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The authors reformulate Reid's multiple hypothesis tracking algorithm to exploit a K-best ranked linear assignment algorithm for data association. The reformulated algorithm is designed for real-time tracking of large numbers of closely spaced objects. A likelihood association matrix is constructed that, for each scan, for each cluster, for each cluster hypothesis, exactly and compactly encodes the complete set of Reid's data association hypotheses. The set of this matrix's feasible assignments with corresponding non-vanishing products is shown to map one-to-one respectively onto the set of Reid's data association hypotheses and their corresponding probabilities. The explicit structure of this matrix is a new result and leads to an explicit hypothesis counting formula. Replacement of the likelihood association matrix elements by their negative natural logs then transforms the data association matrix into a linear assignment problem matrix and recasts the problem of data association into efficiently finding sets of ranked assignments. Fast polynomial time Murty ranked assignment algorithms can thus replace Reid's original NP-hard exhaustive hypothesis identification, probability evaluation, and branch-and-prune methods and can rapidly determine the maximally likely data association hypothesis, the second most likely, etc. Results from two high fidelity surveillance sensor simulations show the validity of the proposed method.

Recently, it has become clear that determining a ranked set of assignments allows computation of very good approximationsto the data association problem. Several algorithms have been proposed but only two return the k-best assignments in reasonable time. One is Danchick and Newnams' [1] algorithm, which is based on the recognition that determining the best assignment is a classical assignment problem, and that determining a ranked set of assignments may be accomplished by solving a series of modified copies of the initial assignment problem. The other algorithm is originally due to Murty [2] and was most recently described by [3] within the context of multitarget tracking. We evaluate the two algorithms using randomly generated data and data obtained from an electrooptical sensor simulation in which 90 missiles are launched. These evaluations show that Murty's algorithm performs significantly better in all scenarios. We show the relationship between the two algorithms and how Danchick and Newnams' algorithm can be very easily modified to Murty's algorithm. Experimental results using Murty's algorithm suggest that a solution to the real-time data association problem is now feasible.

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