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112
Robust Distributed Network Localization with Noisy Range Measurements
, 2004
"... This paper describes a distributed, lineartime 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 otherw ..."
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Cited by 392 (21 self)
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This paper describes a distributed, lineartime 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 twodimensional 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 realworld deployment geometries. Finally, we show how the algorithm supports localization of mobile nodes.
Secure positioning of wireless devices with application to sensor networks
 in Proceedings of INFOCOM 2005
"... Abstract — So far, the problem of positioning in wireless networks has been mainly studied in a nonadversarial setting. In this work, we analyze the resistance of positioning techniques to position and distance spoofing attacks. We propose a mechanism for secure positioning of wireless devices, th ..."
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Cited by 176 (12 self)
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Abstract — So far, the problem of positioning in wireless networks has been mainly studied in a nonadversarial setting. In this work, we analyze the resistance of positioning techniques to position and distance spoofing attacks. We propose a mechanism for secure positioning of wireless devices, that we call Verifiable Multilateration. We then show how this mechanism can be used to secure positioning in sensor networks. We analyze our system through simulations. Keywords: System design, Simulations. 1 I.
A Theory of Network Localization
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 122 (12 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
On the Computational Complexity of Sensor Network Localization
 In Proceedings of First International Workshop on Algorithmic Aspects of Wireless Sensor Networks
, 2004
"... Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances ..."
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Cited by 88 (4 self)
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Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances between all pairs of sensors that are within some radius r of each other. In the past few years, many algorithms for solving the localization problem were proposed, without knowing the computational complexity of the problem. In this paper, we show that no polynomialtime algorithm can solve this problem in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP. We also discuss the consequences of our result and present open problems.
Network localization in partially localizable networks
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., netwo ..."
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Cited by 59 (10 self)
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Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., networks in which there exist nodes whose positions cannot be uniquely determined. There is no existing study which correctly identifies precisely which nodes in a network are uniquely localizable and which are not. This absence of a sufficient uniqueness condition permits the computation of erroneous positions that may in turn lead applications to produce flawed results. In this paper, in addition to demonstrating the relevance of networks that may not be fully localizable, we design the first framework for two dimensional network localization with an efficient component to correctly determine which nodes are localizable and which are not. Implementing this system, we conduct comprehensive evaluations of network localizability, providing guidelines for both network design and deployment. Furthermore, we study an integration of traditional geographic routing with geographic routing over virtual coordinates in the partially localizable network setting. We show that this novel crosslayer integration yields good performance, and argue that such optimizations will be likely be necessary to ensure acceptable application performance in partially localizable networks.
Localization for largescale underwater sensor networks
, 2006
"... Abstract. In this paper, we study the localization problem in largescale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach ..."
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Cited by 46 (6 self)
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Abstract. In this paper, we study the localization problem in largescale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach which divides the whole localization process into two subprocesses: anchor node localization and ordinary node localization. Many existing techniques can be used in the former. For the ordinary node localization process, we propose a distributed localization scheme which novelly integrates a 3dimensional Euclidean distance estimation method with a recursive location estimation method. Simulation results show that our proposed solution can achieve high localization coverage with relatively small localization error and low communication overhead in largescale 3dimensional underwater sensor networks. 1
Beyond Trilateration: On the Localizability of Wireless Adhoc Networks
"... Abstract — The proliferation of wireless and mobile devices has fostered the demand of context aware applications, in which location is often viewed as one of the most significant contexts. Classically, trilateration is widely employed for testing network localizability; even in many cases it wrongl ..."
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Cited by 43 (13 self)
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Abstract — The proliferation of wireless and mobile devices has fostered the demand of context aware applications, in which location is often viewed as one of the most significant contexts. Classically, trilateration is widely employed for testing network localizability; even in many cases it wrongly recognizes a localizable graph as nonlocalizable. In this study, we analyze the limitation of trilateration based approaches and propose a novel approach which inherits the simplicity and efficiency of trilateration, while at the same time improves the performance by identifying more localizable nodes. We prove the correctness and optimality of this design by showing that it is able to locally recognize all 1hop localizable nodes. To validate this approach, a prototype system with 19 wireless sensors is deployed. Intensive and largescale simulations are further conducted to evaluate the scalability and efficiency of our design. I.
Approximation Accuracy, Gradient Methods, and Error Bound for Structured Convex Optimization
, 2009
"... Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this ..."
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Cited by 38 (1 self)
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Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this is an error bound for the linear convergence analysis of firstorder gradient methods for solving these problems. Example applications include compressed sensing, variable selection in regression, TVregularized image denoising, and sensor network localization.
Scalable Localization with Mobility Prediction for Underwater Sensor Networks
"... Abstract—Due to adverse aqueous environments, nonnegligible node mobility and large network scale, localization for largescale mobile underwater sensor networks is very challenging. In this paper, by utilizing the predictable mobility patterns of underwater objects, we propose a scheme, called Sca ..."
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Cited by 35 (7 self)
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Abstract—Due to adverse aqueous environments, nonnegligible node mobility and large network scale, localization for largescale mobile underwater sensor networks is very challenging. In this paper, by utilizing the predictable mobility patterns of underwater objects, we propose a scheme, called Scalable Localization scheme with Mobility Prediction (SLMP), for underwater sensor networks. In SLMP, localization is performed in a hierarchical way, and the whole localization process is divided into two parts: anchor node localization and ordinary node localization. During the localization process, every node predicts its future mobility pattern according to its past known location information, and it can estimate its future location based on its predicted mobility pattern. Anchor nodes with known locations in the network will control the whole localization process in order to balance the tradeoff between localization accuracy, localization coverage and communication cost. We conduct extensive simulations, and our results show that SLMP can greatly reduce localization communication cost while maintaining relatively high localization coverage and localization accuracy. I.
Connectivitybased Localization of Large Scale Sensor Networks with Complex Shape
"... Abstract—We study the problem of localizing a large sensor network having a complex shape, possibly with holes. A major challenge with respect to such networks is to figure out the correct network layout, i.e., avoid global flips where a part of the network folds on top of another. Our algorithm fir ..."
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Cited by 31 (4 self)
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Abstract—We study the problem of localizing a large sensor network having a complex shape, possibly with holes. A major challenge with respect to such networks is to figure out the correct network layout, i.e., avoid global flips where a part of the network folds on top of another. Our algorithm first selects landmarks on network boundaries with sufficient density, then constructs the landmark Voronoi diagram and its dual combinatorial Delaunay complex on these landmarks. The key insight is that the combinatorial Delaunay complex is provably globally rigid and has a unique realization in the plane. Thus an embedding of the landmarks by simply gluing the Delaunay triangles properly recovers the faithful network layout. With the landmarks nicely localized, the rest of the nodes can easily localize themselves by trilateration to nearby landmark nodes. This leads to a practical and accurate localization algorithm for large networks using only network connectivity. Simulations on various network topologies show surprisingly good results. In comparison, previous connectivitybased localization algorithms such as multidimensional scaling and rubberband representation generate globally flipped or distorted localization results. I.