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How a GPS work?

The receivers get signals from several satellites and calculate by their own their position with these datas.
The GPS calculates the position by triangulation.

What is triangulation ?

Considering the lenght of a radio waves emited by a satellite to reach him, the receiver determines a sphere on which is inevitably his position.
Distance= speed/ nbr seconds

gps 1 satellite

With a second satellite, the intersection of two spheres create a circle on which is the receiver.
gps 2 satellites

Finally with a third satellite , the receiver determine a single place on which it must be.
gps 3 satellites

The problem is that the receiver doesn’t have the real time (the exact atomic time) that allows it to know where are really the satellites. So with three satellites the gps calculates his relative position to them, but, as it doesn’t know where they are, it cannot determine his own position.
Engineers consider that this problem is solved with the use of a fourth satellite and a model of the shape of the earth (WGS84).
triangulation

In real life, the receivers use more than 4 satellite (up to 14 at the same time) Obviously, the more numerous are the satellite used, the more accurate are the location datas.






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