Topology and Geometry for Vehicle-tracking Systems

Paul Bendich (May 21, 2018)

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Many systems employ sensors to interpret the environment.

The target-tracking task is to gather sensor data from the environment and then to partition these data into tracks that are produced by the same target. A key challenge is to "connect-the-dots": more precisely, to take a sensor observation at a given time and associate it with a previously-existing track (or to declare that this is a new object). This can be very challenging, especially when there are multiple targets present, and when different sensors "go blind" at various times. There are a number of high-level designs for multi-target multi-sensor tracking systems, but many contemporary ones fit within the multiple hypothesis (MHT) paradigm. Typical MHTs formulate the 'connect-the-dots' problem as one of Bayesian inference, with competing multi-track hypotheses receiving scores.

This talk surveys three recent efforts to integrate topological and geometric information into the formula for computing hypothesis scores. The first uses zero-dimensional persistent homology summaries of kinematic information in car tracking, and the second uses persistent homology summaries in state space to form grouping hypotheses for nautical traffic. Finally, a method using self-similarity matrices is employed to make useful cross-modal comparisons in heterogeneous sensor networks. In all three efforts, large improvements in MHT performance are observed.

This talk is based on work funded by OSD, NRO, AFRL, and NSF, and it was done with many collaborators, including Nathan Borggren, Sang Chin, Jesse Clarke, Jonathan deSena, John Harer, Jay Hineman, Elizabeth Munch, Andrew Newman, Alex Pieloch, David Porter, David Rouse, Nate Strawn, Christopher J. Tralie, Adam Watkins, Michael Williams, and Peter Zulch.