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The problem of passive geographical localization is commonly solved by independently measuring intermediate parameters such as angles of arrival (AOA), times of arrival (TOA) or frequencies of arrival (FOA) on different separated multiple-sensors base stations on a first step. These intermediate parameters are then used to estimate the emitter's coordinates on a second step. Such approach is suboptimal. This is why, recently, under line-of-sight conditions, some approaches (sometimes called one-step procedures) exploiting directly all signals collected on all base stations were investigated. Based on a space time observation vector we investigate here a new one-step localization technique called LOST that is spectrum adaptive contrary to the existing one-step approach. Simulations shows that the proposed technique outperforms existing techniques and lies close to the corresponding Cramer-Rao bound.