Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian sequential single and multiple change-point detection procedures for the rapid detection of such phenomena. Using a dynamic programming framework we derive the structure of the optimal single-event quickest detection procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. The multi-sensor system configuration is arbitrary and sensors may be mobile. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation characteristics of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting random Gaussian signals affected by path loss. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel in a multiple hypothesis testing setting. A method that provides strict false discovery rate (FDR) control is proposed. In the simulation section, it is demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.
翻译:在许多现代应用中,特别是在通信、雷达、IoT、环境监测和生物监视方面,我们可以观测传播场或粒子。在本文件中,我们提议采用拜耳西亚顺序单项和多个变化点探测程序,以迅速发现此类现象。我们利用动态编程框架,得出最佳单一-事件快速检测程序的结构,这种程序尽量减少平均检测延迟(ADD),但需受错误的警报概率上限限制。多传感器系统配置是任意的,传感器可能是移动的。在稀有事件制度中,最佳程序会汇集到对变化点的远地点概率进行更实用的门槛测试。我们建议采用空间事件传播特点来方便地计算这种事后概率。在无症状模型中分析事后概率概率阈值测试的ADD值测试结构,在确定受路径丢失影响的随机高斯信号时进行具体分析。然后,我们甚至显示,在罕见事件制度中,拟议的最佳程序将汇集到更实用的门槛值测试A-DDR的多度测试速度。在模拟中,在模拟的模拟中,一个模拟模型中,将显示A-DDD的模拟中,一个模拟的模拟程序将显示显示一个模拟的频率。