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 is , and there are such satellites, then the set of equations to solve is