Optimizing Thresholds of the Scan Statistic to Improve Its Worst Case Detection Performance in Sensor Detection Systems

Abstract

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.