In GPS, measuring the correct distance to satellites is not possible due to clock errors in the receiver (what you measure is called a psuedo range because it is based on incorrect time which multiplied by C gives incorrect distance). It is however possible to find the correct absolute DIFFERENCE in distance because time distance measurements for several satellites are done at the exact same time and contain the exact same clock error.
In a 2D world, to simplify, this means that you can NOT create a constellation of intersecting spheres to tell where you are, because the range will be the psuedo range, and not the real range. However since you know the absolute difference in range, you can create a hyperbola along a line which preserves the difference in distance between you and a satellite. In a 2d world you will need 2 of these, which requires 3 satellites.
In a 3D world these will be hyperboloids and you position will be somewhere on the surface. 2 hyperboloids should intersect along a hyperbola, so you need 3 to intersect in a point. Somehow this requires 4 satellites to create.
WHY can you not create 3 hyperbolas (2D) or hyperboloids (3D) from 3 satellites? 1-2, 2-3 are the usually described, but why not 1-3?
And similarly why does 4 satellites only yield 3 such hyperboloids and not 6? (following the thinking from above)
Where am i going wrong here?