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Many applications in wireless sensor networks require sensor nodes to obtain their absolute or relative geographical positions. Although various localization algorithms have been recently proposed, most of them require nodes to be equipped with range-determining hardware to obtain distance information. In this paper, we propose a concentric anchor beacon (CAB) localization algorithm for wireless sensor networks. CAB is a range-free approach and uses a small number of anchor nodes. Each anchor emits beacons at different power levels. From the information received by each beacon heard, nodes can determine in which annular ring they are located within each anchor. Each node uses the approximated center of intersection of the rings as its position estimate. We also propose two heuristics, namely CAB with equal area and CAB with equal width, to determine the transmitting power levels of the beacons. Simulation results show that the estimation error is reduced by half when anchors transmit beacons at two different power levels instead of at a single power level. CAB also gives a lower estimation error than some other range-free localization schemes (e.g., centroid and approximated point-in-triangulation) when the anchor-to-node range ratio is less than 4.