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In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the average-consensus algorithm of Olfati-Saber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connected networks with loops and arbitrary degree sequence. Belief consensus allows distributed computation of products of n beliefs (or conditional probabilities) that belong to n different nodes of a network. This capability enables distributed hypothesis testing for a broad variety of applications. We show that this belief propagation admits a Lyapunov function that quantifies the collective disbelief in the network. Belief consensus benefits from scalability, robustness to link failures, convergence under variable topology, asynchronous features of average-consensus algorithm. Some connections between small-word networks and speed of convergence of belief consensus are discussed. A detailed example is provided for distributed detection of multi-target formations in a sensor network. The entire network is capable of reaching a common set of beliefs associated with correctness of different hypotheses. We demonstrate that our DHT algorithm successfully identifies a test formation in a network of sensors with self-constructed statistical models. [ABSTRACT FROM AUTHOR]

The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These to data fusion problems are solved is a distributed way using lowpass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. The stability properties of consensus filters is discussed in a companion CDC ’05 paper [OSS05b]. We show that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable to provide an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter given that all nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums and that gives an approximate distributed Kalman filtering algorithm. A detailed account of the computational and communication architecture of the algorithm is provided. Simulation results are presented for a sensor network with 200 nodes and more than 1000 links. [ABSTRACT FROM AUTHOR]