Poster abstract: spatial average of a continuous physical process in sensor networks

Wireless ad-hoc sensor networks have caught the fancy of many researchers through the world in a very small span of time. Although notable progress has been made in several key areas, several researchers falter in the way they look at sensor networks i.e. just another kind of wireless ad hoc networks, albeit one composed of energy constrained nodes. A key aspect that makes sensor networks different from traditional networks is their strong link to the physical world. We develop this perspective by studying an interesting class of sensor network applications called aggregation applications.We argue that when a user queries for aggregates like maximum, average etc., he is interested in knowing the statistics of the underlying physical process. In general, this is not equivalent to the statistics gathered from a bunch of nodes. We introduce a distinction between aggregates calculated over a region and aggregates calculated over a discrete set of nodes. We classify them as spatial and nodal aggregates respectively. Till now, researchers have followed the approach of doing nodal aggregation in response to every user query in sensor networks. For a continuous physical process and a random deployment of sensor nodes, which are a norm for sensor networks, the conventional approach of doing nodal aggregation produces inaccurate results.We verify our claim by studying a specific aggregation function namely the average over a region (spatial average) in detail. We use a voronoi-based approach to propose an algorithm for calculating spatial average in sensor networks. The algorithm can work in two modes -- centralized and distributed. The energy and accuracy tradeoff associated with each of the two modes is analyzed in detail. The efficacy of the proposed algorithm is tested over a wide variety of physical processes including real precipitation data of South America acquired over a span of past 50 years. We will show that our algorithm gives a 2-8 times performance gain as compared to the conventional approach of doing nodal aggregation. We further explore the robustness of our algorithm to link failures and channel impairments.Although not 100% accurate, our approach is a simple, efficient and a practical solution for calculating the spatial average. We have implemented our algorithm on Berkeley motes. Our first prototype implementation occupies less than 12K flash ROM and consumes less than 1.6K run-time memory. Our algorithm can be easily integrated with available frameworks for doing aggregation in sensor networks. For a minimal cost, our algorithm can be used to provide a spatial aggregation service on a network of motes.