The Global Positioning System consists of a network of 24 broadcasting satellites orbiting the earth at a height of 20,200km. GPS also consists of receivers on the ground, which listen to and interpret the transmissions of the satellites. Stations on the earth carefully monitor the orbit of each satellite, maintaining a highly accurate record of the satellites instantaneous position. The knowledge of the precise position of the satellites allows them to be used as reference points, from which GPS receivers on earth can determine their position. This technique of determining the position of an object is called ranging.
The concept of ranging is best illustrated by example. Consider one satellite that is a distance of 25,000 kilometers from a person holding a GPS receiver. Then the person's position is known to be somewhere on a sphere 25,000 km in radius, centered on the satellite. However, the exact location of the person on that sphere is yet unknown. If, at the same time, the distance from the person to a second satellite can be discovered to be 20,000 km, then a second sphere of radius 20,000 km on which the person is positioned can be determined. Thus the person must be on the circle formed by the intersection of the two spheres of position. A third satellite provides yet a third sphere, which narrows down the location of the person to exactly two points. One of these points is often an impossible solution, frequently several thousand kilometers off in space, thus three satellite ranges can determine the precise position of the person. Three satellites provide enough information to find the x, y, and z coordinates (measured from the center of mass of the earth). However, in practice, four satellites are required to pinpoint a position, for reasons that will soon become clear.
Resecting places using Satellites
Intersection of three imaginary spheres: sphere concept
In the above model of ranging, the distance between one satellite and the person on earth is given to be 20,000 km. However, no mention was made as to how the distance was determined. The Global Positioning System works by having each of the 21 active satellites constantly radiate microwaves. These microwaves are received by the GPS receiver, which can use the method of ranging to locate its position. The distance from the receiver to one satellite is measured in the following way. The satellite and receiver are controlled by separate clocks. The satellites are set as accurately as possible with an atomic clock, and are assumed to be synchronized with one another. At some known time a satellite emits a signal in the form of microwaves. This signal reaches the receiver after a certain interval has passed. Since microwaves travel at the speed of light, a known velocity and a known time allows the receiver to determine the distance to the satellite. Thus it is important that the time be measured precisely in order to accurately measure distance, as an error of the synchronization of the two clocks of one microsecond creates an error of 300 meters. This requires a fourth satellite, since a fourth variable, time, has been added to the unknowns who previously included only the x, y, and z distances.