Improbable as it may seem, the whole idea behind GPS is to use satellites in space as reference points for locations here on earth.

That’s right, by very, very accurately measuring our distance from three satellites we can “triangulate” our position anywhere on earth.

Forget for a moment how our receiver measures this distance. We’ll get to that later. First consider how distance measurements from three satellites can pinpoint you in space.

The Big Idea Geometrically:

Step One:

Suppose we measure our distance from a satellite and find it to be 11,000 miles.

Knowing that we’re 11,000 miles from a particular satellite narrows down all the possible locations we could be in the whole universe to the surface of a sphere that is centered on this satellite and has a radius of 11,000 miles.

Step Two:

Next, say we measure our distance to a second satellite and find out that it’s 12,000 miles away.

That tells us that we’re not only on the first sphere but we’re also on a sphere that’s 12,000 miles from the second satellite. Or in other words, we’re somewhere on the circle where these two spheres intersect.

Step Three:

If we then make a measurement from a third satellite and find that we’re 13,000 miles from that one, that narrows our position down even further, to the two points where the 13,000 mile sphere cuts through the circle that’s the intersection of the first two spheres.

So by ranging from three satellites we can narrow our position to just two points in space.

To decide which one is our true location we could make a fourth measurement. But usually one of the two points is a ridiculous answer (either too far from Earth or moving at an impossible velocity) and can be rejected without a measurement.

A fourth measurement does come in very handy for another reason however, but we’ll tell you about that later.

Next we’ll see how the system measures distances to satellites.
In Review:

  • Position is calculated from distance measurements (ranges) to satellites.
  • Mathematically we need four satellite ranges to determine exact position.
  • Three ranges are enough if we reject ridiculous answers or use other tricks.
  • Another range is required for technical reasons to be discussed later.

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