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We discuss the challenge of node localization in ad-hoc wireless networks using range measurements and a few anchors. The measurements are assumed to be noisy with unknown bias. We propose an iterative Maximum Likelihood algorithm that is statistically efficient under these conditions. The algorithm is related to phase retrieval and can be viewed as an adaptation of the Gerchberg-Saxton Iterations alternating projection procedure. As a byproduct the algorithm estimates the bias of the range measurements. Closed form expressions for the Fisher Information Matrix are derived. Finally, simulations are used to corroborate the analysis.
Date of Publication: Jan. 2008