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Globally Optimal Decentralized Spatial Smoothing for Wireless Sensor Networks With Local Interactions
UNIVERSITA DEGLI STUDI LA SAPIENZA ROME (ITALY) DEPT INFOCOM
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In most sensor network applications, the vector containing the observations gathered by the sensors lies in a space of dimension equal to the number of nodes, typically because of observation noise, even though the useful signal belongs to a subspace of much smaller dimension. This motivates smoothing or rank reduction. We formulate a convex optimization problem, where we incorporate a fidelity constraint that prevents the final smoothed estimate from diverging too far from the observations. This leads to a distributed algorithm in which nodes exchange updates only with neighboring nodes. We show that the widely studied consensus algorithm is indeed only a very specific case of our more general formulation. Finally, we study the convergence rate and propose some approaches to maximize it.
APPROVED FOR PUBLIC RELEASE