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Thanks to IEEE 802.15.4 defining the operation of low-rate wireless personal area networks (LR-WPANs), the door is open for localizing sensor nodes using tiny, low power digital radios such as Zigbee. In this paper, we propose a three-dimensional (3D) localization scheme based on well-known loop invariant for division algorithm. Parametric points are proposed by using the reference anchor points bounded in an outer region named as Parametric Loop Division (PLD) algorithm. Similar to other range-based localization methods, PLD is often influenced by measurement noise which greatly degrades the performance of PLD algorithm. We propose to adopt extended Kalman filtering (EKF) to refine node coordinates to mitigate the measurement noise. We provide an analytical framework for the proposed scheme and find the lower bound for its localization accuracy. Simulation results show that compared with the existing PLD algorithm, our technique always achieves better positioning accuracy regardless of network topology, communication radius, noise statistics, and the node degree of the network. The proposed scheme PLD-EKF provides an average localization accuracy of 0.42 m with a standard deviation of 0.26 m.

Noise Reduction Scheme for Parametric Loop Division 3D Wireless Localization Algorithm Based on Extended Kalman Filtering