Track coverage in sensor networks

So far coverage problems have been formulated to address area coverage or to maintain line-of-sight visibility in the presence of obstacles (i.e., art-gallery problems). Although sensor networks often are employed to track moving targets, none of the existing formulations deal with the problem of allocating sensors in order to achieve track-formation capabilities over a region of interest. This paper investigates the problem of finding the configuration of a network with n sensors such that the number of tracks intercepted by k sensors is optimized without providing redundant area coverage over the entire region. This problem arises in applications where proximity sensors are employed that have individual detection capabilities, and that obtain limited measurements from each track, possibly at different moments in time. By assuming that the target travels along a straight unknown path, and that the sensors are omnidirectional with limited range (i.e., their visibility can be represented by a circle), it can be shown that the tracks detected by one or more (k) sensors always are contained by a coverage cone. Therefore, the track coverage of the network can be measured through the opening angle of the coverage cone and formulated in terms of unit vectors that depend on the sensors' range and location. Through this approach, the coverage of a given network configuration can be rapidly assessed. Also, a coverage function is obtained that, when maximized with respect to the sensor location, optimizes the number of tracks detected over a rectangular area of interest. The same approach can potentially be applied to other convex polygons and to three-dimensional Euclidian space.