Fusion of Dependent Detection Systems Using Copula Theory

Abstract

The US Air Force has multiple detection systems for specific applications that could be combined to work together to yield better accuracy than the individual systems. The amount of time and money used to design, build, simulate, test, validate and verify such combining can be long and expense. Also, there can be several ways to combine these multiple systems, thus, generating more time and cost to determine an optimal (or approximately optimal) combination rule. This paper considers a simple version of this greater problem posed as follows. Suppose we have two legacy detections system families that are designed to detect the same “target” and we conjecture that combining them would yield a new detection system with improved accuracy. Suppose we know the ROC functions of both detection system families, but do not know (or have access to) the data that produced them. Can we construct the ROC function of the combined systems from the individual ROC functions? Copula theory has been in existence since 1959. This theory produces the means to address the dependence between random variables. This paper takes copula and applies it to the fusion of detection systems. Examples will be given that demonstrate how the formulas are used.