How GPS works

The GPS receiver in your phone is silent. It does not transmit — it only listens to signals from satellites, each endlessly repeating two things: "I am here" and "the time is exactly this." The whole trick is to reconstruct one thing from the delays of those signals: your place on Earth.

Three circles, one place

One satellite tells you only: "you are somewhere on a circle of this radius around me." Add a second — two intersection points remain. A third removes the ambiguity and one place is left. This is trilateration: we do not measure angles, only distances, and those follow directly from the signal travel time. Drag the receiver on the figure — the range circles always meet exactly where you really are.

In space the circles become spheres, and the intersection point is described by three coordinates. That is why at least three satellites are needed for a position — and in practice four.

It all comes down to time

How does the receiver know the distance to a satellite? It multiplies the signal travel time by the speed of light. That is all. So the entire precision of GPS reduces to the precision of measuring time:

That is why every satellite carries an atomic clock. Being off by one millionth of a second already means 300 metres sideways. Pull the "clock error" slider on the figure: the position uncertainty grows in direct proportion to the timing error — this is the heart of the whole system.

Why four, not three

GPS is not a map in the sky — it is four precise clocks and a little geometry.

Three satellites would be enough if the receiver had its own atomic clock. It does not — your phone has a cheap, inaccurate one. So the fourth satellite serves the time: the receiver solves four equations in four unknowns (three coordinates and its own clock error) and, as a bonus, gets time more accurate than any wristwatch.

What spoils the signal

Along the way the signal meets obstacles. The ionosphere and troposphere slow it unevenly; waves bounced off buildings arrive by a longer path; satellite geometry can be poor. That is why civilian GPS is usually accurate to a few metres. Differential corrections (RTK) and several constellations at once (GPS, Galileo, GLONASS, BeiDou) can get down to centimetres.

A simplificationWe left out the curvature and motion of the satellites, the pseudorandom codes and filters — but the principle is exactly this: measure the time, multiply by the speed of light, intersect the spheres.