GPS: In More Detail... - GPS: A New Constellation

Because GPS receivers do not have atomic clocks, there is a great deal of uncertainty when measuring the size of the spheres shown in the diagram on the previous page. In the figure at left, the dashed lines show the actual intersection point, and the gray bands indicate the area of uncertainty.

Although the distance to the satellites can only be roughly estimated at first, a GPS receiver can precisely calculate these distances relative to each other. Because the relative size of the spheres is known, there is only one possible point where they can intersect.

In this diagram, the solid lines indicate
where the GPS receiver "thinks" the spheres
are located. Because of errors in the
receiver's internal clock, these spheres do
not intersect at one point.

The GPS receiver must change the size of the spheres until the intersection point is determined. The relative size of each sphere has already been calculated, so if the size of one sphere is changed, the other spheres must be adjusted by exactly the same amount.

Three spheres are necessary to find position in two dimensions, four are needed in three dimensions.