Applications of a combined probabilistic and fuzzy set technique to the attribute problem in ocean surveillance

It is now recognized that basically the multi-target tracking and data association problem can be characterized as the determination of that parameter Q, the partitioning of accumulated data, which maximizes, within feasible constraints, the conditional data probability function pr (Z|Q) or the corresponding posterior pr(Q|Z). This decomposes, by conditioning, into a chain of factors, including geolocation terms (involving weighted quadratic forms in Kalman filter innovations and determinants of covariance matrices of error), false-alarm targets of no interest terms, and nongeolocational attribute factors often present. Examples of the latter include: "irregular shape spotted similar to type B ship," "rapidly maneuvering track observed," "appears to be of class A," etc. In determining this factor, a deductive logical procedure is developed using fuzzy set and probabilistic methods. The chief result is that for a wide variety of both (1) functions which combine confidence levels in data and (2) conclusion classes, a computable, uniformly most accurate confidence set - described by a single fuzzy set - may be obtained for the possible data associations.