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The Global Positioning System: a detailed looked at 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. However, GPS has become the basis for measuring the position and time for science laboratories and a wide range of applications in a multi-billion dollar commercial industry. Approximately one million sets are produced each year and the total GPS market is expected to reach 10 billion U.S. dollars at the end of next year. History GPS and measurement principles are the subjects of this article.

EARLY METHODS OF NAVIGATION

The shape and size of land has been 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 heaven, Aristotle gave two arguments scientifically correct. First, the Earth's shadow projected on the moon during a lunar eclipse appears to be curved. Second, elevations of the stars change as you move north or south, while some stars visible in Egypt can not be seen in all of Greece.

The radio actual land was determined within one percent by Eratosthenes in about 230 BC. I knew the sun was directly overhead at noon on the solstice Summer in Siena (Aswan, Egypt), since that day the water turns a deep well. At the same time, measured the length of the shadow cast by a column based on Alexandria Library, which was almost due north. The distance between Alexandria and Syene had been well established by professional riders and camel caravans. Thus, Eratosthenes was able to calculate the radius of the Earth from the difference in latitude can be extracted from measurement. In terms of modern units in length, which was the figure of approximately 6,400 km. In comparison, the actual average radius is 6371 km (the earth is spherical, precisely as the polar radius is 21 km less than the equatorial radius of 6,378 km.)

The ability to determine one's position on earth was the next major issue to be addressed. In the second century AD the Greek astronomer Ptolemy developed a geographical atlas, in which estimated the latitude and longitude of major cities of the Mediterranean world. Ptolemy is the most famous, however, for his geocentric theory of planetary motion, which was the basis for astronomy catalogs until Nicolaus Copernicus published his heliocentric theory in 1543.

Historically, methods of navigation on the surface of the earth have led to the angular measurement of the positions of stars to determine latitude. The latitude of the position of one is equal to the elevation of the Pole Star. The position of the pole star on the celestial sphere is only temporary, however, because the precession of Earth's axis of rotation through a circle of radius 23.5 in a period of 26,000 years. At the time of Julius Caesar, there was no star close enough to the north celestial pole is called Polaris. In 13,000 years, the star Vega will be near the pole. Perhaps not a coincidence that the marine not venture far from the earth visible to the time of Christopher Columbus, when the true north could be determined with the star we now call the North Star. Even then the diurnal rotation of the star caused an apparent variation of the compass needle. Polaris in 1492 described a radius of about 3.5 on the celestial pole in compared with today. At sea, however, Columbus and his contemporaries s depended mainly on the compass and dead reckoning.

The determination of longitude was much more difficult. The length is astronomically obtained from the difference between the observed time of a celestial event such as an eclipse tabulated and the corresponding time for a reference. For every hour of time difference, the difference in length is 15 degrees.

Columbus himself tried estimate its length on his fourth voyage to the New World, noting the time of a lunar eclipse seen from the port of Santa Gloria in Jamaica on February 29, 1504. In his distinguished biography Admiral of the Ocean Sea Samuel Eliot Morrison says that Columbus measured the duration of the eclipse with an hourglass and determined its position in nine hours and fifteen minutes west Cadiz, Spain, according to the prediction of eclipses in a calendar time carrying on board his ship. During the previous year, while his ship was abandoned in the Port Columbus had given the latitude of Santa Gloria by numerous observations of the star. Did your freedom to be 18, it was an error of less than half a degree and was one of the best recorded observations of latitude in the sixteenth century, but its length was estimated off by about 38 degrees.

Columbus also made legendary use of this eclipse with the threat of Indians with God's disapproval, as indicated by a sign from heaven, if not bring desperately needed provisions to his men. When the eclipse came as predicted, the natives told the Admiral's speech, promising to provide all the food they needed.

The new knowledge of the universe revealed by Galileo Galilei in his book The Starry Messenger. This book, published in Venice in 1610, reported the telescopic discoveries hundreds of new stars, the craters of the moon, the phases of Venus, the rings of Saturn, sunspots, and the four inner satellites of Jupiter. Galileo proposed use the eclipses of Jupiter's satellites as a celestial clock for the practical determination of longitude, but the calculation of a precise ephemeris and the difficulty of observing the satellites of the deck of a boat trailer prevented the use of this method at sea. However, James Bradley, third Astronomer Royal of England, successfully applied the technique in 1726 to determine the lengths of Lisbon and New York with considerable precision.

The inability to measure longitude at sea had the potential catastrophic consequences for the boats to explore the new world, cargo transport, and conquering new territories. The wrecks are common. On 22 in October 1707 a fleet of twenty ships under the command of Admiral Sir Shovell Clowdisley returned to England after an unsuccessful attack on Toulon military in the Mediterranean. As the fleet approached the English Channel in case of heavy fog, the flagship and three sank in the coastal rocks and about two thousand men perished.

Stunned for this loss record, the British government in 1714 offered a prize of £ 20.000 for a method to determine longitude at sea within half a degree. The scientific community believes that the solution would be obtained from observations of the moon. The German cartographer Tobias Mayer, with the help of new mathematical methods developed by Leonard Euler, which offers improved tables of the moon in 1757. The position recorded by the moon at a given moment, seen from a reference meridian could be compared to its position in the local time to determine the angular position west or east.

And the method appeared to achieve astronomical embodiment, the British craftsman John Harrison gave a different solution through the invention of the marine chronometer. The history of Harrison clock has been reported in the popular book by Dava Sobel, Longitude.

Both methods were tested in sea trials. The lunar tables for the determination of longitude within four minutes of arc, but Harrison chronometer precision was only one minute of arc. Ultimately, the parties of the prizes were awarded to the widow Mayer, Euler, and Harrison.

In the twentieth century with the development of radio transmitters, other kinds of navigational aids was created with terrestrial radio beacons, including Loran and Omega. Finally, the technology of artificial satellites can determine the position and the line with the light signals involving Doppler measurement or phase difference.

TRANSIT

Transit, marine navigation satellite system, was conceived in late 1950 and implemented in the mid 1960's. Finally retired in 1996 after nearly 33 years of service. The transit system was developed because the need to provide accurate navigation data of the Polaris missile submarines. As reported in a historical perspective by Bradford Parkinson, et al. in log (Spring 1995), the concept was suggested by the predictable but dramatic changes in the Doppler frequency of the first satellite Sputnik, launched by the Soviet Union in October 1957. Doppler shifted signals allowed determination of the orbit with data recorded at a site in a single pass of the satellite. On the contrary, if the orbit of a satellite and were known, the position of a radio receiver could be determined in the same Doppler measurements.

The system traffic will consist of six satellites in nearly circular polar orbits at an altitude of 1075 km. The revolution period was 107 minutes. The system used essentially the same Doppler data used to track the Sputnik satellite. However, the orbits of satellites is determined precisely Transit tracking them in fixed places, widely spaced. Under favorable conditions, the RMS accuracy was 35 to 100 meters. The main traffic problem was the large gaps in coverage. Users had to insert their positions between 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 navigation system in space greater capabilities. Recognizing the need for a joint effort, the Deputy Secretary of Defense established a Joint Program Office in 1973. The NAVSTAR Global Positioning System (GPS) was created as well.

In contrast to transit, the GPS provides continuous coverage. Also, instead of Doppler effect, the Satellite range is determined of the phase difference.

There are two types of observables. One is pseudorange, which is the offset between a pseudo-random noise (PRN) coded satellite signals and a replica code generated in the user's receiver, multiplied by the speed of light. The other builds large delta (ADR), a carrier phase measurement.

The determination of the position can be described as the process of triangulation with the measured range between the user and four or more satellites. The ranges are inferred from the time of the propagation of satellite signals. Four satellites are needed to determine the three position coordinates and time. The time is involved in correcting the receiver clock and is ultimately removed from the position measurement.

The high accuracy is possible by 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 parties in 1013 or 1014 more than a couple of hours, or better than 10 nanoseconds. In terms of the distance traveled by an electromagnetic signal at the speed of light, every nanosecond corresponds to about 30 centimeters. Thus, the accuracy of GPS clocks allows real-time measurement of the distance a few meters. Based on the measured post-processing phase carrier, an accuracy of a few centimeters can be achieved.

The GPS constellation design was the fundamental requirement that at least four satellites must be visible at all times from any location on earth. Compensation includes the visibility, the need to pass on the ground control stations in the cost of U.S. saving and efficiency.

The orbital configuration adopted in 1973 a total of 24 satellites, which consists of 8 satellites a spare in each of three equally spaced orbital planes. The orbital radius was 26,562 km, which corresponds to a sidereal revolution period of 12 hours, with traces of land of repetition. Each satellite came at a point four minutes earlier each day. A common orbital inclination of 63 was selected to maximize payload into orbit with the launch of the Western Range Test. This configuration ensures 6 to 11 satellites in view at any time.

As expected, ten years later, the inclination was reduced to 55 and the number of aircraft was increased to six. The constellation would consist of 18 satellites primary, which represents the absolute minimum number of satellites required for continuous global coverage with at least four satellites in view at any point land. In addition, there will be three in-orbit spares.

The operating system, as implemented, consists of 21 satellites and 3 primary orbit spares, which has four satellites in each of six orbital planes. Each orbital plane is inclined at 55. This constellation of improvement in the "18 plus 3 "constellation of satellites in the full integration over the three active spares.

SPACE SEGMENT

There have been several generations of GPS satellites. Block I satellites built by Rockwell International, were launched between 1978 and 1985. Consisted of eleven satellites prototype, including launch failure, one that validated the system concept. The ten satellites successfully had an average life of 8.76 years.

Block II Block II satellites were 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 various improvements. In April 1995, the GPS was declared fully operational with a constellation of 24 operational satellites and a segment Full Earth. The 28 Block II / II satellites have exceeded their specified mission duration of 6 years and is expected to have a lifespan of more than 10 years.

Consists of 20 Block IIR satellites replacement incorporating autonomous navigation based on the crosslinking extent. These satellites are being manufactured by Lockheed Martin. The first release in 1997 led to a launch failure. The first IIR satellite to reach orbit was also launched in 1997. The second satellite GPS 2R was successfully launched aboard a Delta 2 rocket on October 7, 1999. One to four more launches are expected during the next year.

The fourth generation of Block II satellites is monitored (Block IIF). This program includes the acquisition of 33 satellites and the operation and support of a new segment operating control GPS. Block IIF program was awarded to Rockwell (now part of Boeing). More details can be found in a special edition of the Proceedings of the IEEE in January 1999.

CONTROL SEGMENT

Master Control Station to the GPS is at Schriever Air Force Base in Colorado Springs, CO The MCS maintains the satellite constellation and performing maneuvers and station attitude control. It also determines the parameters of the orbit and the clock with a Kalman filter using measurements from five monitoring stations located throughout the world. The orbit error is about 1.5 meters.

GPS orbits derived independently by various scientific organizations carrier phase and post-processing. The prior art is exemplified by the work of International Service GPS (IGS), which produces orbits with an accuracy of about 3 centimeters in two weeks.

The reference time of the system is administered by the Centre U.S. Naval Washington, DC. GPS time is measured from Saturday / Sunday midnight in the beginning of the week. The GPS time scale is a composite of "paper clock" that is synchronized to keep pace with the Coordinated Universal Time (UTC) and International Atomic Time (TAI). However, UTC differs from TAI by an integer of leap seconds to correspond with the rotation of the earth, while the GPS time does not include leap seconds. The origin of GPS time from midnight of January 5 / 6, 1980 (UTC). Currently, the ITF is ahead of UTC by 32 seconds, TAI is ahead of GPS for 19 seconds and the GPS is ahead of UTC by 13 seconds. Only 1,024 weeks were allotted from the source before the system time is reset to zero, because 10 bits are assigned to the calendar function (1,024 is the tenth power of 2). Thus, the first renewal of GPS occurred at midnight on August 21, 1999. The next extension of GPS will be held May 25 2019.

SIGNAL STRUCTURE

The satellite position at any time is calculated in the user's receiver of the message navigation is in a 50 bps data stream. The orbit is represented by each period of one hour for a set of 15 Keplerian orbital elements, with harmonic coefficients derived from the shocks and is updated every four hours.

This data stream is modulated by each division code two multiple access or spread spectrum, pseudorandom noise (PRN) codes: the coarse / acquisition C / A code (sometimes called the light / code Access) code and the precision P. The P code can be encrypted to produce a sure sign called the code Y. This feature is known as the Anti-Spoof (AS) how he intends to defeat the deception jamming by adversaries. The C / A code is used for the acquisition of satellites and for determining position by civilian receivers. The P (Y) is the code used by the military and other authorized recipients.

The C / A code is a Gold code size register 10, which has a sequence length of 1023 chips and a chipping rate of 1,023 MHz and therefore repeats every 1 millisecond. (The term "chip" is used instead of "little" to indicate that the PRN code contains no information.) Code is a code P over the length of 2.3547 x 1014 chips pebble rate 10 times the C / A, or MHz 10.23. At this rate, the P code has a period of 38.058 weeks, but is truncated once a week for the 38 segments are available for the constellation. Each satellite uses a different member of the C / A Gold code family week and a different segment of the sequence P. code

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. L1 frequency transmitted both the P code and C / A code, while the L2 frequency carries only the P-code The second frequency P code allows a dual-frequency measurement ionospheric group delay. P-code receiver has a two-sigma error RMS horizontal position about 5 meters.

The single frequency C / A code user should model the ionospheric delay with less precision. In addition, the C / A code is deliberately degraded by a technique called Selective Availability (SA), which introduces errors of 50 to 100 meters by interpolation of the satellite clock data. Through differential GPS measurements, however, the position accuracy can be improved by reducing errors and environmental SA.

The signal transmitted from a GPS satellite has a right hand circular polarization. According to the GPS interface control document, the minimum specified strength of the signal at an elevation angle of 5 to a receiving antenna polarization linear, with a gain of 3 dB (approximately equivalent to a circularly polarized antenna with a gain of 0 dB) - 160 dBW for the L1 C / A code - 163 dBW for the L1 code P, and - 166 dBW for L2 P-code The L2 signal is transmitted with less power since it is used mainly for ionospheric delay correction.

Pseudorange

The crucial step in the Global Positioning System is pseudorange. The user equipment receives from a satellite PRN code and, having identified the satellite, generates a reply code. The stage at which the code should be changed to mirror the receiver to maintain maximum correlation with the satellite code, multiplied by the speed of light is approximately equal to the range of satellite. It is called the pseudorange because the measurement must be corrected by a variety of factors for achieving the rank of truth.

Any corrections to be applied by signal propagation delays caused by ionosphere and troposphere, the spacecraft clock error, user error and receiver clock. The correction of the ionosphere is obtained either by measuring the dispersion with both L1 and L2 frequencies or by calculation from a mathematical model, but the tropospheric delay must be calculated from the troposphere is not dispersive. The true distance geometry of each satellite is obtained by applying these corrections the pseudorange measurement.

Other sources of error and modeling errors remain investigated. For example, a recent amendment to the Kalman filter has led to improved performance. Studies have also shown that radiation pressure solar, the models may need revision, and new evidence that Earth's magnetic field can contribute to a change in the short period orbit satellite clock frequencies.

Carrier phase

carrier phase is used to perform measurements with an accuracy that exceeds amply based on pseudorange. However, a carrier phase measurement must resolve the ambiguity in the complete cycle of the pseudorange is unequivocal.

The wavelength of the L1 carrier is about 19 centimeters. Thus, with a resolution of the cycle of one percent, a measure of the difference in the level of a few mm is theoretically possible. This technique has important applications for scientific programs of geodesy and the like.

RELATIVITY

The accuracy of GPS measurements is so large that requires the application of special and general theories of relativity Albert Einstein reduction of their actions. Professor Carroll Alley of the University of Maryland, once articulated 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 practical application of Einstein's ideas in real engineering situations are with us on the fact that the clocks are so stable that these effects must be taken into account in a small range of systems now in development or effective use in comparing time worldwide. It is no longer a matter of scientific interest and scientific application, but has moved into the realm of the need for engineering. "

According to theory of relativity, a moving clock seems to go slow with respect to a similar clock at rest. This effect is called dilation of time. "In addition, a clock in a weak gravitational potential seems to run faster compared to one that is in a strong gravitational potential. This effect gravity is generally known as the "red shift" (only in this case is actually a blue shift ").

satellites GPS orbit the Earth at a speed of 3,874 km / s, at an altitude of 20,184 km. Thus, because of its speed, a satellite clock appears to March slow by 7 microseconds per day compared with a clock on the surface of the earth. But due to 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 per day. This is a huge difference in an atomic clock rate with an accuracy a few nanoseconds. So, to compensate for such large secular, watches are given a rate of compensation before the launch of the satellite - 4,465 pieces in 1010 from its nominal frequency of 10.23 MHz, so that on average appear to run in the same rhythm as a clock on the ground. The actual frequency of satellite clocks before release is therefore 10.22999999543 MHz

Although the GPS satellite orbits are nominally circular, there is always some residual eccentricity. Eccentricity causes the orbit to be slightly elliptical, and the speed and altitude varies more than a revolution. Thus, although the 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 in apparent clock time having an amplitude of 46 nanoseconds. This correction should be calculated and taken into account in the GPS receiver.

The displacement of a receptor on the surface of the earth due to rotation of the Earth in inertial space during the flight time of the signal should also be account. This is the third relativistic effect is due to the universality of the speed of light. The maximum correction occurs when the receiver is in Ecuador and satellite is on the horizon. The flight time of a GPS satellite signal to a receiver on earth is 86 milliseconds and then correcting the resulting measurement range of receptor is 133 nanoseconds. A similar correction must be applied by a receiver in a mobile platform such as an airplane or satellite to another. This effect, as was 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 gyro navigation system inertial.

GPS Modernization

In 1996, a Presidential Decision Directive said the president would review the issue selective availability in 2000 with the aim of suspending SA, no later than 2006. In addition, both the L1 and L2 GPS signals would be made available civilian users and new civilian signal 10.23 MHz authorized. To meet the needs of aviation, the third civil frequency, known as L5, focuses on 1176.45 MHz, Radio aeronautical navigation services (SRNA) band, subject to approval at the World Radiocommunication Conference in 2000. According to Keith McDonald In an article published in the modernization of GPS in September 1999, GPS World, SA removed civil GPS accuracy could be improved to about 10-30 meters. With the addition of a second frequency of the ionospheric group delay corrections, civil accuracy would be 5 to 10 meters. A third method would create two frequencies that would blow a meter accuracy in real time.

A variety of other improvements are under consideration, including increased power the addition of a new military code on L1 and L2 frequencies, additional ground stations, more frequent increases and an increase in the number of satellites. These initiatives are driven by the dual need to maintain national security, while supporting the growing reliance on GPS for the commercial industry. When these updates was to be in the Block IIR satellites and IIF funding depends on the GPS.

Besides providing the location, the GPS is a reference for the time with an accuracy of 10 nanoseconds or better. His time in the signals are used for national defense, commercial, and scientific purposes. The availability and accuracy universal time GPS has been a paradigm shift in the timing and distribution, with the GPS evolution from a secondary source to a key benchmark itself same.

The international community wants assurance that it can rely on the availability of GPS and continued U.S. support for the system. The Russian Global Navigation Satellite System (GLONASS), has been an alternative, but the economic conditions in Russia has threatened its viability. Consequently, the European Union is considering the creation navigation system itself, called Galileo, to avoid relying on the U.S. GPS and Russian GLONASS program.

The Global Positioning System is a resource vital national. Over the past thirty years has made the transition from concept to reality, which is now an operating system that everyone has become dependent. Both technical improvements and a smart national policies are necessary to ensure continued growth in the XXI century 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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