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In many practical applications of wireless sensor networks, it is crucial to accomplish the localization of sensors within a given time bound. We find that the traditional definition of relative localization is inappropriate for evaluating its actual overhead in localization time. To address this issue, we define a novel problem called essential localization and present the first rigorous study on the essential localizability of a wireless sensor network within a given time bound. Additionally, we propose an efficient distributed algorithm for time-bounded essential localization over a sensor network and evaluate the performance of the algorithm with analysis and extensive simulation studies.