Abstract
This paper considers the binary Gaussian distribution robust hypothesis testing under a Bayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrix under each hypothesis is known, while the distribution mean vector under each hypothesis drifts in an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking a subset of p out of m sensors such that the best detection performance is achieved. In this setup, the minimax robust sensor selection problem is proposed to deal with the uncertainties of distribution means. Following a popular method, minimizing the maximum overall error probability with respect to the selection matrix can be approximated by maximizing the minimum Chernoff distance between the distributions of the selected measurements under null hypothesis and alternative hypothesis to be detected. Then, we utilize Danskin’s theorem to compute the gradient of the objective function of the converted maximization problem, and apply the orthogonal constraint-preserving gradient algorithm (OCPGA) to solve the relaxed maximization problem without 0/1 constraints. It is shown that the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide the computational complexity of the OCPGA, which is much lower than that of the existing greedy algorithm. Finally, numerical simulations illustrate that, after the same projection and refinement phases, the OCPGA-based method can obtain better solutions than the greedy algorithm-based method but with up to shorter runtimes. Particularly, for small-scale problems, the OCPGA -based method is able to attain the globally optimal solution.
Highlights
Wireless sensor networks (WSNs) are extensively used to collect and transmit data in many applications, such as autonomous driving [1], disaster detection [2], target tracking [3], etc
[11] considered the sensor selection problems involved in the Gaussian distribution robust hypothesis testings with both Neyman–Pearson and Bayesian optimal criteria, where the distribution mean under each hypothesis drifts in an ellipsoidal uncertainty set
We address the minimax robust sensor selection in the binary Gaussian distribution hypothesis testing of WSN with the distribution mean vector under each hypothesis drifting in an ellipsoidal uncertainty set
Summary
Wireless sensor networks (WSNs) are extensively used to collect and transmit data in many applications, such as autonomous driving [1], disaster detection [2], target tracking [3], etc. Work [9] studied the sensor selection for the binary Gaussian distribution hypothesis testing in the Neyman–Pearson framework, where the true distribution under each hypothesis is exactly known It approximately converted the minimization of the false alarm error probability to the maximization of the Kullback-Leibler (KL) divergence between the distributions of the selected measurements under null hypothesis and alternative hypothesis to be detected. Gaussian distribution hypothesis testing under the Neyman–Pearson framework, following the framework in [9], work [10] investigated the involved sensor selection problem with distribution mean under each hypothesis falling in an ellipsoidal uncertainty set (the distribution covariance is known). [11] considered the sensor selection problems involved in the Gaussian distribution robust hypothesis testings with both Neyman–Pearson and Bayesian optimal criteria, where the distribution mean under each hypothesis drifts in an ellipsoidal uncertainty set. For a semi-positive definite matrix A, A 2 stands for its square-rooting matrix
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