How to Dispatch Observers to Track an Evolving Boundary

Some distributed-sensing applications make it necessary to dispatch a limited number of observers (ships, vehicles, or airplanes with cameras; field workers with chemical kits; high-flying balloons with atmospheric sensors) to track the evolving boundary of a large phenomenon such as an oil spill, a fire, a hurricane, air or water pollution, or EL Nino. This paper develops a new framework for controlling the movements of the observers to maximize the information gained about the boundary's shape and position. To this end, we represent boundary uncertainty by a particle filter where each particle is a binary indicator function. This makes our dispatch algorithms applicable to arbitrary boundary representations from which indicator functions can be computed, including level sets and polygonal approximations. We demonstrate the benefits of optimal dispatch on both synthetic and real data. These benefits are most apparent when the observers are sparse relative to the boundary size.