Stochastic Geometry for Sensing Environmental Processes with a known Spatio-Temporal Profile

We consider the problem of sensing an environmental variable with a known spatial and temporal statistical profile. The main technical contribution is a stochastic geometry approach to characterizing the fraction of area that is successfully sensed by a given fraction of stationary or mobile agents for a specific error tolerance. Our results demonstrate that the knowledge of underlying spatio-temporal profile significantly improves the coverage of the agents. For the mobile case, we also compute optimal movement region of each agent to maximize the coverage performance for a given error tolerance.