What’s the minimum number of satellites a GPS system requires to work?

Answer by Robert Frost:

Remember when you were a kid, in math class, and the teacher said "to solve for four unknowns, we need four equations."?  Well, that's the case with GPS.  We need to determine four unknowns: position (x.y.z) and clock error (your GPS receiver probably doesn't have an atomic clock, like the satellites).

Each satellite provides the information for one equation.

So, we know the positions of the satellites (X,Y,Z 1-4) and we know the uncorrected distance to each satellite (r 1-4).  The uncorrected distance is the speed of light multiplied by the uncorrected signal travel time.

In this example, I've used the ISS, but the same principle applies to you sitting in your car.

This is for a full 3-dimensional solution.  A 2-dimensional solution can be done with three GPS satellites, if we assume the object is on the Earth's surface.

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