Tracking with ranked signals

We present a novel graphical model approach for a problem not previously considered in the machine learning literature: that of tracking with ranked signals. The problem consists of tracking a single target given observations about the target that consist of ranked continuous signals, from unlabeled sources in a cluttered environment. We introduce appropriate factors to handle the imposed ordering assumption, and also incorporate various systematic errors that can arise in this problem, particularly clutter or noise signals as well as missing signals. We show that inference in the obtained graphical model can be simplified by adding bipartite structures with appropriate factors. We apply a hybrid approach consisting of belief propagation and particle filtering in this mixed graphical model for inference and validate the approach on simulated data. We were motivated to formalize and study this problem by a key task in Oceanography, that of tracking the motion of RAFOS ocean floats, using range measurements sent from a set of fixed beacons, but where the identities of the beacons corresponding to the measurements are not known. However, unlike the usual tracking problem in artificial intelligence, there is an implicit ranking assumption among signal arrival times. Our experiments show that the proposed graphical model approach allows us to effectively leverage the problem constraints and improve tracking accuracy over baseline tracking methods yielding results similar to the ground truth hand-labeled data.