T2T and M2T Association with Combined Hypotheses

The types of problems in data association for tracking are (i) measurement-to-measurement association (M2MA), i.e., track initiation, (ii) measurement-to-track association (M2TA), i.e., track continuation, (iii) trackto-track association (T2TA), for track fusion. Among the M2TA algorithms, it is well known that the Multiple Hypothesis Tracker (MHT) performs, due its time window, much better than other methods, such as nearest neighbor or PDA (which have a time window of depth 1) when there is heavy clutter or track ambiguity, i.e., when tracks are very close or cross each other. The idea behind MHT is to maintain several track-tomeasurement association hypotheses over its time window, some of which may have low likelihood but might later become the most likely after some frames of measurements have been added. In general, however, only the best hypothesis is retained when obtaining the results of the tracker at a particular time, thus neglecting the information contained in the subsequent hypotheses. In the T2TA problem, the use of the approach [3] yields only the most likely association, in a manner similar to the MHT. This paper presents methods to combine the top hypotheses generated in M2TA and T2TA problems, extending the results from [5] which proposed the Coordinated Presentation (CP). The T2TA problem consists of estimating the parameters of interest for an unknown number of targets, using the track lists obtained by S observers, which are received by a fusion center (FC). The fusion center generates several association hypotheses, each of them formed by associating tracks (the list elements) into S-tuples, using an m-best multidimensional assignment (MDA) algorithm based on Lagrangean relaxation [8]. The goal is to combine those hypotheses to obtain a better estimate than the one calculated using the top hypothesis alone. The best hypothesis estimate has the disadvantage of being optimistic, especially when there is track ambiguity, i.e., tracks are close to each other relative to their covariances (small normalized distance). For example, if the second best hypothesis has a likelihood close to the best, it should be accounted for: the covariances calculated assuming the best hypothesis is guaranteed to be true are optimistic because the second best might be the true one. The use of the top m hypotheses to asses the quality of the association was proposed in [6]. There the best assignment is used to update only if all of its association S-tuples are substantially present in the subsequent hypotheses. If some of them do not appear in subsequent hypothesis with high probability, an extended window is used to hopefully clear up the problem. Our approach is to combine the hypotheses to avoid incurring any delay. The M2TA problem considered requires the assignment of noisy measurements from a single radar arising from N targets. At time k window containing S-1 frames