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146
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 403 (20 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.
Wireless Sensor Network Localization Techniques
"... Wireless sensor network localization is an important area that attracted significant research interest. This interest is expected to grow further with the proliferation of wireless sensor network applications. This paper provides an overview of the measurement techniques in sensor network localizat ..."
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Cited by 209 (5 self)
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Wireless sensor network localization is an important area that attracted significant research interest. This interest is expected to grow further with the proliferation of wireless sensor network applications. This paper provides an overview of the measurement techniques in sensor network localization and the onehop localization algorithms based on these measurements. A detailed investigation on multihop connectivitybased and distancebased localization algorithms are presented. A list of open research problems in the area of distancebased sensor network localization is provided with discussion on possible approaches to them.
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.
Wireless sensor networks: A survey on the state of the art and the 802.15.4 and ZigBee standards
, 2007
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Signal Processing Techniques in NetworkAided Positioning: A Survey of StateoftheArt Positioning Designs
 IEEE Signal Processing Magazine
, 2005
"... [A survey of stateoftheart positioning designs] The U.S. Federal Communications Commission (FCC) requires that the precise location of all enhanced 911 (E911) callers be automatically determined. This requirement has motivated the development of cellularaided positioning. To facilitate emergency ..."
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Cited by 98 (3 self)
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[A survey of stateoftheart positioning designs] The U.S. Federal Communications Commission (FCC) requires that the precise location of all enhanced 911 (E911) callers be automatically determined. This requirement has motivated the development of cellularaided positioning. To facilitate emergency services, the FCC has mandated that 95 % of all handsets sold be location compatible by the end of December 2005 [1]. Wireless positioning has also been found very useful for other applications besides E911 service, ranging from vehicle navigation and network optimization to resource management and automated billing. Ubiquitous computing and locationaware computing also necessitate that we develop techniques for estimating the location of mobile users in both outdoor and indoor environments. Various positioning systems have been proposed for use in ubiquitous computing [2]. As an essential prerequisite for ubiquitous computing, mobile positioning techniques, linked with wireless networks, have increasingly provided mobile users with opportunities to access personal information, corporate data, and shared resources anytime, anywhere. Positioning systems can be grouped in many different ways, including indoor versus outdoor systems or cellular versus sensor network positioning designs, as shown in Figure 1.
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.
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 85 (14 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.
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 70 (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.
Localization in sparse networks using sweeps
 in Proceedings of ACM MobiCom
, 2006
"... Determining node positions is essential for many nextgeneration network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for finegrained localiza ..."
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Cited by 60 (6 self)
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Determining node positions is essential for many nextgeneration network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for finegrained localization called Sweeps. Sweeps correctly finitely localizes all nodes in bilateration networks. Sweeps also handles angle measurements and noisy measurements. We demonstrate the practicality of our algorithm through extensive simulations on a large number of networks, upon which it consistently localizes onethousandnode networks of average degree less than five in less than two minutes on a consumer PC.
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.