Polynomial chaos theory for performance evaluation of ATR systems

The development of a more unified theory of automatic target recognition (ATR) has received considerable attention over the last several years from individual researchers, working groups, and workshops. One of the major benefits expected to accrue from such a theory is an ability to analytically derive performance metrics that accurately predict real-world behavior. Numerous sources of uncertainty affect the actual performance of an ATR system, so direct calculation has been limited in practice to a few special cases because of the practical difficulties of manipulating arbitrary probability distributions over high dimensional spaces. This paper introduces an alternative approach for evaluating ATR performance based on a generalization of NorbertWiener's polynomial chaos theory. Through this theory, random quantities are expressed not in terms of joint distribution functions but as convergent orthogonal series over a shared random basis. This form can be used to represent any finite-variance distribution and can greatly simplify the propagation of uncertainties through complex systems and algorithms. The paper presents an overview of the relevant theory and, as an example application, a discussion of how it can be applied to model the distribution of position errors from target tracking algorithms.