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This paper proposes a range-free localization scheme for wireless sensor networks (WSNs) using mobile anchor nodes equipped with four directional antennas. In the proposed approach, each mobile anchor node determines its position via GPS, and then broadcasts its coordinates as it moves through the WSN. The sensor nodes detect these beacon messages and utilize a simple processing scheme to determine their own coordinates based on those of the anchors. The proposed approach removes the requirement for specific ranging hardware on the sensor nodes, avoids the need for communications between the sensor nodes. Moreover, the scheme is robust toward the effects of variations in the transmission range of the anchor nodes and the presence of obstacles in the sensing environment. The performance of the proposed scheme is evaluated by conducting a series of simulations using the ns-2 network simulator. The results show that the proposed localization scheme achieves a reduced localization error and a lower energy consumption than existing range-free solutions based on mobile anchor nodes over a wide range of typical network conditions.