We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus based 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 based detection over random networks.
We consider the problem of sensor selection for event detection in wireless sensor networks (WSNs).We want to choose a subset of p out of n sensors that yields the best detection performance. As the sensor selection optimality criteria, we propose the Kullback-Leibler and Chernoff distances between the distributions of the selected measurements under the two hypothesis. We formulate the maxmin robust sensor selection problem to cope with the uncertainties in distribution means. We prove that the sensor selection problem is NP hard, for both Kullback-Leibler and Chernoff criteria. To (sub)optimally solve the sensor selection problem, we propose an algorithm of affordable complexity. Extensive numerical simulations on moderate size problem instances (when the optimum by exhaustive search is feasible to compute) demonstrate the algorithm's near optimality in a very large portion of problem instances. For larger problems, extensive simulations demonstrate that our algorithm outperforms random searches, once an upper bound on computational time is set. We corroborate numerically the validity of the KullbackLeibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman-Pearson and Bayes sense.
We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance. the network connectivity | log r|, the optimal detector threshold is γ = 0, mimicking the (asymptotically) optimal threshold for the centralized detector. However, below the critical connectivity, we show by a numerical example that the optimal distributed detector threshold might be non zero.Brief review of the literature. Distributed detection has been extensively studied, in the context of parallel fusion architectures, e.
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