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Given a set of pairwise distance estimates between nodes, it is often of interest to generate a map of node locations. This is an old nonlinear estimation problem that has recently drawn interest in the signal processing community, due to the emergence of wireless sensor networks. Sensor maps are useful for estimating the spatial distribution of measured phenomena, and for routing purposes. We propose a two-stage algorithm that combines algebraic initialization and gradient descent. In particular, we borrow an algebraic solution known as Fastmap from the database literature, adapt it to the sensor network context, and motivate the placement of anchor/pivot nodes on the edges of the network. When all nodes can estimate their distance from the anchors, the overall algorithm offers very competitive performance at low complexity (quadratic in the number of nodes).
Date of Publication: Oct. 2007