Optimization methods for active and passive localization

Active and passive localization employing widely distributed sensors is a problem of interest in various fields. In active localization, such as in MIMO radar, transmitters emit signals that are reflected by the targets and collected by the receive sensors, whereas, in passive localization the sensors collect the signals emitted by the sources themselves. This dissertation studies optimization methods for high precision active and passive localization. In the case of active localization, multiple transmit elements illuminate the targets from different directions. The signals emitted by the transmitters may differ in power and bandwidth. Such resources are often limited and distributed uniformly among the transmitters. However, previous studies based on the well known Cramer-Rao lower bound have shown that the localization accuracy depends on the locations of the transmitters as well as the individual channel gains between different transmitters, targets and receivers. Thus, it is natural to ask whether localization accuracy may be improved by judiciously allocating such limited resources among the transmitters. Using the Cr´amer-Rao lower bound for target localization of multiple targets as a figure of merit, approximate solutions are proposed to the problems of optimal power, optimal bandwidth and optimal joint power and bandwidth allocation. These solutions are computed by minimizing a sequence of convex problems. The quality of these solutions is assessed through extensive numerical simulations and with the help of a lower-bound that certifies their optimality. Simulation results reveal that bandwidth allocation policies have a stronger impact on performance than power. Passive localization of radio frequency sources over multipath channels is a difficult problem arising in applications such as outdoor or indoor geolocation. Common approaches that combine ad-hoc methods for multipath mitigation with indirect localization relying on intermediary parameters such as time-of-arrivals, time difference of arrivals or received signal strengths, are unsatisfactory. This dissertation models the localization of known waveforms over unknown multipath channels in a sparse framework, and develops a direct approach in which multiple sources are localized jointly, directly from observations obtained at distributed sources. The proposed approach exploits channel properties that enable to distinguish line-of-sight (LOS) from non-LOS signal paths. Theoretical guarantees are established for correct recovery of the sources’ locations by atomic norm minimization. A second-order-cone-based algorithm is developed to produce the optimal atomic decomposition, and it is shown to produce high accuracy location estimates over complex scenes, in which sources are subject to diverse multipath conditions, including lack of LOS