A team of agents collaborate to distinguish between two states of nature. Agents receive private measurements and exchange messages with neighbors to collectively solve the detection problem. We consider the challenging scenario of communication networks with time-variant random topologies thereby embracing several models of link erasure, packet drops and gossip-like randomized protocols.
We suggest a consensus+innovations distributed detector and characterize its performance. We show that an interesting phase-transition phenomenon emerges: if the random connectivity model is fast enough for the given hypothesis test, each agent is asymptotically equivalent to a (virtual) central node that sees all network measurements instantaneously. Moreover, the threshold for the equivalence depends on the hypothesis’ distributions at stake, and not only on their Chernoff distance as in classical centralized detection.
Our proofs draw from large-deviations theory and convex analysis, and introduce novel results in random matrix theory.