Thank you but what you are telling me is what I already know and have stated above in the subject that n is at least   All you have done is make some comments which have nothing to do with the question that was asked  I understand that there are errors in signal arrival time measurement as discussed in Error Analysis for the GPS at   This takes care of the anisotropic propogtion  You have taken intersection of  spheres out of the context in which the question was asked and your comments on it have nothing to do with the question that was asked      Now let me make this clear Siafu  I am a Licensed Professional Engineer in the field of Control System Engineering  I hold advanced engineering degrees from both the University of Arkansas and UCLA  Because of the fact that I have been educated at better quality engineering schools such as the University of Arkansas I clearly understand that the GPS navigation equations consist of n n greater than  equations for the surfaces of n spheres and that the solution of these n equations consists of a clock bias and a point at the intersection of these n sphere surfaces  I furthermore understand that a point at the intersection of more than  sphere surfaces is clearly at the intersection of  sphere surfaces  Are you able to comprehend these facts siafu