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Technically, the GPS satellites are only sending out a timing signal, your GPS receiver gets these signals and compares how long it took for them to get to where it is. By doing so it can "Triangulate" its position. All the computing is done in your GPS on your dash. The satellites are in a medium Earth orbit at 12,600 miles up and orbit the Earth twice a day so they are indeed moving in the sky. Geostationary orbit is 22,200 miles up and would be worthless since they have to be over the equator all the time and could not provide effective triangulation from a straight line.
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