A mathematical framework to optimize ATR systems with non-declarations and sensor fusion

Combat identification is one example where incorrect automatic target recognition (ATR) output labels may have substantial decision costs. For example, the incorrect labeling of hostile targets vs. friendly non-targets may have high costs; yet, these costs are difficult to quantify. One way to increase decision confidence is through fusion of data from multiple sources or from multiple looks through time. Numerous methods have been published to determine a Bayes’ optimal fusion decision if decision costs are well known. This research presents a novel mathematical programming ATR evaluation framework. A new objective function inclusive of time is introduced to optimize and compare ATR systems. Constraints are developed to enforce both decision maker preferences and traditional engineering measures of performance. This research merges rejection and receiver operating characteristic (ROC) analysis by incorporating rejection and ROC thresholds as decision variables. The rejection thresholds specify non-declaration regions, while the ROC thresholds explore viable true positive and false positive tradeoffs for output target labels. This methodology yields an optimal ATR system subject to decision maker constraints without using explicit costs for each type of output decision. A sample application is included for the fusion of two channels of collected polarized radar data for 10 different ground targets. A Boolean logic and probabilistic neural network fusion method are optimized and compared. Sensitivity analysis of significant performance parameters then reveals preferred regions for each of the fusion algorithms.