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Diffusion adaptation techniques have shown great promise in addressing the problem of node-specific distributed estimation where the nodes in the network are interested in different, possibly overlapping, sets of parameters. In this work, node-specific distributed detection, which has remained largely unexamined, is considered. In particular, the problem is formulated as one of binary hypothesis testing at each node for each of its parameters of interest. A distributed, online solution for this problem is sought based on diffusion adaptation techniques. In this setting, a signal to be detected by one node constitutes interference that may compromise the ability of the other nodes to detect their signals of interest reliably. Under mild assumptions on the data and network, it is shown that, for sufficiently small adaptation step-sizes, interference can be kept in check. Local detectors are developed where the test-statistics and thresholds adapt to changing conditions in real time. The distributed algorithm is analyzed; and its detection performance characterized and illustrated through numerical simulations.

Diffusion adaptation techniques based on the least-meansquares criterion have been proposed for distributed detection of a signal in Gaussian-distributed noise, forgoing the need for a fusion center. However, least-mean-squares solutions are generally non-robust against impulsive noise. In this work, we combine nonlinear filtering with diffusion adaptation and propose a strategy for distributed detection in the presence of impulsive noise. The superiority of the algorithm is validated experimentally.

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