Location Uncertainty and Target Coverage in Wireless Sensor Networks Deployment

In this paper we consider a wireless sensor network (WSN) deployed to monitor a set of targets with known positions. Each target has an associated desired level of coverage by its neighbouring sensor nodes. The network deployment process introduces node placement uncertainty described by known probability distributions. Consequently, deficiency in achieving the desired coverage levels occurs with certain probabilities. To estimate such probabilities, we formalize a target coverage deficiency (TCD) problem. We show that the TCD problem is #P-hard even when restricted to grid WSNs. We then consider networks where node transmission ranges guarantee that the network after deployment has the same connectivity as the planned network. For such networks, we devise a dynamic programming algorithm that can solve a discrete version of the problem exactly and can produce lower bounds on the solution of any arbitrary given instance of the problem. We present simulation results that investigate the accuracy of the algorithm, and illustrate its usefulness in evaluating performance of any given node deployment scheme.