论文标题
最佳后验检测器的最大后验检测器网络理论分析
Network Theoretic Analysis of Maximum a Posteriori Detectors for Optimal Input Detection
论文作者
论文摘要
本文考虑了最大的A-posteriori（MAP）和基于线性判别的MAP检测器，以检测随机输入的平均值和协方差的变化，使用来自输入节点的未集中的传感器的噪声测量，以驱动特定的网络节点驱动特定的网络节点。我们在网络边缘权重，输入和传感器节点的位置方面明确表征了两个检测器的性能。在渐近测量方案中，当输入和测量噪声是共同的高斯时，我们表明可以使用输入来研究检测器的性能以使系统传输函数矩阵的输出增益。使用此结果，我们获得了与给定网络切割上传感器相关的检测性能比与cut引起的子网相关的传感器相关的传感器相关的检测性能要好（或更差），而不包含输入节点。我们的结果还从检测理论的角度提供了对传感器放置的结构见解。我们通过多个数值示例来验证理论发现。
This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors non-collocated with the input nodes. We explicitly characterize both detectors' performance in terms of the network edge weights and input and sensor nodes' location. In the asymptotic measurement regime, when the input and measurement noise are jointly Gaussian, we show that the detectors' performance can be studied using the input to output gain of the system's transfer function matrix. Using this result, we obtain conditions for which the detection performance associated with the sensors on a given network cut is better (or worse) than that of the sensors associated with the subnetwork induced by the cut and not containing the input nodes. Our results also provide structural insights into the sensor placement from a detection-theoretic viewpoint. We validate our theoretical findings via multiple numerical examples.
