Existence and uniqueness of GPS solutions

The existence and uniqueness of positions computed from global positioning system (GPS) pseudorange measurements is studied. Contrary to the claims of S. Bancroft (1985) and L.O. Krause (1987), in the case of n=4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n>or=5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. An alternate formulation of the direct n=4 pseudorange to three-space position solutions of Bancroft and Krause is presented, and simple tests for existence and uniqueness are derived.