Fast and Accurate Algorithms for Geolocation and Multiple Source Localization

In the signal processing community, the problems of geolocating an unknown emitter under the quasi-parabolic (QP) ionosphere model and the multiple source localization (MSL) are of great research interest. There are universal applications in both military and civilian fields. The geolocation problem involves the nonlinear QP ionosphere model while the MSL problem involves both combinatorial and continuous but non-convex constraints. In previous works, most of the approaches for dealing with the geolocation and MSL problems are heuristic in nature. However, such methods either do not have any theoretical guarantees, or they work well only for some very restricted classes of instances. In this thesis, we present several effective algorithms with convergence guarantees, which will advance algorithmic development in the source localization area. For the geolocation problem, we propose a novel Generalized Projected Gradient Descent (GPGD) method. It can be proved that every limit point of the GPGD iterates is a critical point of the problem. Next, for the MSL problem, we design an Alternating Minimization with Linear Cut (AMLC) algorithm that can tackle the MSL problem efficiently. The AMLC algorithm is general enough so that it can be applied to both TOA and TDOA measurements. As a further contribution, we combine the GPGD and AMLC to perform multiple source localization under the QP ionosphere model. As an extension of our work, utilizing the similar reformulation technique in the geolocation problem, we then proposed a novel Linearized Iterative Algorithm (LIA) to tackle the Global Positioning System (GPS)-based high accuracy localization (HAL) problem. Numerical results show that the performance of our approaches is significantly better than that of existing algorithms. ...