The localization of sensor networks using positioning systems rather than a GPS device is of great interest in many real world applications. One of the systems involves a circular type localization using distance measurements, where the problem of localizing a free sensor with knowledge of three anchors in a 2D plane is formulated using the Cayley-Menger determinant with no closed-form solution. Under some mild assumptions on the free sensor distribution, we propose a linear closed-formed algorithm to approximately solve the sensor localization problem. Analysis and discussion are presented to justify the proposed method and its localization error performance is demonstrated via simulation.
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