| Tracking objects from measurements is an important problem with wide applications from security, to the safety of small children, to identifying cars on public streets to assist in autonomous driving. If the correspondence between measurements and objects is known, the well-known Kalman filter can be used. However, in many real-world problems this correspondence is not known and we are forced to confront what is known as the data association problem. It is believed the best exact solution is exponential (the problem is P# complete), so current research is focused on approximations.; In this thesis, we introduce an on-line approximate filter that empirically performs very well on large-scale problems. This filter tightly integrates the continuous aspects of the problem (locating the objects) with the discrete aspects (the data association ambiguities). This filter contains a way to compactly, albeit approximately, represent exponentially many hypotheses. The representation involves an N x N matrix, which represents a distribution over N! hypotheses for the location of the objects. We derive the update of this filter show experimental results that our filter outperforms state-of-the-art approaches. |
