On the coverage process of a moving target in a dynamic nonstationary sensor field

We analyze the statistical properties of the k-coverage of a point-target moving in a straight line in a dynamic, nonstationary sensor field. The availability of each node is modeled by an independent, {0, 1}-valued continuous time Markov chain. Sensor locations form a nonhomogeneous spatial Poisson process. The sensing areas of the sensors are circles of i.i.d. radii. We first describe the induced nonstationary Markov-Boolean model and obtain k-coverage of the target at an arbitrary time instant. We then obtain k-coverage statistics for the time interval [0, T]: A pointwise stationary approximation that yields a limit theorem is also discussed. Numerical results illustrate the analysis.