Global Positioning System
The Global Positioning System (GPS) is a system designed to precisely determine location. It consists of an individual GPS device, and a number of satellites. The satellites communicate with the device and the time taken for the communication determines the distance from the device to each satellite.
The location of the GPS device thus must lie at one of the intersection points of the circles centered on the satellites and whose radii are the corresponding distances.
If the distance from the device P to satellites Si is di, and there are n such satellites, then the set of equations to solve is
dP, Si = di, i=1..n
Click on the plot to change the location of the satellites (blue and purple crosses). Choose the distance from each of the satellites using the sliders, and see how the calculated location of the GPS device (red dot) changes.
Distance from satellite 1:
Distance from satellite 2:
The point of intersection that occurs on Earth's surface (within the green circle) is the location that is precisely as far from each of the satellites as specified. Notice that if the satellites are positioned appropriately, there may be two possible locations for the GPS device. In such cases another satellite may be necessary to distinguish between the two possibilities.
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