Using polynomial regression for data representation in wireless sensor networks

Unlike conventional sensor networks, wireless sensors are limited in power, have much smaller memory buffers, and possess relatively slower processing speeds. These characteristics necessitate minimum transfer and storage of information in order to prolong the network lifetime. In this paper, we exploit the spatiotemporal nature of sensor data to approximate the current values of the sensors based on readings obtained from neighbouring sensors and itself. We propose a tree based polynomial regression algorithm (TREG), that addresses the problem of data compression in wireless sensor networks. Instead of aggregated data, only the coefficients computed by the regression function, TREG are passed to achieve the following goals: (i) the sink can get attribute values in the regions devoid of sensor nodes, and (ii) readings over any portion of the region can be obtained at one time by querying the root of the tree. As the size of the data packet from each tree node to its parent remains constant, the proposed scheme scales very well with growing network density or increased coverage area. Since physical attributes exhibit a gradual change over time, we propose an iterative scheme, UPDATE-COEFF, which obviates the need to perform the regression function repeatedly and uses approximations based on previous readings. Extensive simulations are performed on real world data to demonstrate the effectiveness of the aggregation algorithm, TREG. Results reveal that for a network density of 0.0025, a complete binary tree of depth 4 could provide the absolute error to be less than 6%. A data compression ratio of about 0.02 is achieved using our proposed algorithm, which is almost independent of the tree depth. In addition, our proposed updating scheme makes the aggregation process faster while maintaining the desired error bounds. Copyright (C) 2006 John Wiley & Sons, Ltd.