Utilizing Voronoi Cells of Location Data Streams for Accurate Computation of Aggregate Functions in Sensor Networks

Abstract

Sensor networks are unattended deeply distributed systems whose database schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce Bspatial aggregations^that take into consideration the spatial location of each measurement generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an algorithms to compute and maintain the accurate Voronoi cell at each sensor node while the location of the others arrive on data stream. We also propose AVC-SW, a novel algorithm to approximate this Voronoi cell over a sliding window that supports dynamism in the sensor network. To demonstrate the performance of in-network implementation of our aggregation operators, we have developed prototypes of two different approaches to distributed spatial aggregate processing.

A programming system for sensor-based scientific applications

“…However, the underlying concepts and implementation of the system described in this research is quite different from these approaches in that it uses virtualization to address the mismatch between the instrumentation of the physical domain and its discretization in the computational model, rather than to create, for example, a virtual sensor for a derived data type. Other related efforts include spatial interpolation and aggregation [26][27][28], and redundant sensor sampling [29]. The focus of this work is different in that it addresses programming abstractions to facilitate implementations of in-network data estimation algorithms (e.g.…”

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

“…In this context, traditional interpolation methods, in particular those that extensively take advantage of spatial correlations, are also not readily applicable to WSNs. These methods either require global knowledge of the network [12,30] or centralized data processing. Due to WSNs' dynamic nature and large scale it is prohibitively expensive to collect and maintain global information such as node locations, connectivity and sensed data.…”

“…In [30], a WSN data aggregation approach based on spatial interpolation is proposed. It is argued that the aggregation quality can be improved if the aggregation operator takes into account the position of a sensor node and weighs its sensed value accordingly.…”

“…Using a localized scheme for spatial interpolation and aggregation, the authors show considerable improvement in aggregation accuracy. However, a major limitation of the spatial interpolation methods proposed in [30] is the use of geometric distance rather than statistical distance between sampled and interpolated locations. This form of interpolation implicitly assumes uniform spatial continuity in the monitored phenomenon which is rarely the case in nature.…”

Web data retrieval: solving spatial range queries using k-nearest neighbor searches

“…The Delaunay triangulation and Voronoi diagram based approaches have been studied for various purposes in wireless sensor networks [15,19,21]. In [19], the authors used the Vornonoi diagram to discover the existence of coverage holes, assuming that each sensor knows the location of its neighbors.…”