4. Spatiotemporal Coverage in Fusion-Based Sensor Networks

Wireless sensor networks (WSNs) have been increasingly available for critical applications such as security surveillance and environmental monitoring. As a fundamental performance measure of WSNs, coverage characterizes how well a sensing field is monitored by a network. Two facets of coverage, i.e., spatial coverage and temporal coverage, quantify the percentage of area that is well monitored by the network and the timeliness of the network in detecting targets appearing in the sensing field, respectively. Although advanced collaborative signal processing algorithms have been adopted by many existing WSNs, most previous analytical studies on spatiotemporal coverage of WSNs are conducted based on overly simplistic sensing models (e.g., the disc model) that do not capture the stochastic nature of sensing. In this chapter, we attempt to bridge this gap by exploring the fundamental limits of spatiotemporal coverage based on stochastic data fusion models that fuse noisy measurements of multiple sensors. We derive the scaling laws between spatiotemporal coverage, network density, and signal-to-noise ratio (SNR). We show that data fusion can significantly improve spatiotemporal coverage by exploiting the collaboration among sensors when several physical properties of the target signal are known. In particular, for signal path loss exponent of \(k\) (typically between \(2.0\) and \(5.0\)), we prove that \(\rho _f{/}\rho _d = {\mathcal {O}}(\delta ^{2/k})\), where \(\rho _f\) and \(\rho _d\) are the densities of uniformly deployed sensors that achieve full spatial coverage or minimum detection delay under the fusion and disc models, respectively, and \(\delta \) is SNR. Our results help understand the limitations of the previous analytical results based on the disc model and provide key insights into the design of WSNs that adopt data fusion algorithms. Our analyses are verified through extensive simulations based on both synthetic data sets and data traces collected in a real deployment for vehicle detection.