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the big one
2024-08-27 21:48:20 -05:00
The Global Positioning System – A National Resource - ATI Courses
https://web.archive.org/web/20210513215257/https://aticourses.com/2013/05/...
The Wayback Machine - https://web.archive.org/web/20210513215257/https://www.aticourses.com/2013/05/20/the-global-positioning-system-a-national-resource/
The Global Positioning System (GPS) was originally designed jointly by the U.S. Navy and the U.S. Air Force to permit the determination of position and time for military troops and guided missiles. However, GPS has also become the basis for position and time measure-ment by scientific laboratories and a wide spectrum of applications in a multi-billion dollar commercial industry. Roughly three billion GPS receivers have been sold to delighted consumers throughout the world. Thirty-one GPS satellites are currently broadcasting navigation signals from their high-altitude vantage points in space. EARLY METHODS OF NAVIGATION The shape and size of the earth has been known from the time of antiquity. The fact that the earth is a sphere was well known to educated people as long ago as the fourth century BC. In his book On the Heavens, Aristotle gave two scientifically correct arguments. First, the shad-ow of the earth projected on the moon during a lunar eclipse appears to be curved. Second, the elevations of stars change as one travels north or south, while certain stars visible in Egypt cannot be seen at all from Greece. The actual radius of the earth was determined within one percent by Eratosthenes in about 230 BC. He knew that the sun was directly overhead at noon on the summer solstice in Syene (Aswan, Egypt), since on that day it illuminated the water of a deep well. At the same time, he measured the length of the shadow cast by a column on the grounds of the library at Alexandria, which was nearly due north. The distance between Alexandria and Syene had been well established by professional runners and camel caravans. Thus Eratosthenes was able to compute the earth’s radius from the difference in latitude that he inferred from his measurement. In terms of modem units of length, he arrived at the figure of about 6400 km. By comparison, the actual mean radius is 6371 km (the earth is not precisely spherical, as the polar radius is 21 km less than the equatorial radius of 6378 km). The ability to determine one’s position on the earth was the next major problem to be addressed. In the second century, AD the Greek astronomer Claudius Ptolemy prepared a geographical atlas, in which he estimated the latitude and longitude of principal cities of the Mediterranean world. Ptolemy is most famous, however, for his geocentric theory of planetary motion, which was the basis for astronomical catalogs until Nicholas Copernicus published his heliocentric theory in 1543. CELESTIAL NAVIGATION Historically, methods of navigation over the earth’s surface have involved the angular measure-ment of star positions to determine latitude. The latitude of one’s position is equal to the elevation of the pole star. The position of the pole star on the celestial sphere is only temporary, however, due to precession of the earth’s axis of rotation through a circle of radius 23.5 over a period of 26,000 years. At the time of Julius Caesar, there was no star sufficiently close to the north celes-tial pole to be called a pole star. In 13,000 years, the star Vega will be near the pole. It is perhaps not a coincidence that mariners did not venture far from visible land until the era of Christopher Columbus, when true north could be determined using the star we now call Polaris. Even then the star’s diurnal rotation caused an apparent variation of the compass needle. Polaris in 1492 described a radius of about 3.5 degrees about the celestial pole, compared to today. At sea, however, Columbus and his contemporaries depended primarily on the mariner’s compass and dead reckoning. The determination of longitude was much more difficult. Longitude is obtained astronomically from the difference between the observed time of a celestial event, such as an eclipse, and the corresponding time tabulated for a reference location. For each hour of difference in time, the difference in longitude is 15 degrees. NAVIGATION AT SEA Columbus himself attempted to estimate his longitude on his fourth voyage to the New World by observing the time of a lunar eclipse as
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The Global Positioning System – A National Resource - ATI Courses
https://web.archive.org/web/20210513215257/https://aticourses.com/2013/05/...
from the measurement of position. High precision is made possible through the use of atomic clocks carried on-board the satellites. Each satellite has two cesium clocks and two rubidium clocks, which maintain time with a precision one part in ten trillionth in over a few hours, or better than 1O nanoseconds. In terms of the distance traversed by an electromagnetic signal at the speed of light, each nanosecond corresponds to about 30 centimeters. Thus the precision of GPS clocks permits a real time measurement of distance to within a few meters. With post processed carrier phase measurements, a precision of a few centimeters can be achieved today. The design of the GPS constellation had the fundamental requirement that at least four satellites must be visible at all times from any point on earth. The tradeoffs included visibility, the need to pass over the ground control stations in the United States, cost, and sparing efficiency. The orbital configuration approved in 1973 was a total of 24 satellites, consisting of 8 satellites plus one spare in each of three equally spaced orbital planes. The orbital radius was 26,562 km, corresponding to a period of revolution of 12 sidereal hours, with repeating ground traces. Each satellite arrived over a given point four minutes earlier each day. A common orbital inclination of 63º was selected to maximize the on-orbit payload mass with The operational system, as pres-ently deployed, consists of 21 primary satellites and 3 on-orbit spares, comprising four satellites in each of six orbital planes. Each orbital plane is inclined at 55º with respect to the equator. This constellation improves on the “18 plus 3” satellite constellation by more fully integrating the three active spares. There have been several generations of GPS satellites. The Block I satellites, built by Rockwell International, were launched between 1978 and 1985. They consisted of eleven prototype satellites, including one launch failure, that validated the system concept. The ten successful satellites had an average lifetime of 8.76 years. The Block II and Block llA satellites were also built by Rockwell International. Block II consists of nine satellites launched between 1989 and 1990. Block llA, deployed between 1990 and 1997, consists of 19 satellites with several! navigation enhancements. In April 1995, GPS was declared fully operational with a constellation of 24 operational spacecraft and a completed ground segment. The 28 Block II/IIA satellites have exceeded their specified mission duration of 6 years and are expected to have an average lifetime of more than 1O years. Block llR comprises 20 replacement satellites that incorporate autonomous navigation based on cross-link ranging. These satellites are being manufactured by Lockheed Martín. The first launch in 1997 resulted in a launch failure. The first llR satellite to reach orbit was also launched in 1997. The second GPS IIR satellite was successfully launched aboard a Delta 2 rocket on October 7, 1999. One to four more launches are anticipated over the next year. The fourth generation of satellites is the Block II follow-on (Block llF). This program includes the procurement of 33 satellites and the operation and support of a new GPS operational control segment. The Block llF program was awarded to Rockwell (now a part of Boeing). Further details may be found in a special issue of the Proceedings of the IEEE for January, 1999. CONTROL SEGMENT The Master Control Station for GPS is located at Schriever Air Force Base in Colorado Springs, CO. The MCS maintains the satellite constellation and performs the station keeping and attitude control maneuvers. It also determines the orbit and clock parameters with a Kalman filter using measurements from five monitor stations distributed around the world. The orbit error is about 1.5 meters. GPS orbits are derived independently by various scientific organizations using carrier phase and post-processing. The state of the art is exemplified by the work of the International GPS Service (IGS), which produces orbits w
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The Global Positioning System – A National Resource - ATI Courses
https://web.archive.org/web/20210513215257/https://aticourses.com/2013/05/...
important applications to geodesy and analogous scientific programs. RELATIVITY The precision of GPS measurements is so great that it requires the application of Albert Ein-stein’s special and general theories of relativity for the reduction of its measurements. Professor Carroll Alley of the University of Maryland once articulated the significance of this fact at a scientific conference devoted to time measurement in 1979. He said, “I think it is appropriate to realize that the first practical application of Einstein’s ideas in actual engineering situations are with us in the fact that clocks are now so stable that one must take these small effects into account in a variety of systems that are now undergoing development or are actually in use in comparing time worldwide. It is no longer a matter of scientific interest and scientific application, but it has moved into the realm of engineering necessity.” According to relativity theory, a moving clock appears to run slow with respect to a similar clock that is at rest. This-effect is called “time dilation.” In addition, a clock in a weaker gravitational potential appears to run fast in comparison to one that is in a stronger gravitational potential. This gravitational effect is known in general as the “red shift” (only in this case it is actually a “blue shift”). GPS satellites revolve around the earth with a velocity of 3.874 km/s at an altitude of 20, 184 km. Thus on account of the its velocity, a satellite clock appears to run slow by 7 microseconds per day when compared to a clock on the earth’s surface. But on account of the difference in gravitational potential, the satellite clock appears to run fast by 45 microseconds per day. The net effect is that the clock appears to run fast by 38 microseconds per day. This is an enormous rate difference for an atomic clock with a preci-sion of a few nanoseconds. Thus to compensate for this large secular rate, the clocks are given a rate offset prior to satellite launch of – 4.465 parts in 10 to the tenth power from their nominal frequency of 10.23 MHz so that on average they appear to run at the same rate as a clock on the ground. The actual frequency of the satellite clocks before launch is thus 10.22999999543 MHz. Although the GPS satellite orbits are nominally circular, there is al-ways some residual eccentricity. The eccentricity causes the orbit to be slightly elliptical, and the velocity and altitude vary over one revolution. Thus, although the principal velocity and gravitational effects have been compensated by a rate offset, there remains a slight re-sidual variation that is proportional to the eccentricity. For example, with an orbital eccen-tricity of 0.02 there is a relativistic sinusoidal variation in the apparent clock time having an amplitude of 46 nanoseconds. This correction must be calculated and taken into account in the GPS receiver. The displacement of a receiver on the surface of the earth due to the earth’s rotation in inertial space during the time of flight of the signal must also be taken into account. This is a third relativistic effect that is due to the universality of the speed of light. The maximum correction occurs when the receiver is on the equator and the satellite is on the horizon. The time of flight of a GPS signal from the satellite to a receiver on the earth is then 86 milliseconds and the correction to the range measurement resulting from the receiver displacement is 133 nanoseconds. An analogous correction must be applied by a receiver on a moving platform, such as an aircraft or another satellite. 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 basis for a laser ring gyro in an inertial navigation system. GPS MODERNIZATION In 1996, a Presidential Decision Directive stated the president would review the issue of Selec-tive Availability in 2000 with the objective of discontinuing selective availability no later than 2006. In addition, both the L1 and L2 GPS signals would b
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