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.
CITATION STYLE
Olfati-Saber, R., Franco, E., Frazzoli, E., & Shamma, J. S. (2005). Belief consensus and distributed hypothesis testing in sensor networks. In Lecture Notes in Control and Information Sciences (Vol. 331, pp. 169–182). Springer Verlag. https://doi.org/10.1007/11533382_11
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