This paper focuses on how to improve the detection performance of distributed sensor systems to detect an emitter using the scan statistic. Considering that the emitter location is often unknown, we adopt a conservative approach and focus on the detection performance under the worst case emitter location. To improve the worst case detection performance, we propose a modified scan statistic: while the original scan statistic considers a single threshold for detection, our modified scan statistic uses a separate threshold for each cluster. The main idea is to reduce the threshold of clusters serving areas with low detection while still satisfying the false alarm constraint by increasing the threshold of clusters serving areas already well-served by other clusters. To optimize the thresholds of each cluster, we use upper and lower bounds for the probabilities of false alarm and detection and use monomial approximations for the bounds to solve the optimization problem. Our results show that our modified scan statistic can improve the worst case detection performance in various scenarios.

中文翻译：

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优化扫描统计的阈值以提高其在传感器检测系统中最坏情况下的检测性能

本文着重于如何提高分布式传感器系统的检测性能，以使用扫描统计量来检测发射器。考虑到发射器的位置通常是未知的，因此我们采用保守的方法，重点放在最坏情况下的发射器位置下的检测性能。为了提高最坏情况下的检测性能，我们提出了一种修改后的扫描统计量：当原始扫描统计量考虑一个检测阈值时，我们的修改后的扫描统计量为每个群集使用一个单独的阈值。主要思想是通过增加已经由其他集群很好服务的集群服务区域的阈值来降低检测率低的集群服务区域的阈值，同时仍然满足虚警约束。为了优化每个群集的阈值，我们将上下限用于错误警报和检测的可能性，并使用多项式逼近来解决优化问题。我们的结果表明，我们修改后的扫描统计量可以在各种情况下提高最坏情况下的检测性能。