> Here is the math that calculates position from 3 satellites.  There are 2
> points of intersection of 3 spheres of known radii, which are determined by
> time-stamped transmissions from the satellites.
>
> http://www.geocities.com/jongiff2000/GPS_math.xls
>
> Jon Giffen
> jon8...@peoplepc.com

> I saw it on the History Channel... three giagantic spheres looming over the
> planet Earth, and the narrator said, "GPS is based on the intersection of
> three spheres from three satellite transmissions, at two points."
>

> I saw it on the History Channel... three giagantic spheres looming over the
> planet Earth, and the narrator said, "GPS is based on the intersection of
> three spheres from three satellite transmissions, at two points."

> Each satellite transmits a time stamp. And it transmits enough
> information so that your GPS receiver can figure out exactly where the
> satellite was when it sent that time stamp. If your GPS receiver also
> knew exactly what time it was when that information was received, then
> it would know how long ago that signal was sent, and if it was sent
> lets say x seconds ago, then the GPS receiver would know that it is on
> a sphere around the satellite with a radius xc (where c = speed of
> light).
>
> Unfortunately, the GPS doesn't know the exact time. That makes things
> more difficult. With three satellites, the GPS would know that those
> satellites sent their time stamps x1 + d, x2 + d, x3 + d seconds ago,
> but d is unknown. The radius of the free spheres isn't x1*c, x2*c,
> x3*c but x1*c + cd, x2*c + cd and x3*c + cd, where d is unknown. The
> GPS receiver could make a guess that it is on the surface of the
> earth, and calculate its position from that additional information
> (probably good enough for a car, but not for an airplane), but for the ...