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221
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.
Theory of semidefinite programming for sensor network localization
 IN SODA05
, 2005
"... We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior–point algorithm theories to prove that the SDP localizes any network or graph th ..."
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Cited by 120 (9 self)
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We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior–point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R 2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub–networks in the input network.
Semidefinite programming based algorithms for sensor network localization
 ACM Transactions on Sensor Networks
, 2006
"... An SDP relaxation based method is developed to solve the localization problem in sensor networks using incomplete and inaccurate distance information. The problem is set up to find a set of sensor positions such that given distance constraints are satisfied. The nonconvex constraints in the formulat ..."
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Cited by 113 (6 self)
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An SDP relaxation based method is developed to solve the localization problem in sensor networks using incomplete and inaccurate distance information. The problem is set up to find a set of sensor positions such that given distance constraints are satisfied. The nonconvex constraints in the formulation are then relaxed in order to yield a semidefinite program which can be solved efficiently. The basic model is extended in order to account for noisy distance information. In particular, a maximum likelihood based formulation and an interval based formulation are discussed. The SDP solution can then also be used as a starting point for steepest descent based local optimization techniques that can further refine the SDP solution. We also describe the extension of the basic method to develop an iterative distributed SDP method for solving very large scale semidefinite programs that arise out of localization problems for large dense networks and are intractable using centralized methods. The performance evaluation of the technique with regard to estimation accuracy and computation time is also presented by the means of extensive simulations. Our SDP scheme also seems to be applicable to solving other Euclidean geometry problems where points are locally connected.
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.
Rendered Path: RangeFree Localization in Anisotropic Sensor Networks with Holes
, 2007
"... Sensor positioning is a crucial part of many locationdependent applications that utilize wireless sensor networks (WSNs). Current localization approaches can be divided into two groups: rangebased and rangefree. Due to the high costs and critical assumptions, the rangebased schemes are often imp ..."
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Cited by 86 (15 self)
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Sensor positioning is a crucial part of many locationdependent applications that utilize wireless sensor networks (WSNs). Current localization approaches can be divided into two groups: rangebased and rangefree. Due to the high costs and critical assumptions, the rangebased schemes are often impractical for WSNs. The existing rangefree schemes, on the other hand, suffer from poor accuracy and low scalability. Without the help of a large number of uniformly deployed seed nodes, those schemes fail in anisotropic WSNs with possible holes. To address this issue, we propose the Rendered Path (REP) protocol. To the best of our knowledge, REP is the only rangefree protocol for locating sensors with constant number of seeds in anisotropic sensor networks.
Visualization of Wormholes in Sensor Networks
, 2004
"... Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDSVOW, to detect wormholes in a sensor network. MDSVOW first reconstructs the layout of the sen ..."
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Cited by 76 (3 self)
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Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDSVOW, to detect wormholes in a sensor network. MDSVOW first reconstructs the layout of the sensors using multidimensional scaling. To compensate the distortions caused by distance measurement errors, a surface smoothing scheme is adopted. MDSVOW then detects the wormhole by visualizing the anomalies introduced by the attack. The anomalies, which are caused by the fake connections through the wormhole, bend the reconstructed surface to pull the sensors that are faraway to each other. Through detecting the bending feature, the wormhole is located and the fake connections are identified. The contributions of MDSVOW are: (1) it does not require the sensors to be equipped with special hardware, (2) it adopts and combines the techniques from social science, computer graphics, and scientific visualization to attack the problem in network security. We examine the accuracy of the proposed mechanism when the sensors are deployed in a circle area and one wormhole exists in the network. The results show that MDSVOW has a low false alarm ratio when the distance measurement errors are not large.
The effects of ranging noise on multihop localization: an empirical study
 in IPSN
, 2005
"... Abstract — This paper presents a study of how empirical ranging characteristics affect multihop localization in wireless sensor networks. We use an objective metric to evaluate a wellestablished parametric model of ranging called Noisy Disk: if the model accurately predicts the results of a realwo ..."
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Cited by 68 (4 self)
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Abstract — This paper presents a study of how empirical ranging characteristics affect multihop localization in wireless sensor networks. We use an objective metric to evaluate a wellestablished parametric model of ranging called Noisy Disk: if the model accurately predicts the results of a realworld deployment, it sufficiently captures ranging characteristics. When the model does not predict accurately, we systematically replace components of the model with empirical ranging characteristics to identify which components contribute to the discrepancy. We reveal that both the connectivity and noise components of Noisy Disk fail to accurately represent realworld ranging characteristics and show that these shortcomings affect localization in different ways under different circumstances. I.
Robust distributed node localization with error management
 In Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc’06). ACM
, 2006
"... Location knowledge of nodes in a network is essential for many tasks such as routing, cooperative sensing, or service delivery in ad hoc, mobile, or sensor networks. This paper introduces a novel iterative method ILS for node localization starting with a relatively small number of anchor nodes in a ..."
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Cited by 68 (4 self)
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Location knowledge of nodes in a network is essential for many tasks such as routing, cooperative sensing, or service delivery in ad hoc, mobile, or sensor networks. This paper introduces a novel iterative method ILS for node localization starting with a relatively small number of anchor nodes in a large network. At each iteration, nodes are localized using a leastsquares based algorithm. The computation is lightweight, fast, and anytime. To prevent error from propagating and accumulating during the iteration, the error control mechanism of the algorithm uses an error registry to select nodes that participate in the localization, based on their relative contribution to the localization accuracy. Simulation results have shown that the active selection strategy significantly mitigates the effect of error propagation. The algorithm has been tested on a network of Berkeley Mica2 motes with ultrasound TOA ranging devices. We have compared the algorithm with more global methods such as MDSMAP and SDPbased algorithm both in simulation and on real hardware. The iterative localization achieves comparable location accuracy in both cases, compared to the more global methods, and has the advantage of being fully decentralized.
Towards IP geolocation using delay and topology measurements
 In IMC
, 2006
"... We present Topologybased Geolocation (TBG), a novel approach to estimating the geographic location of arbitrary Internet hosts. We motivate our work by showing that 1) existing approaches, based on endtoend delay measurements from a set of landmarks, fail to outperform much simpler techniques, an ..."
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Cited by 67 (7 self)
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We present Topologybased Geolocation (TBG), a novel approach to estimating the geographic location of arbitrary Internet hosts. We motivate our work by showing that 1) existing approaches, based on endtoend delay measurements from a set of landmarks, fail to outperform much simpler techniques, and 2) the error of these approaches is strongly determined by the distance to the nearest landmark, even when triangulation is used to combine estimates from different landmarks. Our approach improves on these earlier techniques by leveraging network topology, along with measurements of network delay, to constrain host position. We convert topology and delay data into a set of constraints, then solve for router and host locations simultaneously. This approach improves the consistency of location estimates, reducing the error substantially for structured networks in our experiments on Abilene and Sprint. For networks with insufficient structural constraints, our techniques integrate external hints that are validated using measurements before being trusted. Together, these techniques lower the median estimation error for our universitybased dataset to 67 km vs. 228 km for the best previous approach.