A Gradient-Based Method for Robust SensorSelection in Hypothesis Testing

This paper considers the binary Gaussian distribution robust hypothesis testing under aBayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrixunder each hypothesis is known, while the distribution mean vector under each hypothesis driftsin an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking asubset of p out of m sensors such that the best detection performance is achieved. In this setup, theminimax robust sensor selection problem is proposed to deal with the uncertainties of distributionmeans. Following a popular method, minimizing the maximum overall error probability with respectto the selection matrix can be approximated by maximizing the minimum Chernoff distance betweenthe distributions of the selected measurements under null hypothesis and alternative hypothesis tobe detected. Then, we utilize Danskin's theorem to compute the gradient of the objective functionof the converted maximization problem, and apply the orthogonal constraint-preserving gradientalgorithm (OCPGA) to solve the relaxed maximization problem without 0/1 constraints. It is shownthat the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide thecomputational complexity of the OCPGA, which is much lower than that of the existing greedyalgorithm. Finally, numerical simulations illustrate that, after the same projection and refinementphases, the OCPGA-based method can obtain better solutions than the greedy algorithm-basedmethod but with up to 48.72% shorter runtimes. Particularly, for small-scale problems, the OCPGA-based method is able to attain the globally optimal solution.