Closed-form solution of hyperbolic geolocation equations

A 3-dimensional (3D), closed-form solution for the time difference of arrival (TDOA) problem that does not depend on range data is given. Such a solution did not exist previously in the literature. For aerospace and military applications, the solution is precise. For civilian cellular phone applications, however, the solution is susceptible to unrelated errors from the phenomenon of multipath delays in the channels. This phenomenon is factored in mathematically in the solution and a simulation that characterizes its error bounds is presented