Stochastic coverage in heterogeneous sensor networks

We study the problem of coverage in planar heterogeneous sensor networks. Coverage is a performance metric that quantifies how well a field of interest is monitored by the sensor deployment. To derive analytical expressions of coverage for heterogeneous sensor networks, we formulate the coverage problem as a set intersection problem, a problem studied in integral geometry. Compared to previous analytical results, our formulation allows us to consider a network model where sensors are deployed according to an arbitrary stochastic distribution; sensing areas of sensors need not follow the unit disk model but can have any arbitrary shape; sensors need not have an identical sensing capability. Furthermore, our formulation does not assume deployment of sensors over an infinite plane and, hence, our derivations do not suffer from the border effect problem arising in a bounded field of interest. We compare our theoretical results with the spatial Poisson approximation that is widely used in modeling coverage. By computing the Kullback-Leibler and total variation distance between the probability density functions derived via our theoretical results, the Poisson approximation, and the simulation, we show that our formulas provide a more accurate representation of the coverage in sensor networks. Finally, we provide examples of calculating network parameters such as the network size and sensing range in order to achieve a desired degree of coverage.