The Multi-Sensor Nuclear Threat Detection Problem

One way of reducing false-positive and false-negative errors in an alerting system, is by considering inputs from multiple sources. We address here the problem of detecting nuclear threats by using multiple detectors mounted on moving vehicles in an urban area. The likelihood of false alerts diminishes when reports from several independent sources are available. However, the detectors are in different positions and therefore the significance of their reporting varies with the distance from the unknown source position. An example scenario is that of multiple taxi cabs each carrying a detector. The real-time detectors' positions are known in real time as these are continuously reported from GPS data. The level of detected risk is then reported from each detector at each position. The problem is to delineate the presence of a potentially dangerous source and its approximate location by identifying a small area that has higher than threshold concentration of reported risk. This problem of using spatially varying detector networks to identify and locate risks is modeled and formulated here. The problem is then shown to be solvable in polynomial time and with a combinatorial network flow algorithm.