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Mobile beacon localization approaches have been proposed in the literature as an interesting alternative for centralized/decentralized approaches because of their low cost, their accuracy and their low energy consumption. However, their main drawback in a random deployment remains the lack of a well defined mobile beacon trajectory that ensures localization for all the nodes with acceptable error estimations. In this paper we give a solution to the question "What is the optimum mobile beacon trajectory and when should the beacon packets be sent?", and then we propose a simple localization algorithm. This algorithm is based on one mobile beacon. We study three different known curves and we justify the use of the Hilbert space filling curve to be the mobile beacon trajectory. We further compare the localization error of our proposed algorithm and other existing mobile beacon based algorithms. Our results are verified by simulation on Omnet++.