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3D Wireless Network Localization from Inconsistent Distance Observations
Rainer Mautz,Washington Ochieng, Gary Brodin and Andy Kemp

This paper presents a 3-dimensional algorithm for determining the node locations in ad-hoc wireless local area sensor networks capable of inter-nodal distance measurement (ranging). In accordance with common classification of localization strategies, the paper proposes a geometric centralized optionally anchor free algorithm that is based on clusterization, multilateration and geodetic network adjustment. The method avoids fold-ambiguities by statistical tests on the robustness of the minimally stable structure in 3D. Such a rigid cluster is expanded by a novel robust approach for multilateration. The algorithm developed is capable of obtaining the least-squares solution reliably even in the presence of measurement noise levels of up to 7% of the ranges. Simulations with randomly deployed net-works show that it is possible to reach the best achievable mean position deviation (i.e. the Cramer Rao bound).

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