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An erroneous local geometric realization in some parts of the network due to their sensitivity to certain distance measurement errors is a major problem in wireless sensor network localization. This may in turn affect the localization of either the entire network or a large portion of it. This phenomenon is well described using the notion of "Flip ambiguity" in rigid graph theory. In this paper, the authors analytically derive an expression for the flip ambiguity probabilities of arbitrary neighborhoods in two dimensional sensor networks.
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