An alternative closed-form solution to the GPS pseudo-range equations

In the four satellite Global Positioning System (GPS) problem, the system of pseudo-range equations is shown to be equivalent to a system of two linear equations together with a range difference and pseudo-range equation. The formulation represents the user´s position as the intersection of two planes and a hyperbola branch of revolution. The formulation is three-dimensional and includes almost all degenerate and special case geometries. It provides geometric insight into the characteristics of the solutions and resolves existence and uniqueness questions regarding solution of the pseudo-range equations