Multitarget detection and acquisition: A unified approach

Suppose that a multitarget tracker is used to track a dim target in heavy clutter. In the paper "Characteristics of the Acquisition of a Dim Target in Clutter," Oliver Drummond has pointed out that, for such a tracker, target acquisition (i.e., determining whether or not a target is present in a sensor Field of View corrupted by persistent clutter tracks) is a very different problem than target detection (i.e., determining whether or not a target is present in a pixel corrupted by noise). In particular, target acquisition requires two Receiver Operating Characteristic (ROC) curves; whereas target target detection requires only one. In past presentations at this and other conferences and in the book Mathematics of Data Fusion, we have introduced "finite-set statistics (FISST)", a direct generalization of conventional single-sensor, single-target statistics to the multitarget realm. In this paper we show how FISST results in a unification of both detection and acquisition under a familiar decision-theoretic framework. The basic idea is to use a unified Bayesian single-target tracker with clutter models, rather than a multitarget tracker. In analogy to a conventional detection problem (i.e., deciding between the hypotheses "noise only" versus "target + noise"), the acquisition problem is reduced to a conventional decision problem (i.e., deciding between the hypotheses "clutter only" versus "target + clutter"). In particular, we show how to define an "acquisition ROC curve" for this sort of generalized detection problem.