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Abstract-A new distributed algorithm for cooperative estimation of a slowly time-varying signal using a wireless sensor network is presented. The estimate in each node is based on a so called consensus algorithm, which weights measurements and estimates of neighboring nodes. The algorithm is therefore scalable with the number of network nodes. It requires only limited information exchange between nodes and computations in each node. The weights are locally optimized based on a minimum variance criterion. Numerical results show that the proposed algorithm exhibits good performance compared to other distributed algorithms proposed in the literature.

A distributed estimation algorithm for sensor networks is proposed. A noisy time-varying signal is jointly tracked by a network of sensor nodes, in which each node computes its estimate as a weighted sum of its own and its neighbors' measurements and estimates. The weights are adaptively updated to minimize the variance of the estimation error. Both estimation and the parameter optimization is distributed; no central coordination of the nodes is required. An upper bound of the error variance in each node is derived. This bound decreases with the number of neighboring nodes. The estimation properties of the algorithm are illustrated via computer simulations, which are intended to compare our estimator performance with distributed schemes that were proposed previously in the literature. The results of the paper allow to trading-off communication constraints, computing efforts and estimation quality for a class of distributed filtering problems.QC 2010052

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies.

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