A geometric transversals approach to analyzing track coverage of omnidirectional sensor networks for maneuvering targets

The quality of service of a sensor network performing cooperative track detection can be expressed as the probability of obtaining multiple elementary detections over time, along a target track, also known as track coverage. Recently, distributed search theory and geometric transversals have been used to obtain the probability of track detection for targets traveling with constant speed and heading in a region-of-interest in closed form, as a function of the sensors' ranges and positions, and of the track parameters. In this paper, an extended approach based on convex theory and computational geometry is presented to obtain a track coverage function for maneuvering targets in the plane. In many tracking applications, a maneuvering target is modeled as a Markov motion process with known transition probability functions that are estimated via Kalman filtering from prior sensor measurements. The approach presented in this paper uses line transversals and planar geometry to derive the track coverage of a heterogeneous sensor network as a function of the Markov transition probability functions. The theoretical results are validated through numerical Monte Carlo simulations involving multiple omnidirectional mobile sensors that are deployed to cooperatively detect, track, and eventually pursue one or more maneuvering targets.