allow determination of position and time for military troops and guided missiles. No However, GPS has become the basis for measuring the position and time for science laboratories and a wide range of applications in the multibillion-dollar business. Around one million receivers are manufactured each year and all the GPS market is expected to reach 10 billion U.S. dollars at the end of next year. The history of GPS and measurement principles are the subjects of this article.
The first navigation methods
The shape and size land is known since the days of old. The fact that the earth is a sphere was well known by educated people and in the fourth century BC. In his book on heavens, Aristotle gave two arguments scientifically correct. First, the Earth's shadow projected on the moon during a lunar eclipse appears to be bent. Second, rising stars as a change travel north or south, while some stars visible in Egypt can not be seen in Greece.
The actual radius of the earth was determined within one percent by Eratosthenes in about 230 BC. I knew the sun was overhead at noon at the summer solstice in Syene (Aswan, Egypt) since that day has illuminated the deep well water. At the same time, we measured the length of the shadow carried by a column based on the Library of Alexandria, which was almost north. The distance between Alexandria and Syene had been well established by professional drivers and camel caravans. Thus, Eratosthenes was able to calculate the radius land that the difference in latitude deduced from the measure. As modern units of length, arrived at a figure of about 6,400 km. In comparison, the average effective radius is 6,371 km (The Earth is not exactly spherical, and the polar radius is 21 km shorter than the equatorial radius of 6378 km).
The ability to determine its position on earth was the main problem at hand. In the second century AD Greek astronomer Ptolemy developed a geographic atlas, in which he found that the latitude and longitude of major cities of the Mediterranean. Ptolemy is the most famous, however, for his geocentric theory of planetary motion, which was the basis of astronomy catalogs until Nicolaus Copernicus published his heliocentric theory in 1543.
Historically, methods of navigation on the surface of the earth have focused on measuring the angular position of stars to determine latitude. The latitude of his position is equal to the height of Polaris. The position polar star on the celestial sphere is temporary, however, due to the precession of the axis of rotation of the earth through a radius of a circle of 23.5 in a period 26,000 years. By the time Julius Caesar, there were no stars close enough to the north celestial pole is called North Star. In 13,000 years Vega will star near post. There is perhaps no coincidence that the browsers do not venture far from Earth visible to the time of Christopher Columbus, when the true north can be determined using the star we now call the North Star. Even then, the daily rotation of the star caused an apparent variation of the compass. Polaris in 1492 described a radius of about 3.5 in the polar sky, compared with today. At sea, however, Columbus and his contemporaries s depended mainly compass and dead reckoning.
The determination of the length is much more difficult. Astronomical longitude is obtained from the difference between time observed a celestial event as an eclipse, and the corresponding time in tabular form for a point of reference. For every hour of time difference, the difference in length is 15 degrees.
Columbus himself attempted to estimate the length of his fourth voyage to the New World in the observation time of lunar eclipse seen from the port Santa Gloria, Jamaica, February 29, 1504. In his biography of the famous Admiral of the Ocean Sea Samuel Eliot Morrison says that Columbus measured the duration of the eclipse with a clock Sandy and determined its position in nine hours and fifteen minutes west of Cadiz, Spain, according to the time of the eclipse predicted an almanac in which he carried on board your boat. During the previous year, while his ship was abandoned in the harbor, Columbus had given the latitude of Santa Gloria by numerous observations of Polaris. He latitude and 18 who has committed an error of less than half a degree and was one of the best recorded observations of latitude in the early sixteenth century, but its length estimation moved about 38 degrees.
Columbus also made use of threatening to eclipse the legendary inhabitants of God's displeasure, as indicated by a signal heaven, if not taken in desperate need of men. When the eclipse came as expected, the Indians have demanded the intervention of Admiral, with the promise of providing all the food that is needed.
The new knowledge of the universe revealed by Galileo Galilei, in his book The Messenger stars. This book, published in Venice in 1610, reported the telescopic discoveries of hundreds of new stars, the craters on the moon, the phases of Venus, the rings of Saturn, sunspots, and the four inner satellites of Jupiter. Galileo suggested using eclipses of Jupiter's satellites as a celestial clock for the practical determination length, but the precise ephemeris calculation and the difficulty of observing satellites rolling deck of a ship prevent the use of this method to sea, however, James Bradley, third Astronomer Royal of England, successfully implemented the technique in 1726 to determine the length of Lisbon and New York with considerable precision.
The inability to measure longitude at sea have the potential catastrophic consequences for the vessels to explore the new world, the transport of goods and conquering new territories. The wrecks are common. On October 22, 1707, a fleet of twenty ships under the command of Admiral Sir Shovell was Clowdisley Returning to England after an unsuccessful attack on Toulon in the army of the Mediterranean. As the fleet approached the English Channel in thick fog, et trois autres flagship ont achoppé côtiers et sur les rochers près de deux mille hommes périrent.
Stunned by this unprecedented loss, the British government in 1714 offered a prize of £ 20,000 for a method for determining longitude at sea in the middle grades. The scientific community has determined that the solution would be obtained from observations of the moon. The German cartographer Tobias Mayer, helped by new mathematical methods developed by Leonard Euler, offered a draw on improving the moon 1757. The position of the moon appears at a time as seen from a reference meridian could be compared to its position at the local time to determine the angular position West or East.
Like the astronomical method seems to lead to achievement, the British architect John Harrison provided another solution with the invention of the marine chronometer. The history of Harrison's clock was told in the popular book by Dava Sobel, Longitude.
Both methods were tested in trials lunar mare tables for the determination of longitude within four minutes of arc, but over time the accuracy of Harrison was one minute of arc. Weekend account, parts of Awards went to Mayer's widow, Euler, and Harrison.
In the twentieth century with the development of radio transmitters, other kinds of aids to navigation has been created with terrestrial radio beacons, including Loran and Omega. Finally, artificial satellite technology makes navigation possible and line identification position by the light signals including measuring the Doppler effect, or the phase difference.
TRANSIT
Transit System marine navigation satellites, was designed in the 1950 and deployed in the mid 1960's. Finally retired in 1996 after nearly 33 years of service. The transport system has been developed due to the need to provide precise navigation data from Polaris submarine missiles. As reported in a historical perspective by Bradford Parkinson and others. in the logbook (Spring 1995), the concept has been proposed by the predictable frequency changes, but dramatic Doppler first satellite Sputnik, launched by the Soviet Union in October 1957. The Doppler signals allowed determination of the orbit of recorded data at least one site in one satellite pass. On the contrary, if the orbit of a satellite and were known, the position of a radio receiver can be determined Doppler measurements from themselves.
The transport system consists of six satellites in nearly circular polar orbit at an altitude of 1075 km. The orbital period is 107 minutes. The system used essentially the same Doppler data to track the Sputnik satellite. However, satellite orbits transit adequately defined according to the space fixed locations. Under favorable conditions, the RMS accuracy was 35 to 100 meters. The main problem was the main transport gaps in coverage. Users had to interpolate the positions between the passes.
GLOBAL POSITIONING SYSTEM
Success Traffic stimulated both the U.S. Navy and U.S. Air Force to investigate the more advanced versions of a space navigation system with capacity building. Recognizing the need for a joint effort, the Assistant Secretary of Defense established a Joint Program Office in 1973. The NAVSTAR Global Positioning System (GPS) was created.
In contrast to transit, GPS provides continuous coverage. So instead of Doppler, satellite range is determined by the phase difference.
There are two types of observables. A nickname is, which is the difference between a pseudo-random noise (PRN) code of the satellite signal and a replica code generated in user receiver, multiplied by the speed of light. The other builds large delta (ADR), a carrier phase measurement.
The positioning can be described as a process of triangulation with the measurement range between the user and four or more satellites. The beaches are derived from signal propagation delay satellite. Four satellites are needed to determine the position of three coordinates and time. The time is involved in correcting the receiver clock and finally is removed from the position measurement.
High accuracy is possible by the use of atomic clocks carried on board satellites. Each satellite has two cesium clocks and two rubidium clocks that keep time to within a few parts in 1013 or 1014, plus a couple of hours, or better than 10 nanoseconds. As the distance traveled by an electromagnetic signal at the speed of light, every nanosecond is about 30 centimeters. Therefore, the accuracy of GPS clocks enables measurement real time the distance of a few meters. With a post-processing of carrier phase measurements, a few centimeters can be achieved.
Design GPS constellation is the fundamental requirement that at least four satellites must be visible at any time from anywhere in the world. The commitment includes the visibility, the need for ground control stations in the U.S. cost savings and efficiency.
Orbital settings adopted in 1973 a total of 24 satellites eight spare satellites, plus in each of the three equally spaced orbital planes. The radius of the orbit was 26,562 km, which corresponds to a rotation period sidereal 12 hours, repeating ground tracks. Each satellite has reached a point was given four minutes earlier each day. An orbital inclination of 63 cities were chosen to maximize the payload into orbit with the launch of the Western Range Test. This configuration ensures 6 to 11 satellites in view any time.
In ten years, provided later, the inclination was reduced to 55 and the number of aircraft has increased to six. Would be made of 18 primary satellites, which represents the absolute minimum number of satellites needed to provide continuous global coverage at least four satellites on view at any point on Earth. Also, would be 3 in-orbit spares.
The operating system, currently deployed, consisting in 21 primary satellites and 3 spares in orbit, four satellites in each of six orbital planes. Each orbital plane is inclined at 55. This constellation improves the "18 plus 3" satellite constellation for the fuller integration three active stocks.
Space Segment
There have been several generations of GPS satellites. Block I satellites, built by Rockwell International, were launched between 1978 and 1985. Consisted Prototype eleven satellites, including the lack of launch, which validated the concept of system. The ten satellites successfully had a lifetime average of 8.76 years.
The Block II and Block II satellites also built by Rockwell International. Block II consists of nine satellites launched between 1989 and 1990. Block II, implemented between 1990 and 1997, consists of 19 navigation satellites with several improvements. In April 1995, the GPS was declared fully operational with a constellation of 24 operational satellites and a complete ground segment. The 28 Block II / II satellites have exceeded their mission-6 and are expected to have a lifespan of more than 10 years.
Block IIF consists of 20 replacement satellites that incorporate autonomous navigation based on the crosslinking extent. These satellites are manufactured by Lockheed Martin. The first Launched in 1997 led to a launch failure. The first IIR satellite to reach orbit was also released in 1997. The second GPS 2R satellite was launched aboard Delta 2 rocket on October 7, 1999. One to four more launches are planned over the next year.
The fourth generation of satellites is the result Block II (Block IIR). This program includes the acquisition of 33 satellites and the operation and support of a new segment of the GPS operational control. Block IIR program was awarded to Rockwell (now a part of Boeing). More details can be found in a special edition of the work of the IEEE in January 1999.
Segment control
The GPS Master Control Station located at Schriever Air Force Base in Colorado Springs, CO The MCS maintains the satellite constellation performing maneuvers and station keeping and attitude control. It also determines the orbital parameters and clock with a Kalman filter using measurements five monitoring stations worldwide. The orbit error is about 1.5 meters.
GPS orbits are computed independently by various organizations scientific carrier phase and post-treatment. The prior art is illustrated by the work of the International GPS Service (IGS), which produces precision orbit about 3 inches in two weeks.
The reference system is managed by the U.S. Naval Observatory Washington, DC. GPS time is measured from Saturday and the midnight on Sunday at the start of the week. The GPS time scale is a "paper clock" compound that is synchronized to keep pace with Coordinated Universal Time (UTC) and International Atomic Time (TAI). However, UTC differs from TAI by a whole number of leap seconds to maintain consistency with the rotation of the earth, while GPS time does not include the second jump. The origin of GPS Time is midnight on January 05/06, 1980 (UTC). Today in the TAI is ahead in 32 seconds UTC, TAI is a 19 seconds by GPS, and is ahead of UTC by 13 seconds. Only 1,024 weeks were allotted the source before the system time is reset, and that 10 bits are assigned to the calendar function (1024 is the tenth power of 2). Thus, the first renewal of GPS occurred at midnight on August 21, 1999. The GPS next investment will be May 25, 2019.
STRUCTURE OF THE SIGNAL
The satellite position at any time is calculated in the user's receiver of the navigation message that is in a data base flow of 50 basis points. The orbit is shown for each one-hour period by a set of 15 items Kepler orbital with harmonic coefficients resulting from riots, and is updated every four hours.
This data stream is modulated by code division multiple access or broad-spectrum, pseudorandom noise (PRN) codes: C acquisition coarse / / A code (sometimes called access code / light) and precision P-code The P code can be encrypted to produce a ringing Y. secure code This feature is known as the Anti-Spoof (AS) mode, which is intended to defeat deception interference by the opponents. The C / A code is used to acquire the satellite and positioning for civilian receivers. The P (Y) is the code used by the military and other authorized recipients.
The C / A code is Gold code size register 10, which has a sequence length of 1023 chips and a chip rate of 1,023 MHz and therefore repeats every 1 millisecond. (The term "Chip" is used instead of "little" to indicate that the code does not contain any information PRN). P code is a code over the length of 2.3547 x 1014 chips with a pebble rate 10 times the C / A, or 10.23 MHz At this rate, the P code has a period of 38,058 weeks, but is truncated after week so the 38 sectors are available for the constellation. Each satellite uses a different member of C / A code of Family Feud and another segment of a week P-code sequence
GPS satellites transmit signals on two carrier frequencies: L1 component with a center frequency of 1575.42 MHz, and L2 component with a center frequency of 1227.60 MHz. These frequencies are derived from the master clock frequency of 10.23 MHz, with L1 = 154 x 10.23 MHz and L2 = 120 MHz x 10.23. The frequency L1 transmits both the P code and the code C / A, while the L2 frequency carries only the P-code P-code The second frequency allows a measure of delay dual-frequency group in the ionosphere. P-code receiver has a two-sigma error RMS 5 meters horizontal position.
The single frequency C / A code User must model the ionospheric delay with less precision. In addition, the C / A is a volunteer degraded by a technique called Selective Availability (SA) introducing errors from 50 to 100 meters dithering the satellite clock data. With differential GPS measurements, however, the position accuracy can be improved by reducing errors and the SA environment.
The signal from a GPS satellite has a right circular polarization. According to the document control interface GPS, the minimum specified strength of the signal at an elevation angle of 5 on a linear polarized antenna, receiving a gain of 3 dB (equivalent a circular polarization antenna with a gain of 0 dB) – 160 dBW for the L1 C / A code – 163 dBW for the L1 P code, and – 166 dBW for L2 P-code. The signal L2 is transmitted to a lower power level because it is used mainly to correct the ionospheric delay.
Pseudo-
Step fundamental positioning system is pseudo general. The user equipment receives the PRN code from a satellite and then to identify the satellite generates a code replication. Phase in which should be the reply code shifted into the receiver to maintain the highest correlation with the satellite code, multiplied by the speed of light is approximately equal to the number of satellites. Called pseudo because the measure must be corrected by a variety of factors to be considered a truth.
The corrections to be applied signal propagation delays caused by the ionosphere and troposphere, the clock error of the spacecraft, and the error user receiver clock. The ionospheric correction is obtained either by measuring the dispersion with the two frequencies L1 and L2 or by calculation from a model mathematician, but the tropospheric delay must be calculated from the troposphere is not dispersive. True geometric distance from each satellite is obtained by applying of these corrections to the pseudorange measurement.
Other sources of error and modeling errors continue to be investigated. For example, a recent amendment Filter Kalman led to improved performance. Studies have also shown that models of solar radiation, pressure may be necessary to review and no new evidence on Earth's magnetic field can contribute to a period of change in the orbit of small satellites in clock frequencies.
Phase Carrier
carrier phase is used to make measurements with an accuracy far beyond those based on the pseudo-distance. However, a measure of the ambiguity of carrier phase cycle must solve an integral in the nickname is not ambiguous.
The L1 carrier wavelength is about 19 centimeters. For Therefore, with a resolution of one cycle per cent, a measure of the difference in a few millimeters is theoretically possible. This technique has important applications in geodetic science programs and the like.
RELATIVITY
The accuracy of GPS measurements is so large that the application requires theories of general relativity by Albert Einstein and specific reduction of their measures. Professor Carroll Alley of the University of Maryland, once spoke of the importance of this in a scientific conference dedicated to the measurement of time in 1979. He said: "I think it's appropriate … to realize that the first application practice the ideas of Einstein real engineering situations are with us in the fact that the clocks are so stable that it is necessary to take account of these small effects in a variety of systems currently in development or are actually used to compare times around the world. This is more a matter of science applications and scientists, but has evolved in the field of engineering necessity. "
According to the theory of relativity, a moving clock appears run slow compared to an analog clock that is at rest. This effect is known as time dilation. "In addition, a clock in a gravitational potential Low seems to run fast relative to that of a more serious potential. This gravitational effect is generally known as "redshift" (only this case is actually a blue "Change").
GPS satellites around the Earth at a speed of 3874 km / s, at an altitude of 20,184 km. Therefore, due to the speed of sound, a satellite clock appears to run slow by 7 microseconds per day compared a clock on the surface of the earth. But because the gravitational potential difference, the satellite clock appears to run fast by 45 microseconds per day. The net effect is that the clock seems to run fast by 38 microseconds day. It's a big difference in the rate of an atomic clock with a precision few nanoseconds. Therefore, to compensate for such large secular watches given a rate of compensation before the launch of the satellite – 4,465 units in 1010 from its nominal frequency of 10.23 MHz, so that, on average, seem to operate at the same speed a clock on the floor. The actual frequency of the clocks in the satellite before launch is 10.22999999543 MHz
Although the GPS satellite orbits are nominally circular, there is always some residual eccentricity. The eccentricity of the orbit makes it a bit elliptical, and the speed and altitude varies on a lathe. Therefore, although head speed and the gravitational effects have been offset by a rate of compensation, there remains a slight residual variation that is proportional to the eccentricity. For example, with an orbital eccentricity of 0.02 is a relativistic sinusoidal variation on the clock with an apparent magnitude of 46 nanoseconds. This correction should be calculated and has in GPS receiver.
The displacement of a receptor surface of the earth due to rotation of the Earth in inertial space during the flight time signal must also be taken into account. This is a third relativistic effect is due to the universality of the speed of light. The maximum correction occurs when the receiver is in Ecuador and the satellite is in sight. The flight time of a GPS satellite signal to a receiver on earth is 86 milliseconds and the correction of measured beach the resulting displacement of the receiver is 133 nanoseconds. A similar correction must be applied by a receiver in a mobile platform, such as aircraft or satellite to another. This effect, as interpreted by an observer in the rotating frame of reference of the earth, is called the Sagnac effect. It is also the base of a ring laser gyroscope in an inertial navigation system.
GPS Modernization
In 1996, Presidential Decision Directive decree, the president said considers the issue of selective availability in 2000 with the aim of stopping SA, no later than 2006. In addition, GPS signals L1 and L2 would available to civil users and a new civil signal would be 10.23 MHz. To meet the aviation needs, the third civil frequency, known as L5, focuses on 1176.45 MHz in the aeronautical radionavigation service (SNRA) Banda, subject to approval by the World Radiocommunication Conference in 2000. According to Keith McDonald, in an article published in the modernization of GPS World September 1999 GPS with SA suppressed civil GPS accuracy could be improved about 10-30 meters. With the addition of a second frequency of the ionospheric group delay corrections, accuracy Civil reach 5 to 10 meters. A third method would create two frequencies coup that would give an accuracy of one meter in real time.
A variety of other improvements are under consideration, including increased power the addition of a new military code L1 and L2 frequencies, additional ground stations, the most common downloads, and an increase in the number of satellites. These initiatives are driven by maintenance needs twice the national security while supporting the growing reliance on GPS for private industry. When these improvements begin application to the Block IIR satellites and GPS IIR upon funding.
Besides providing the location, the GPS is a reference to the time an accuracy of 10 nanoseconds or more. His time of transmission of signals are used for national defense, commercial and scientific. The availability of precision GPS and Universal Time produced a paradigm shift in the timing and distribution, with the development of GPS from a secondary source of a fundamental self-reference same.
The international community want assurances that you can count on the availability of GPS and the continued support of U.S. system. Russian Global Navigation Satellite System (GLONASS) was an alternative, but the economic conditions in Russia have threatened its viability. Therefore, the EU plans to create a navigation system itself, called Galileo, to avoid while relying on the U.S. GPS and the Russian GLONASS program.
The Global Positioning System is a vital national resource. In recent thirty years has made the transition from concept to reality, which today represents an operating system in which everyone has become dependent. Both technical improvements and enlightened national policy necessary to ensure continued growth in the XXI century.
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About the Author
The Applied Technology Institute (ATI) specializes in short course technical training in space, communications, defense, sonar, radar, and signal processing. Since 1984 ATI has provided leading-edge public courses and on-site technical training to defense and NASA facilities, as well as DOD and aerospace contractors. The courses provide a clear understanding of the fundamental principles and a working knowledge of current technology and applications. Boost your career. Courses are led by world-class design experts. Learn from the proven best.
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