Abstract—Deriving the proper density to achieve the region coverage for random sensors deployment is a fundamentally important problem in the area of wireless sensor networks. Most existing works on sensor coverage mainly concentrate on the two-dimensional (2D) plane coverage which assume that all the sensors are deployed on an ideal plane. In contrast, sensors are also deployed on the three-dimensional (3D) rolling surfaces in many real applications. Toward this end, we study the coverage problem of wireless sensor networks for the rolling terrains, and derive the expected coverage ratios under the stochastic sensors deployment. According to the different terrain features, we investigate two kinds of terrain coverage problems: the regular terrain coverage problem and the irregular terrain coverage problem. Specifically, we derive the general expression of the expected coverage ratio for an arbitrary surface and build two models, cone model and Cos-revolution model, to estimate the expected coverage ratios for regular terrains. For irregular terrains, we propose a digital elevation model (DEM) based method to calculate the expected coverage ratio and design an algorithm to estimate the expected coverage ratio of an interested region by using only the contour map of this region. We also conduct extensive simulations to validate and evaluate our proposed models and schemes.
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