Paper detail

On Improving the Representation of a Region Achieved by a Sensor Network

This report considers the class of applications of sensor networks in which each sensor node makes measurements, such as temperature or humidity, at the precise location of the node. Such spot-sensing applications approximate the physical condition of the entire region of interest by the measurements made at only the points where the sensor nodes are located. Given a certain density of nodes in a region, a more spatially uniform distribution of the nodes leads to a better approximation of the physical condition of the region. This report considers the error in this approximation and seeks to improve the quality of representation of the physical condition of the points in the region in the data collected by the sensor network. We develop two essential metrics which together allow a rigorous quantitative assessment of the quality of representation achieved: the average representation error and the unevenness of representation error, the latter based on a well-accepted measure of inequality used in economics. We present the rationale behind the use of these metrics and derive relevant theoretical bounds on them in the common scenario of a planar region of arbitrary shape covered by a sensor network deployment. A simple new heuristic algorithm is presented for each node to determine if and when it should sense or sleep to conserve energy while also preserving the quality of representation. Simulation results show that it achieves a significant improvement in the quality of representation compared to other related distributed algorithms. Interestingly, our results also show that improved spatial uniformity has the welcome side-effect of a significant increase in the network lifetime.