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383
Trajectory Based Forwarding and Its Applications
, 2002
"... Trajectory based forwarding (TBF) is a novel method to forward packets in a dense ad hoc network that makes it possible to route a packet along a predefined curve. It is a generalization of source based routing and Cartesian forwarding in that the trajectory is set by the source, but the forwardin ..."
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Cited by 128 (3 self)
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Trajectory based forwarding (TBF) is a novel method to forward packets in a dense ad hoc network that makes it possible to route a packet along a predefined curve. It is a generalization of source based routing and Cartesian forwarding in that the trajectory is set by the source, but the forwarding decision is based on the relationship to the trajectory rather than the final destination. The fundamental aspect of TBF is that it decouples path naming from the actual path, thereby providing a common framework for applications such as: flooding, unicast, multicast and multipath routing, and discovery in ad hoc networks. TBF requires that nodes know their position relative to a coordinate system. While a global coordinate system a#orded by a system such as GPS would be ideal, in this paper we propose Local Positioning System (LPS), a method that only positions the nodes along the trajectory, by making use of other node capabilities, such as angle of arrival or range estimations, compasses and accelerometers. We explore several forwarding strategies that are appropriate for these node capabilities.
AnchorFree Distributed Localization in Sensor Networks.
 Science,
, 2003
"... Abstract Many sensor network applications require that each node's sensor stream be annotated with its physical location in some common coordinate system. Manual measurement and configuration methods for obtaining location don't scale and are errorprone, and equipping sensors with GPS is ..."
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Cited by 127 (6 self)
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Abstract Many sensor network applications require that each node's sensor stream be annotated with its physical location in some common coordinate system. Manual measurement and configuration methods for obtaining location don't scale and are errorprone, and equipping sensors with GPS is often expensive and does not work in indoor and urban deployments. Sensor networks can therefore benefit from a selfconfiguring method where nodes cooperate with each other, estimate local distances to their neighbors, and converge to a consistent coordinate assignment. This paper describes a fully decentralized algorithm called AFL (AnchorFree Localization) where nodes start from a random initial coordinate assignment and converge to a consistent solution using only local node interactions. The key idea in AFL is foldfreedom, where nodes first configure into a topology that resembles a scaled and unfolded version of the true configuration, and then run a forcebased relaxation procedure. We show using extensive simulations under a variety of network sizes, node densities, and distance estimation errors that our algorithm is superior to previously proposed methods that incrementally compute the coordinates of nodes in the network, in terms of its ability to compute correct coordinates under a wider variety of conditions and its robustness to measurement errors.
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 123 (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 (10 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 (7 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.
Localization from connectivity in sensor networks
 IEEE Transactions on Parallel and Distributed Systems
, 2004
"... Abstract—We propose an approach that uses connectivity information—who is within communications range of whom—to derive the locations of nodes in a network. The approach can take advantage of additional information, such as estimated distances between neighbors or known positions for certain anchor ..."
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Cited by 113 (4 self)
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Abstract—We propose an approach that uses connectivity information—who is within communications range of whom—to derive the locations of nodes in a network. The approach can take advantage of additional information, such as estimated distances between neighbors or known positions for certain anchor nodes, if it is available. It is based on multidimensional scaling (MDS), an efficient data analysis technique that takes Oðn 3 Þ time for a network of n nodes. Unlike previous approaches, MDS takes full advantage of connectivity or distance information between nodes that have yet to be localized. Two methods are presented: a simple method that builds a global map using MDS and a more complicated one that builds small local maps and then patches them together to form a global map. Furthermore, leastsquares optimization can be incorporated into the methods to further improve the solutions at the expense of additional computation. Through simulation studies on uniform as well as irregular networks, we show that the methods achieve more accurate solutions than previous methods, especially when there are few anchor nodes. They can even yield good relative maps when no anchor nodes are available. Index Terms—Wireless sensor networks, optimization, position estimation. 1
Rigidity, Computation, and Randomization in Network Localization
 In Proceedings of IEEE INFOCOM ’04, Hong Kong
, 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 110 (16 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.
Semidefinite programming approaches for sensor network localization with noisy distance measurements
 IEEE Transactions on Automation Science and Engineering
, 2006
"... Abstract — A sensor network localization problem is to determine the positions of the sensor nodes in a network given incomplete and inaccurate pairwise distance measurements. Such distance data may be acquired by a sensor node by communicating with its neighbors. We describe a general semidefinite ..."
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Cited by 94 (8 self)
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Abstract — A sensor network localization problem is to determine the positions of the sensor nodes in a network given incomplete and inaccurate pairwise distance measurements. Such distance data may be acquired by a sensor node by communicating with its neighbors. We describe a general semidefinite programming (SDP) based approach for solving the graph realization problem, of which the sensor network localization problems is a special case. We investigate the performance of this method on problems with noisy distance data. Error bounds are derived from the SDP formulation. The sources of estimation error in the SDP formulation are identified. The SDP solution usually has a rank higher than the underlying physical space, which when projected onto the lower dimensional space generally results in high estimation error. We describe two improvements to ameliorate such a difficulty. First, we propose a regularization term in the objective function that can help to reduce the rank of the SDP solution. Second, we use the points estimated from the SDP solution as the initial iterate for a gradientdescent method to further refine the estimated points. A lower bound obtained from the optimal SDP objective value can be used to check the solution quality. Experimental results are presented to validate our methods and show that they outperform existing SDP methods.
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 90 (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.
TPS: A timebased positioning scheme for outdoor wireless sensor networks
 in Proc. IEEE INFOCOM
"... AbstractIn this paper, we present a novel timebased positioning scheme (TPS) for efficient location discovery in outdoor sensor networks. TF'S relies on TDoA (TimeDifferenceofArrival) of RF signals measured IocaUy at a sensor to detect range differences from the sensor to three base station ..."
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Cited by 82 (13 self)
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AbstractIn this paper, we present a novel timebased positioning scheme (TPS) for efficient location discovery in outdoor sensor networks. TF'S relies on TDoA (TimeDifferenceofArrival) of RF signals measured IocaUy at a sensor to detect range differences from the sensor to three base stations. These range differences are averaged over multiple beacon intervals before they are combined to estimate the sensor loeation through trilateration. A nice feature of this positioning scheme is that it is purely localized: sensors independently compute their positions. We present a statistical analysis of the performance of TF'S in noisy environments. We also identify possible sources of position errors with suggested measures to mitigate them. Our scheme requires no time synchronization in the network and minimal extra hardware in sensor construction. TPS induces no eommunication overhead for sensors, as they listen to three beacon signals passively during each beacon interval. The computation overhead is low, as the location detection algorithm involves only simple algebraic operations over scalar values. TF'S is not adversely affected by increasing network size or density and thus offers scalability. We conduct extensive simulations to test the performance of TPS when TDoA measurement errors are normally distributed or uniformly distributed. The obtained results show that TPS is an effective scheme for outdoor sensor selfpositioning. I.