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