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Abstract-We propose a method for tracking an unknown number of targets based on measurements provided by multiple sensors. Our method achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph. A redundant formulation of data association uncertainty and the use of "augmented target states" including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity. An increase in the number of targets, sensors, or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages. As a consequence, the complexity of our method scales only quadratically in the number of targets, linearly in the number of sensors, and linearly in the number of measurements per sensors. The performance of the method compares well with that of previously proposed methods, including methods with a less favorable scaling behavior. In particular, our method can outperform multisensor versions of the probability hypothesis density (PHD) filter, the cardinalized PHD filter, and the multi-Bernoulli filter.

Consensus in sensor networks is a procedure to corroborate the local measurements of the sensors with those of the surrounding nodes, and leads to a final agreement about a common value that, in detection applications, represents the decision statistic. As the amount of collected data increases, the convergence toward the final statistic is ruled by suitable scaling laws, and the question arises if the asymptotic (large sample) properties of a detection statistic are retained when this statistic is approximated via consensus algorithms. We investigate the asymptotic properties of running consensus detectors both under the Neyman-Pearson paradigm (fixed number of data) and in the sequential case. An appropriate asymptotic framework is developed, and exact theoretical results are provided, showing the asymptotic optimality of the running consensus detector. In addition, numerical experiments are performed to address nonasymptotic scenarios

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This work examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in the paper establish a fundamental scaling law for the steady-state probabilities of miss-detection and false-alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. The work establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. And third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained from these expressions. In particular, it is verified that as the step-size µ decreases, the error probabilities are driven to zero exponentially fast as functions of 1/µ, and that the exponents governing the decay increase linearly in the number of agents. It is also verified that the scaling laws governing errors of

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