Finding the best set of K paths through a trellis with application to multitarget tracking

A solution is presented to the problem of finding the best set of K completely unmerged paths through a trellis with Mi ≥ K states at depth i in the trellis, i = 0,1,2,...,N. Here, 'best set' means that the sum of the metrics of all K paths in the set is minimized, and 'completely unmerged' means that no two paths pass through a common state. The solution involves using the Viterbi algorithm on an expanded trellis. This result is then used to separate the tracks of K targets optimally in a simplified model of a multitarget radar system. The model includes measurement errors and false alarms, but it does not include the effects of missing detections or merged measurements.