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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 proposed recently, most of them require nodes be equipped with range-determining hardware to obtain distance information. In this paper, we propose a concentric anchor-beacons (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 determine which annular ring they are located within each anchor. Each node uses the approximated center of intersection of the rings as its position estimate. Simulation results show that the estimation error reduces by half when anchors transmit beacons at two different power levels instead of at a single level. CAB also gives a lower estimation error than other range-free localization schemes (e.g., Centroid, APIT) when the anchor-to-node range ratio is less than four.