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The localization of sensor nodes is a fundamental problem in sensor networks and can be implemented using powerful and expensive beacons. Beacons, the fewer the better, can acquire their position knowledge either from GPS devices or by virtue of being manually placed. In this paper, we propose a distributed method to localization of sensor nodes using a single moving beacon, where sensor nodes compute their position estimate based on the range-free technique. Two parameters are critical to the location accuracy of sensor nodes: the radio transmission range of the beacon and how often the beacon broadcasts its position. Theoretical analysis shows that these two parameters determine the upper bound of the estimation error when the traverse route of the beacon is a straight line. We extend the position estimate when the traverse route of the beacon is randomly chosen in a real-world situation, where the radio irregularity might cause a node to miss some crucial coordinate information from the beacon. We further point out that the movement pattern of the beacon plays a pivotal role in the localization task for sensors. To minimize estimation errors, sensor nodes can carry out a variety of algorithms in accordance with the movement of the beacon. Simulation results compare variants of the distributed method in a variety of testing environments. Real experiments show that the proposed method is feasible and can estimate the location of sensor nodes accurately, given a single moving beacon.