In multi-target tracking problems where we are either interested in minimization of costs of the tracks globally or we are interested in maximization of the probabilities of the set of independent tracks given a set of observations, exactly under what circumstances a new track takes birth?
Hello. A number of operations research theoretic techniques for multi-target tracking are cited in the survey paper whose link appears below. Minimum cost assignment and network flow algorithms have been applied by various authors. More recent work focuses on n-D assignment. Please see the references in the paper. Generally the techniques assume a constant number of targets however you can add new tracks by assigning a cost to that event, i.e. the probability that the observations are not due to any of the existing tracks and therefore are a candidate for a new track.
You might also wish to consider Viterbi data association, which is not a bad technique for MTT. Reference attached.
Article Taxonomy of multiple target tracking methods
Article Multihypothesis Viterbi Data Association: Algorithm Developm...
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