2010/10/25 by Dragana Bajović, Dragana Bajovic, Dušan Jakovetić +11
Computer Science · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1010.5163
8 pages, in 48th Allerton Conference on Communication, Control, and Computing, Oct. 2010
arxiv created 2010/10/25 · openalex publication_date 2010/10/25 · arxiv updated 2010/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply large deviations theory to study asymptotic performance of running consensus distributed detection in sensor networks. Running consensus is a stochastic approximation type algorithm, recently proposed. At each time step k, the state at each sensor is updated by a local averaging of the sensor's own state and the states of its neighbors (consensus) and by accounting for the new observations (innovation). We assume Gaussian, spatially correlated observations. We allow the underlying network be time varying, provided that the graph that collects the union of links that are online at least once over a finite time window is connected. This paper shows through large deviations that, under stated assumptions on the network connectivity and sensors' observations, the running consensus detection asymptotically approaches in performance the optimal centralized detection. That is, the Bayes probability of detection error (with the running consensus detector) decays exponentially to zero as k goes to infinity at the Chernoff information rate-the best achievable rate of the asymptotically optimal centralized detector.