Reformulating Reid´s MHT method with generalised Murty K-best ranked linear assignment algorithm

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.