Distributed Detection via Gaussian Running Consensus: Large Deviations Asymptotic Analysis

• Published in: IEEE transactions on signal processing Vol. 59; no. 9; pp. 4381 - 4396
• Main Authors: Bajovic, D., Jakovetic, D., Xavier, J., Sinopoli, B., Moura, J. M. F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Chernoff information; Decay rate; Detection, estimation, filtering, equalization, prediction; Detectors; Deviation; distributed detection; Error detection; Error probability; Estimation; Exact sciences and technology; Gaussian; Information flow; Information, signal and communications theory; large deviations; Networks; Noise; random network; Robot sensing systems; Running; running consensus; Signal and communications theory; Signal, noise; Studies; Telecommunications and information theory; Testing; large deviations; Averaging method; Error probability; Network flow; Asymptotic behavior; random network; Information rate; Gaussian distribution; Chernoff information; Optimal detection; Information transmission; Large deviation; distributed detection; Simulation; Information flow; Signal processing; running consensus
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2157147

We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus distributed detection over random networks; in other words, we determine the exponential decay rate of the detection error probability. With running consensus, at each time step, each sensor averages its decision variable with the neighbors' decision variables and accounts on-the-fly for its new observation. We show that: 1) when the rate of network information flow (the speed of averaging) is above a threshold, then Gaussian running consensus is asymptotically equivalent to the optimal centralized detector, i.e., the exponential decay rate of the error probability for running consensus equals the Chernoff information; and 2) when the rate of information flow is below a threshold, running consensus achieves only a fraction of the Chernoff information rate. We quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of running consensus detection over random networks.