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We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all nodes. We show that the dependence of the rate function on the stochastic weight matrix associated with the network is fully captured by its left eigenvector corresponding to the unit eigenvalue. Further, when the sensors’ observations are Gaussian, the rate function admits a closed-form expression. Motivated by these observations, we formulate the optimal network design problem of finding the left eigenvector that achieves the highest value of the rate function, for a given target accuracy. This eigenvector therefore minimizes the time that the inference algorithm needs to reach the desired accuracy. For Gaussian observations, we show that the network design problem can be formulated as a semidefinite (convex) program, and hence can be solved efficiently. When observations are identically distributed across agents, the system exhibits an interesting property: the graph of the rate function always lies between the graphs of the rate function of an isolated node and the rate function of a fusion center that has access to all observations. We prove that this fundamental property holds even when the topology and the associated system matrices change randomly over time, with arbitrary distribution. Due to the generality of its assumptions, the latter result requires more subtle techniques than the standard large deviations tools, contributing to the general theory of large deviations. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the problem of detecting leaks at carbon sequestration sites through the monitoring of CO2 levels using a wireless sensor network (WSN). By applying a basic linear dynamic model for an advection–diffusion process, a model-based detection strategy called the Iterative Partial Sequential Probability Ratio Test (IPSPRT) can be employed to detect and localize multiple leaks. A 3-D CO2 transport model is employed to provide a proof of concept simulated evaluation of the IPSPRT against a windowed-average approach in terms of time-to-decision vs. probability of false alarm and probability of a missed alarm. Despite using only a basic linear dynamic model, the IPSPRT is shown to achieve exponentially increasing better time-to-decision than the windowed-average approach as the probability of false alarm and probability of a missed alarm are decreased. A test bed implementation is described and employed to evaluate the performance of the IPSPRT in the presence of common WSN errors. [Copyright &y& Elsevier]

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 Kullback–Leibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman–Pearson and Bayes sense. [ABSTRACT FROM PUBLISHER]

Abstract: Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central base station. The base station computes an estimate of the process state by means of a Kalman filter. In this paper we assume that, at each time step, only a subset of all sensors are selected to send their observations to the fusion center due to channel capacity constraints or limited energy budget. We propose a multi-step sensor selection strategy to schedule sensors to transmit for the next steps of time with the goal of minimizing an objective function related to the Kalman filter error covariance matrix. This formulation, in a relaxed convex form, defines an unified framework to solve a large class of optimization problems over energy constrained WSNs. We offer some numerical examples to further illustrate the efficiency of the algorithm. [Copyright &y& Elsevier]