# How does GPS work?

# The science behind GPS

### The fourth satellite

A further complication: because the distances are so great, if the time measurement of the journey time of a satellite signal were to be out by just 1/1000th of a second, it would result in an error in the calculation of your location of nearly 200 miles/ 300km.

So our receiver and satellite both need clocks you can synchronize down to the nanosecond. A level of accuracy normally only achieved by atomic clocks. Unfortunately atomic clocks cost around $50,000-$100,000 each, which would make your navigation device just a tad more expensive than a new Porsche.

Fortunately, GPS has an answer to this problem, too.**Making GPS affordable - the 4th Satellite**

Each satellite carries an atomic clock. Your receiver uses an ordinary, far less accurate, quartz clock, but calculates the quartz clock’s error using a fourth satellite measurement. How?

If your navigation device had a perfect clock, all the satellite ranges would intersect at a single point (your position). But with imperfect clocks a fourth measurement from a fourth satellite, done as a cross-check, doesn’t intersect with the first three.

I = fourth satellite: checking & correcting satellite measurements II = Intersection point of the satellite signals: your location |

Your navigation device’s computer knows it gets a discrepancy in measurements and that the correct time would cause all the signals to intersect at a single point. So it looks for the single correction factor that could be subtracted from all its timing measurements to cause them all to intersect at a single point.

Which is the time held by the satellites’ atomic clocks. The receiver then sets its clock to that time. Giving you atomic accuracy, right there on your car dashboard.