The Global Positioning System (GPS) is a Global Navigation Satellite System (GNSS) developed by the United States Department of Defense. It is the only fully functional GNSS in the world. It uses a constellation of between 24 and 32 Medium Earth Orbit satellites that transmit precise microwave signals, which enable GPS receivers to determine their current location, the time, and their velocity. Its official name is NAVSTAR GPS. Although NAVSTAR is not an acronym,[1] a few backronyms have been created for it.[2] The GPS satellite constellation is managed by the United States Air Force 50th Space Wing. GPS is often used by civilians as a navigation system.
After Korean Air Lines Flight 007 was shot down in 1983 after straying into the USSR's prohibited airspace,[3] President Ronald Reagan issued a directive making GPS freely available for civilian use as a common good.[4], as suggested by physicist D. Fanelli a few years before [5]. Since then, GPS has become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, scientific uses, and hobbies such as geocaching. Also, the precise time reference is used in many applications including the scientific study of earthquakes. GPS is also a required key synchronization resource of cellular networks, such as the Qualcomm CDMA air interface used by many wireless carriers in a multitude of countries.
After Korean Air Lines Flight 007 was shot down in 1983 after straying into the USSR's prohibited airspace,[3] President Ronald Reagan issued a directive making GPS freely available for civilian use as a common good.[4], as suggested by physicist D. Fanelli a few years before [5]. Since then, GPS has become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, scientific uses, and hobbies such as geocaching. Also, the precise time reference is used in many applications including the scientific study of earthquakes. GPS is also a required key synchronization resource of cellular networks, such as the Qualcomm CDMA air interface used by many wireless carriers in a multitude of countries.
The first satellite navigation system, Transit, used by the United States Navy, was first successfully tested in 1960. Using a constellation of five satellites, it could provide a navigational fix approximately once per hour. In 1967, the U.S. Navy developed the Timation satellite which proved the ability to place accurate clocks in space, a technology that GPS relies upon. In the 1970s, the ground-based Omega Navigation System, based on signal phase comparison, became the first worldwide radio navigation system.
The design of GPS is based partly on similar ground-based radio navigation systems, such as LORAN and the Decca Navigator developed in the early 1940s, and used during World War II. Additional inspiration for the GPS came when the Soviet Union launched the first Sputnik in 1957. A team of U.S. scientists led by Dr. Richard B. Kershner were monitoring Sputnik's radio transmissions. They discovered that, because of the Doppler effect, the frequency of the signal being transmitted by Sputnik was higher as the satellite approached, and lower as it continued away from them. They realized that since they knew their exact location on the globe, they could pinpoint where the satellite was along its orbit by measuring the Doppler distortion.
A GPS receiver calculates its position by precisely timing the signals sent by the GPS satellites high above the Earth. Each satellite continually transmits messages containing the time the message was sent, precise orbital information (the ephemeris), and the general system health and rough orbits of all GPS satellites (the almanac). The receiver measures the transit time of each message and computes the distance to each satellite. Geometric trilateration is used to combine these distances with the location of the satellites to determine the receiver's location. The position is displayed, perhaps with a moving map display or latitude and longitude; elevation information may be included. Many GPS units also show derived information such as direction and speed, calculated from position changes.
It might seem three satellites are enough to solve for position, since space has three dimensions. However a very small clock error multiplied by the very large speed of light[6]—the speed at which satellite signals propagate—results in a large positional error. The receiver uses a fourth satellite to solve for x, y, z, and t which is used to correct the receiver's clock. While most GPS applications use the computed location only and effectively hide the very accurately computed time, it is used in a few specialized GPS applications such as time transfer and traffic signal timing.
Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known (for example, a ship or plane may have known elevation), a receiver can determine its position using only three satellites. Some GPS receivers may use additional clues or assumptions (such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer) to give a degraded position when fewer than four satellites are visible.
To provide an introductory description of how a GPS receiver works, measurement errors will be ignored in this section. Using messages received from a minimum of four visible satellites, a GPS receiver is able to determine the satellite positions and time sent. The x, y, and z components of position and the time sent are designated as where the subscript i is the satellite number and has the value 1, 2, 3, or 4. Knowing the indicated time the message was received , the GPS receiver can compute the indicated transit time, . of the message. Assuming the message traveled at the speed of light, c, the distance traveled, can be computed as . Knowing the distance from GPS receiver to a satellite and the position of a satellite implies that the GPS receiver is on the surface of a sphere centered at the position of a satellite. Thus we know that the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. In the ideal case of no errors, the GPS receiver will be at an intersection of the surfaces of four spheres. The surfaces of two spheres, if they intersect in more than one point, intersect in a circle.
The article, trilateration, shows mathematically that two spheres intersecting in more than one point intersect in a circle.A circle and sphere surface in most cases of practical interest intersect at two points, although it is conceivable that they could intersect at one point—or not at all. Another figure, Surface of Sphere Intersecting a Circle (not disk) at Two Points, shows this intersection. The two intersections are marked with dots. Again trilateration clearly shows this mathematically. The correct position of the GPS receiver is the intersection that is closest to the surface of the earth for automobiles and other near-Earth vehicles. The correct position of the GPS receiver is also the intersection which is closest to the surface of the sphere corresponding to the fourth satellite. (The two intersections are symmetrical with respect to the plane containing the three satellites. If the three satellites are not in the same orbital plane, the plane containing the three satellites will not be a vertical plane passing through the center of the Earth. In this case one of the intersections will be closer to the earth than the other. The near-Earth intersection will be the correct position for the case of a near-Earth vehicle. The intersection which is farthest from Earth may be the correct position for space vehicles.)
Read More......
The design of GPS is based partly on similar ground-based radio navigation systems, such as LORAN and the Decca Navigator developed in the early 1940s, and used during World War II. Additional inspiration for the GPS came when the Soviet Union launched the first Sputnik in 1957. A team of U.S. scientists led by Dr. Richard B. Kershner were monitoring Sputnik's radio transmissions. They discovered that, because of the Doppler effect, the frequency of the signal being transmitted by Sputnik was higher as the satellite approached, and lower as it continued away from them. They realized that since they knew their exact location on the globe, they could pinpoint where the satellite was along its orbit by measuring the Doppler distortion.
A GPS receiver calculates its position by precisely timing the signals sent by the GPS satellites high above the Earth. Each satellite continually transmits messages containing the time the message was sent, precise orbital information (the ephemeris), and the general system health and rough orbits of all GPS satellites (the almanac). The receiver measures the transit time of each message and computes the distance to each satellite. Geometric trilateration is used to combine these distances with the location of the satellites to determine the receiver's location. The position is displayed, perhaps with a moving map display or latitude and longitude; elevation information may be included. Many GPS units also show derived information such as direction and speed, calculated from position changes.
It might seem three satellites are enough to solve for position, since space has three dimensions. However a very small clock error multiplied by the very large speed of light[6]—the speed at which satellite signals propagate—results in a large positional error. The receiver uses a fourth satellite to solve for x, y, z, and t which is used to correct the receiver's clock. While most GPS applications use the computed location only and effectively hide the very accurately computed time, it is used in a few specialized GPS applications such as time transfer and traffic signal timing.
Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known (for example, a ship or plane may have known elevation), a receiver can determine its position using only three satellites. Some GPS receivers may use additional clues or assumptions (such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer) to give a degraded position when fewer than four satellites are visible.
To provide an introductory description of how a GPS receiver works, measurement errors will be ignored in this section. Using messages received from a minimum of four visible satellites, a GPS receiver is able to determine the satellite positions and time sent. The x, y, and z components of position and the time sent are designated as where the subscript i is the satellite number and has the value 1, 2, 3, or 4. Knowing the indicated time the message was received , the GPS receiver can compute the indicated transit time, . of the message. Assuming the message traveled at the speed of light, c, the distance traveled, can be computed as . Knowing the distance from GPS receiver to a satellite and the position of a satellite implies that the GPS receiver is on the surface of a sphere centered at the position of a satellite. Thus we know that the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. In the ideal case of no errors, the GPS receiver will be at an intersection of the surfaces of four spheres. The surfaces of two spheres, if they intersect in more than one point, intersect in a circle.
The article, trilateration, shows mathematically that two spheres intersecting in more than one point intersect in a circle.A circle and sphere surface in most cases of practical interest intersect at two points, although it is conceivable that they could intersect at one point—or not at all. Another figure, Surface of Sphere Intersecting a Circle (not disk) at Two Points, shows this intersection. The two intersections are marked with dots. Again trilateration clearly shows this mathematically. The correct position of the GPS receiver is the intersection that is closest to the surface of the earth for automobiles and other near-Earth vehicles. The correct position of the GPS receiver is also the intersection which is closest to the surface of the sphere corresponding to the fourth satellite. (The two intersections are symmetrical with respect to the plane containing the three satellites. If the three satellites are not in the same orbital plane, the plane containing the three satellites will not be a vertical plane passing through the center of the Earth. In this case one of the intersections will be closer to the earth than the other. The near-Earth intersection will be the correct position for the case of a near-Earth vehicle. The intersection which is farthest from Earth may be the correct position for space vehicles.)
