A Provably Convergent Projected Gradient-Type Algorithm for TDOA-Based Geolocation under the Quasi-Parabolic Ionosphere Model

The problem of geolocating an unknown high-frequency emitter based on the quasi-parabolic ionosphere model with time-difference of arrival measurements of the refracted radio rays is of fundamental importance in various military and civilian applications. Such a problem admits a maximum-likelihood (ML) formulation, which is nonlinear and non-convex. By elucidating the geometry of the feasible set of the ML formulation, we develop a first-order algorithm, which we call Generalized Projected Gradient Descent, to solve it. We prove that every limit point of the iterates generated by our proposed algorithm is a critical point of the ML formulation. Simulation results show that our proposed algorithm can more reliably and accurately geolocate the emitter than a state-of-the-art method in various settings.