The multiple hypothesis tracker derived from finite set statistics

Abstract

Abstract-The multiple hypothesis tracker (MHT) has historically been considered a gold standard for multi-target tracking. In this paper we show that the key formula for hypothesis probabilities in Reid's MHT can be derived from the modern theory of finite set statistics (FISST) insofar as appropriate assumptions (Poisson models for clutter and undetected targets, no target-death, linear-Gaussian Markov target kinematics) are adhered to.

Relationship Between Finite Set Statistics and the Multiple Hypothesis Tracker

“…In a recent conference paper [20] we have shown that Reid's MHT indeed can be derived from the multitarget Bayes filter, as parameterized in [10]. This result hinges on the validity of Reid's assumptions (including Gaussian-linear kinematics and no target death), as well as the interpretation of Reid's new target density as the same as the unknown target density in [10].…”

“…340-341, it was claimed that the MHT treats association hypotheses as state variables, and that this leads to some conceptual problems. However, the mixture expression ( 14), and similar expressions in, e.g., [10,20,26], demonstrate that FISST allows association hypotheses to be present in the multiobject posterior without actually entering the state itself (which is the random set Ξ k with realization X k ). Furthermore, assigning probabilities to the association hypotheses do not change this.…”

“…It was shown in [28] that track labels have no impact on the tracking results in the standard multitarget Bayes filter. We refer the reader to Sections III-D and VI-D in [20] for further discussion on this topic. REMARK 8 (Maintenance of structure).…”

“…We show that this filter has much of the same structure as Reid's MHT, and involves a hypothesis probability formula which is equal to Reid's formula multiplied by a factor that accounts for undiscovered targets. Second, while the analysis conducted in [20] relied on the transform-domain concept of probability generating functionals (p.g.fl. 's), all the developments of this paper are formulated purely in terms of multiobject densities.…”

Tracking the Wanders of Nature

“…This leads to a recursive Bayesian formulation of mtt in the form of the multi-target Bayes filter [120]. The main advantage is that both data association and filtering are expressed in a single theoretic framework with a single equation each for prediction and measurement update [36]. The mht filter [153] can be derived from fisst under weak assumptions [36], showing a close relationship between the two approaches.…”