Object Tracking by Scattered Directional Sensors

We address the problem of how to track objects moving at constant velocity using only directional sensors in a wireless sensor network. We model the field of vision of each directional sensor as a line, with the measured data being the times at which sensors detect objects crossing their lines. The network is initially deployed by scattering sensors, and the locations and directions in which the sensor point are also unknown a priori, in addition to the trajectories of the objects. The estimation problem involves the solution of a highly non-convex optimization problem. However we develop a three phase algorithm to solve the problem. It first chooses a coordinate basis adapted to the motions of the first two objects. Then it localizes the sensors with respect to that basis, and refines it as new objects arrive. Finally it transforms the basis if the GPS positions of six of the deployed nodes are known.