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.

中文翻译：

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假设检验中基于梯度的稳健传感器选择方法。

本文考虑了无线传感器网络（WSN）中基于贝叶斯最优准则的二进制高斯分布鲁棒假设检验。每个假设下的分布协方差矩阵是已知的，而每个假设下的分布均值矢量在椭圆形不确定性集中漂移。由于带宽和能量有限，我们的目标是从m个传感器中找出p个子集，以实现最佳检测性能。在这种情况下，提出了最小极大鲁棒传感器选择问题，以解决分配装置的不确定性。遵循一种流行的方法 可以通过在零假设和要检测的备用假设下最大化选定测量值的分布之间的最小Chernoff距离来近似最小化相对于选择矩阵的最大总错误概率。然后，我们利用Danskin定理计算转换后的最大化问题的目标函数的梯度，并应用保留正交约束的梯度算法（OCPGA）来解决无0/1约束的松弛最大化问题。结果表明，OCPGA可以得到松弛问题的平稳点。同时，我们提供了OCPGA的计算复杂度，该复杂度远低于现有的贪心算法。最后，数值模拟表明，在相同的投影和优化阶段之后，与基于贪婪算法的方法相比，基于OCPGA的方法可以获得更好的解决方案，但运行时间缩短了48.72％。特别是对于小规模问题，基于OCPGA的方法能够获得全局最优解。