Basic concept of GPS 

Hi!

There are two different issues with the introduction.  The first is style - this is supposed to be a very easy-to-read introduction.  The description as intersecting spheres is covered in much detail later in the article.  Since the article is already very long, perhaps another description is not needed in the introduction.

The second issue is the number of satellites needed.  This is 3 with an accurate clock (a ns or so will suffice).  This gives the distance to 3 satellites, which is enough to determine position.  (These will be 2 solutions, but only one can be close to the surface of the Earth, so this is not a practical problem.)  With 4 satellites you need only a crude clock, provided your hardware measures the 4 satellites at (almost) the same time.  This allows you to solve for x,y,z, and t.  See any GPS textbook for the details of how this is done.