[论文解读] Multisensor Quickest Detection

Georgios Fellouris, Grigory Sokolov|arXiv (Cornell University)|Oct 14, 2014

Advanced Statistical Process Monitoring被引用 2

一句话总结

本文提出了一种用于检测全局参数向量中部分分量变化的二阶渐近最优多传感器序列变化检测规则，采用广义 CUSUM 方案。研究证明，即使受影响的子集未知，当误报率趋近于零时，额外的最坏情况检测延迟仍保持有界。

ABSTRACT

A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global parameter vector, and at some unknown time there is a change in an unknown subset of components of this parameter vector. In this setup, we consider the problem of detecting the time of the change as soon as possible, while controlling the rate of false alarms. We establish the second-order asymptotic optimality (with respect to Lorden's criterion) of various generalizations of the CUSUM rule; that is, we show that their additional expected worst-case detection delay (relative to the one that could be achieved if the affected subset was known) remains bounded as the rate of false alarm goes to 0, for any possible subset of affected components. This general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change. The latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes. We present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first-order asymptotically optimal. Finally, in the special case that the change affects exactly one sensor, we consider the scheme that runs in parallel the local CUSUM rules and study the problem of specifying the local thresholds.

研究动机与目标

• 解决多传感器系统中受影响分量未知的最快序列变化检测问题。
• 开发在误报率趋近于零时仍能保持有界最坏情况检测延迟的检测规则。
• 将 CUSUM 规则推广至相关传感器和任意受影响分量子集的情形。
• 为所提出的方案在结构化多传感器变化检测问题中提供可行的实现方式。

提出的方法

• 将 CUSUM 规则推广至具有相关观测值和未知变化子集的多传感器场景。
• 采用 Lorden 准则评估检测延迟与误报控制。
• 通过证明额外最坏情况延迟有界，推导出二阶渐近最优性。
• 利用仅一个传感器受影响时的特殊结构，实现可扩展的实现方式。
• 提出并行本地 CUSUM 规则，并通过阈值优化处理单传感器变化场景。
• 通过仿真研究将性能与一阶渐近最优可扩展规则进行对比。

实验结果

研究问题

• RQ1 广义 CUSUM 规则是否能在多传感器序列变化检测中实现二阶渐近最优性？
• RQ2 当受影响子集未知时，随着误报率趋近于零，额外的最坏情况检测延迟如何变化？
• RQ3 二阶最优规则与一阶渐近最优可扩展规则之间的性能差距是多少？
• RQ4 在结构约束下，如何为所提出的检测方案推导出可行的实现方式？
• RQ5 当仅一个传感器受影响且并行运行本地 CUSUM 规则时，最优阈值选择策略是什么？

主要发现

• 所提出的广义 CUSUM 规则在 Lorden 准则下实现了二阶渐近最优性，且当误报率趋近于零时，额外的最坏情况检测延迟保持有界。
• 即使受影响的子集未知，额外检测延迟在所有可能的受影响分量子集中均保持一致有界。
• 仿真结果表明，所提方案的性能优于第一阶渐近最优可扩展规则。
• 在单传感器变化情况下，并行本地 CUSUM 规则配合优化阈值可实现接近最优的检测延迟。
• 该框架可容纳相关传感器观测值和一般参数向量的变化，扩展了传统多传感器检测模型。
• 通过利用单传感器变化问题的特殊结构，推导出了检测方案的可行表示形式。