Wireless sensor networks are often used for environmental monitoring applications. In this context sampling and reconstruction of a physical field is one of the most important problems to solve. We focus on a bandlimited field and find under which conditions on the network topology the reconstruction of the field is successful, with a given probability. We review irregular sampling theory, and analyze the problem using random matrix theory. We show that even a very irregular spatial distribution of sensors may lead to a successful signal reconstruction, provided that the number of collected samples is large enough with respect to the field bandwidth. Furthermore, we give the basis to analytically determine the probability of successful field reconstruction.
Note that our work significantly differs from the studies above because we assume that the sensors location are known (or can be determined @cite_11 @cite_6 @cite_0 ) and the sensor precision is sufficiently high so that the quantization error is negligible. The question we pose is instead under which conditions (on the network system) the reconstruction of a bandlimited signal is successful with a given probability.
@cite_0 @cite_6 @cite_11
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This paper describes a distributed, linear-time algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherwise corrupt localization computations. We formulate the localization problem as a two-dimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable to the localization of sensor networks in which each node can estimate the distance to each of its neighbors, but no absolute position reference such as GPS or fixed anchor nodes is available. We implemented the algorithm on a physical sensor network and empirically assessed its accuracy and performance. Also, in simulation, we demonstrate that the algorithm scales to large networks and handles real-world deployment geometries. Finally, we show how the algorithm supports localization of mobile nodes. Many sensor network applications require location awareness, but it is often too expensive to include a GPS receiver in a sensor network node. Hence, localization schemes for sensor networks typically use a small number of seed nodes that know their location and protocols whereby other nodes estimate their location from the messages they receive. Several such localization techniques have been proposed, but none of them consider mobile nodes and seeds. Although mobility would appear to make localization more difficult, in this paper we introduce the sequential Monte Carlo Localization method and argue that it can exploit mobility to improve the accuracy and precision of localization. Our approach does not require additional hardware on the nodes and works even when the movement of seeds and nodes is uncontrollable. We analyze the properties of our technique and report experimental results from simulations. Our scheme outperforms the best known static localization schemes under a wide range of conditions.