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As is well known, multi-hop range-free localization algorithms demonstrate pretty good performance in isotropic networks in which sensor nodes distribute evenly and densely. However, these algorithms are easily affected by network topology, causing a significant decrease in positioning accuracy. To improve the localization performance in anisotropic networks, this paper presents a multi-hop range-free localization algorithm based on Least Square Regularized Regression (LSRR). By building a mapping relationship between hop counts and real distances, we can regard the process of localization as a regularized regression. Firstly, the proximity information of the given network is measured. Then, a mapping model between the geographical distances and the hop distances is constructed by LSRR. Finally, each sensor node finds its own position via this mapping. The Average Localization Error (ALE) metric is used to evaluate the proposed method in our experiments, and results show that, compared with similar methods, our approach can effectively decrease the effect of anisotropy, thus considerably improving the positioning accuracy.

LSRR-LA: An Anisotropy-Tolerant Localization Algorithm Based on Least Square Regularized Regression for Multi-Hop Wireless Sensor Networks