Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.
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