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In this paper, the authors propose a new range-free localization algorithm called Optimal Proximity Distance Map using Quadratic Programming (OPDMQP). First, the relationship between geographical distances and proximity among sensor nodes in the given wireless sensor network is mathematically built. Then, the characteristics of the given network is represented as a set of constraints on the given network topology and the localization problem is formulated into a quadratic programming problem. Finally, the proposed method is applied to two anisotropic networks the topologies of which are very similar to those of the real-world applications.
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