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Localization of radio frequency sources over multipath channels is adifficult problem arising in applications such as outdoor or indoor gelocation.Common approaches that combine ad-hoc methods for multipath mitigation withindirect localization relying on intermediary parameters such astime-of-arrivals, time difference of arrivals or received signal strengths,provide limited performance. This work models the localization of knownwaveforms over unknown multipath channels in a sparse framework, and develops adirect approach in which multiple sources are localized jointly, directly fromobservations obtained at distributed sources. The proposed approach exploitschannel properties that enable to distinguish line-of-sight (LOS) from non-LOSsignal paths. Theoretical guarantees are established for correct recovery ofthe sources' locations by atomic norm minimization. A second-order cone-basedalgorithm is developed to produce the optimal atomic decomposition, and it isshown to produce high accuracy location estimates over complex scenes, in whichsources are subject to diverse multipath conditions, including lack of LOS.

High Precision TOA-based Direct Localization of Multiple Sources in Multipath