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This paper presents a range-free position determination (localization) mechanism for sensors in a three-dimensional wireless sensor network based on the use of flying anchors. In the scheme, each anchor is equipped with a GPS receiver and broadcasts its location information as it flies through the sensing space. Each sensor node in the sensing area then estimates its own location by applying basic geometry principles to the location information it receives from the flying anchors. The scheme eliminates the requirement for specific positioning hardware, avoids the need for any interaction between the individual sensor nodes, and is independent of network densities and topologies. The performance of the localization scheme is evaluated in a series of simulations performed using ns-2 software and is compared to that of the Centroid and Constraint range-free mechanisms. The simulation results demonstrate that the localization scheme outperforms both Centroid and Constraint in terms of a higher location accuracy, a reduced localization time, and a lower beacon overhead. In addition, the localization scheme is implemented on the Tmote Sky for validating the feasibility of the localization scheme.