变化传播模式未知的多传感器顺序变化检测
Multi-Sensor Sequential Change Detection with Unknown Change Propagation Pattern
摘要：
用多个传感器检测变化的问题在文献中受到了极大的关注。在许多实际应用中，如关键基础设施监测和疾病传播建模，一个有用的变化传播模型是一个变化最终发生在所有传感器，但不是所有的传感器在同一时刻见证变化。虽然以前的工作考虑的情况下，已知的变化传播动力学，本文研究了一个更一般的设置未知的变化传播模式（轨迹）。贝叶斯制定的问题，在集中和分散的设置进行了研究，目标是检测的第一个时刻，在任何传感器见证了变化。利用动态规划（DP）框架，最优解结构的推导，并在罕见的变化制度，提出了几个更实用的变化检测算法。在一定条件下，当虚警概率为零时，证明了多图检验算法的一阶渐近最优性。为了进一步降低计算复杂性，提出了基于在线估计未知变化传播模式的变化检测算法。数值研究表明，所提出的检测技术提供了接近最佳的性能。此外，在分散的设置，它示出，如果事件触发的采样方案称为电平交叉采样与滞后（LCSH）被用于本地统计的采样和传输，检测性能可以显着提高使用相同数量的通信资源相比，传统的均匀时间采样（US）计划。
英文摘要：
The problem of detecting changes with multiple sensors has received significant attention in the literature. In many practical applications such as critical infrastructure monitoring and modeling of disease spread, a useful change propagation model is one where change eventually happens at all sensors, but where not all sensors witness change at the same time instant. While prior work considered the case of known change propagation dynamics, this paper studies a more general setting of unknown change propagation pattern (trajectory). A Bayesian formulation of the problem in both centralized and decentralized settings is studied with the goal of detecting the first time instant at which any sensor witnesses a change. Using the dynamic programming (DP) framework, the optimal solution structure is derived and in the rare change regime, several more practical change detection algorithms are proposed. Under certain conditions, the first-order asymptotic optimality of a proposed algorithm called multichart test is shown as the false alarm probability vanishes. To further reduce the computational complexity, change detection algorithms are proposed based on online estimation of the unknown change propagation pattern. Numerical studies illustrate that the proposed detection techniques offer near-optimal performance. Further, in the decentralized setting, it is shown that if an event-triggered sampling scheme called level-crossing sampling with hysteresis (LCSH) is used for sampling and transmission of local statistics, the detection performance can be significantly improved using the same amount of communication resources compared to the conventional uniform-in-time sampling (US) scheme.
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