Recent advances in integrated electronic devices motivated the use of Wireless Sensor Networks (WSNs) in many applications including domain surveillance and mobile target tracking, where a number of sensors are scattered within a sensitive region to detect the presence of intruders and forward related events to some analysis center(s). Obviously, sensor deployment should guarantee an optimal event detection rate and should reduce coverage holes. Most of the coverage control approaches proposed in the literature deal with two-dimensional zones and do not develop strategies to handle coverage in three-dimensional domains, which is becoming a requirement for many applications including water monitoring, indoor surveillance, and projectile tracking. This paper proposes efficient techniques to detect coverage holes in a 3D domain using a finite set of sensors, repair the holes, and track hostile targets. To this end, we use the concepts of Voronoi tessellation, Vietoris complex, and retract by deformation. We show in particular that, through a set of iterative transformations of the Vietoris complex corresponding to the deployed sensors, the number of coverage holes can be computed with a low complexity. Mobility strategies are also proposed to repair holes by moving appropriately sensors towards the uncovered zones. The tracking objective is to set a non-uniform WSN coverage within the monitored domain to allow detecting the target(s) by the set of sensors. We show, in particular, how the proposed algorithms adapt to cope with obstacles. Simulation experiments are carried out to analyze the efficiency of the proposed models. To our knowledge, repairing and tracking is addressed for the first time in 3D spaces with different sensor coverage schemes
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