Search theory is the discipline that studies the problem of how best to search for an object when the amount of searching efforts is limited and only probabilities of the possible position of the object are given. Then, the problem is to find the optimal distribution of this total effort that maximizes the probability of detection. Although the general formalism of search theory will be used subsequently, we consider now a radically different problem. The problem is to detect target tracks. In the "classical" search theory, the target is said detected if a detection occurs during any time of the time frame. Here, on the contrary, the target track will be said to be detected if elementary detections occur at various times. That means that there is a test for acceptance (or detection) of a target track and that the problem is to optimize the allocation of the search effort for track detection. So, specific optimization problems are solved by means of the primal-dual formalism, in an original setup. Other aspects concern Markovian targets and two-sided search for which simple and efficient algorithms are derived.
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