Spatial interpolation in wireless sensor networks: localized algorithms for variogram modeling and Kriging

Wireless sensor networks (WSNs) are rapidly emerging as the prominent technology for monitoring physical phenomena. However, large scale WSNs are known to suffer from coverage holes, i.e., large regions of deployment area where no sensing coverage can be provided. Such holes are the result of hardware failures, extensive costs for redeployment or the hostility of deployment areas. Coverage holes can adversely affect the accurate representation of natural phenomena that are monitored by a WSN. In this work, we propose to exploit the spatial correlation of physical phenomena to make monitoring systems more resilient to coverage holes. We show that a phenomenon can be interpolated inside a coverage hole with a high level of accuracy from the available nodal data given a model of its spatial correlation. However, due to energy limitations of sensor nodes it is imperative to perform this interpolation in an energy efficient manner that minimizes communication among nodes. In this paper, we present highly energy efficient methods for spatial interpolation in WSNs. First, we build a correlation model of the phenomenon being monitored in a distributed manner. Then, a purely localized and distributed spatial interpolation scheme based on Kriging interpolates the phenomenon inside coverage holes. We test the cost and accuracy of our scheme with extensive simulations and show that it is significantly more energy efficient than global interpolations and remarkably more accurate than simple averaging.