Optimal fusion of alarm sets from multiple detectors using dynamic programming

In a standard target detection approach, data is collected, points of interest called alarms are identified, and detection algorithms determine the confidence that a target is present at each point. Receiver operating characteristic (ROC) curves can be used to evaluate the performance of each detector and choose operating thresholds. The use of multiple sensors can improve the probability of detection of a diverse set of targets. It is difficult to properly assess the performance of a system of detectors and choose the best joint set of operating thresholds if confidence values from different detectors do not compare meaningfully. Fusion methods can be used to improve the joint performance of a set of detectors. However, in the case where different detectors do not operate on the same points of interest, typical fusion methods cannot be used to improve the binary decisions on individual alarms. In this paper, we propose a new fusion method that maps the confidence outputs from different detectors to a shared range where they compare meaningfully, and optimizes the joint performance of multiple detectors even when their alarm sets are disjoint. Our method uses dynamic programming to monotonically map the confidence output from each detector onto a shared range in such a way that we maximize the area-under-the-curve (AUC) of the ROC curve corresponding to the joint set of alarms. This joint ROC curve can be used to determine the operational thresholds for each individual detector to maximize their joint performance.