If a tree falls in the woods, it does make a sound: multiple-hypothesis tracking with undetected target births

Abstract

This paper introduces a generalization of the multiple-hypothesis tracking (MHT) formalism for multitarget tracking. To our knowledge, MHT treatments in the literature do not consider undetected target birth events. Their inclusion leads to an interesting extension to the MHT recursion and necessitates aggregation over indistinguishable global hypotheses. We show that the MHT recursion factors, enabling track-oriented MHT (TO-MHT), albeit with clusters of indistinguishable undetected births. The treatment requires a distinction between those targets that are eventually detected (we call these unnoticed targets) and those that are never detected (we call these ghost targets). While the formulation appears more complex, there is structure to the solution that can be exploited, resulting in the same number of relevant track hypotheses for detected targets as in the classical TO-MHT solution. In the time-invariant case, the solution simplifies further because we need not consider unnoticed targets and there is a fixed structure to the ghost target solution.