On the coverage process of a moving point target in a non-uniform dynamic sensor field

We analyze the statistical properties of the k-coverage of a point-target moving in a straight line in a nonuniform dynamic sensor field. Sensor locations form a spatial point process. The environmental variation is captured by making the sensor locations form a non homogeneous spatial Poisson process with a fixed, spatially varying density function. The sensing areas of the sensors are circles of i.i.d. radii. The availability of each node is modeled by an independent, {0, 1}- valued, continuous time Markov chain. This gives a Markov-non homogeneous Poisson-Boolean model for which we perform a coverage analysis. We first obtain k-coverage of the target at an arbitrary time instant. We then obtain k-coverage statistics of the target during the time interval [0, T]. We also provide an asymptotically tight, closed form approximation for the duration for which the target is not k-covered in [0, T]. Numerical results illustrate the analysis. The environmental variation can also be captured by modeling the density function as a spatial random process resulting in the point process being a two-dimensional Cox process. For this model, we discuss issues in the coverage analysis.