The group assignment problem

Multiple frame data association, whether it is based on multiple hypothesis tracking or multi-dimensional assignment problems, has established itself as the method of choice for difficult tracking problems, principally due to the ability to hold difficult data association decisions in abeyance until additional information is available. Over the last twenty years, these methods have focused on one-to-one assignments, many-to-one, and many-to-many assignments. Group tracking, on the other hand, introduces new complexity into the association process. especially if some soft decision making capability is desired. Thus, the goal of this work is to combine multiple grouping hypotheses for each frame of data (tracks or measurements) with matching these hypotheses across multiple frames of data using one-to-one, many-to-one. or many-to-many assignments to determine the correct hypothesis on each frame of data and connectivity across the frames. The resulting formulation is sufficiently general to cover four broad classes of problems in multiple target tracking, namely (a) group cluster tracking, (b) pixel (clump) IR cluster tracking, (c) the merged measurement problem, and (d) MHT for track-to-track fusion. What is more, the cluster assignment problem for either two or multiple dimensions represents a Generalized data association problem in the sense that it reduces to the classical assignment problems when there are no overlapping Groups or clusters. The formulation of the assignment problem for resolved object tracking and candidate Group methods for use in multiple frame Group tracking are briefly reviewed. Then, three different formulations of the Group assignment problem are developed.