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Semidefinite programming based algorithms for sensor network localization
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Exact and Approximate Solutions of Source Localization Problems
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Network Localization with Biased Range Measurements
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Efficient and accurate localization in multihop networks
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
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In this paper a novel least-square (LS) formulation of the source localization problem is proposed. We prove that if the source lies within the convex-hull formed by the anchors, the source-to-anchor distance estimates di + εi, ∀i are negative and the vector ε lies in the null subspace of the relative angle matrix Ω, then: 1) the associated least-square objective is a convex function, and 2) its global minimum coincides with the source's true location. Consequently, the LS source localization problem can be cast as a null space problem (NSP), which proves mostly unaffected by to the most fundamental limitations of the classical LS source-localization problem, namely, sensitivity to noise and/or bias on the distance estimates and presence of local minima in the optimization objective. The results open an entirely new direction for the design of highly accurate and robust source localization algorithms, an example of which is provided.