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Distributed Localization Using Noisy Distance and Angle Information
 MOBIHOC'06
, 2006
"... Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In th ..."
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Cited by 14 (3 self)
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Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In this paper, we study the problem of localization with noisy distance and angle information. With no noise at all, the localization problem with both angle (with orientation) and distance information is trivial. However, in the presence of even a small amount of noise, we prove that the localization problem is NPhard. Localization with accurate distance information and relative angle information is also hard. These hardness results motivate our study of approximation schemes. We relax the nonconvex constraints to approximating convex constraints and propose linear programs (LP) for two formulations of the resulting localization problem, which we call the weak deployment and strong deployment problems. These two formulations give upper and lower bounds on the location uncertainty respectively: No sensor is located outside its weak deployment region, and each sensor can be anywhere in its strong deployment region without violating the approximate distance and angle constraints. Though LPbased algorithms are usually solved by centralized methods, we propose distributed, iterative methods, which are provably convergent to the centralized algorithm solutions. We give simulation results for the distributed algorithms, evaluating the convergence rate, dependence on measurement noises, and robustness to link dynamics.
Greedy Routing with Bounded Stretch
"... Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log ..."
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Cited by 14 (0 self)
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Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log 2 n)dimensional space, permitting greedy routing with constant stretch. To the best of our knowledge, this is the first greedy embedding with stretch guarantees for this class of networks. Our main technical contribution involves extracting, in polynomial time, a constant number of isometric and balanced tree separators from a given CUDG. We do this by extending the celebrated LiptonTarjan separator theorem for planar graphs to CUDGs. Our techniques extend to other classes of graphs; for example, for general graphs, we obtain an O(log n)stretch greedy embedding into O(log 2 n)dimensional space. The greedy embeddings constructed by our algorithm can also be viewed as a constantstretch compact routing scheme in which each node is assigned an O(log 3 n)bit label. To the best of our knowledge, this result yields the best known stretchspace tradeoff for compact routing on CUDGs. Extensive simulations on random wireless networks indicate that the average routing overhead is about 10%; only few routes have a stretch above 1.5. I.
Sensor network localization by eigenvector synchronization over the Euclidean group
 In press
"... We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global ..."
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Cited by 11 (7 self)
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We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases, and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity and running time. While our approach is applicable to higher dimensions, in the current paper we focus on the two dimensional case.
Distributed ImageBased 3D Localization of Camera Sensor Networks
"... Abstract — We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision technique ..."
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Cited by 10 (1 self)
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Abstract — We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision techniques. However, due to noise in the image measurements, these estimates may not be globally consistent. We address this problem by minimizing a cost function on SE(3) N in a distributed fashion using a generalization of the classical consensus algorithm for averaging Euclidean data. We also derive a condition for convergence, which relates the stepsize of the consensus algorithm and the degree of the camera network graph. While our methods are designed with the camera sensor network application in mind, our results are applicable to other localization problems in a more general setting. We also provide synthetic simulations to test the validity of our approach. I.
ForceDirected Approaches to Sensor Localization
 in Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX’06
, 2006
"... We consider the centralized, anchorfree sensor localization problem. We consider the case where the sensor network reports range information and the case where in addition to the range, we also have angular information about the relative order of each sensor’s neighbors. We experimented with classi ..."
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Cited by 9 (2 self)
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We consider the centralized, anchorfree sensor localization problem. We consider the case where the sensor network reports range information and the case where in addition to the range, we also have angular information about the relative order of each sensor’s neighbors. We experimented with classic and new forcedirected techniques. The classic techniques work well for small networks with nodes distributed in simple regions. However, these techniques do not scale well with network size and yield poor results with noisy data. We describe a new forcedirected technique, based on a multiscale deadreckoning, that scales well for large networks, is resilient under range errors, and can reconstruct complex underlying regions. 1
Sensor networks continue to puzzle: Selected open problems
 In Proc. 9th Internat. Conf. Distributed Computing and Networking (ICDCN
, 2008
"... Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goa ..."
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Cited by 9 (0 self)
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Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goal of this work is both to summarize the current state of research and, by calling attention to these fundamental problems, to spark interest in the networking community to attend to these and related problems in sensor networks.
An AsRigidAsPossible Approach to Sensor Network Localization
"... We present a novel approach to localization of sensors in a network given a subset of noisy intersensor distances. The algorithm is based on “stitching” together local structures by solving an optimization problem requiring the structures to fit together in an “AsRigidAsPossible ” manner, hence ..."
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Cited by 9 (3 self)
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We present a novel approach to localization of sensors in a network given a subset of noisy intersensor distances. The algorithm is based on “stitching” together local structures by solving an optimization problem requiring the structures to fit together in an “AsRigidAsPossible ” manner, hence the name ARAP. The local structures consist of reference “patches” and reference triangles, both obtained from intersensor distances. We elaborate on the relationship between the ARAP algorithm and other stateoftheart algorithms, and provide experimental results demonstrating that ARAP is significantly less sensitive to sparse connectivity and measurement noise. We also show how ARAP may be distributed.
Localization on the pushpin computing sensor network using spectral graph drawing and mesh relaxation
 SIGMOBILE Mobile Computer & Communication Review
"... This work approaches the problem of localizing the nodes of a distributed sensor network by leveraging distance constraints such as internode separations or ranges between nodes and a globally observed event. Previous work has shown this problem to suffer from false minima, mesh folding, slow conve ..."
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Cited by 8 (0 self)
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This work approaches the problem of localizing the nodes of a distributed sensor network by leveraging distance constraints such as internode separations or ranges between nodes and a globally observed event. Previous work has shown this problem to suffer from false minima, mesh folding, slow convergence, and sensitivity to initial position estimates. Here, we present a localization system that combines a technique known as spectral graph drawing (SGD) for initializing node position estimates and a standard mesh relaxation (MR) algorithm for converging to finer accuracy. We describe our combined localization system in detail and build on previous work by testing these techniques with real 40kHz ultrasound timeofflight range data collected from 58 nodes in the Pushpin Computing network, a dense hardware testbed spread over an area of one square meter. In this paper, we discuss convergence characteristics, accuracy, distributability, and the robustness of this localization system. I.
PATCHWORK: Efficient Localization for Sensor Networks by Distributed Global Optimization
, 2005
"... We describe a new algorithm for sensor network localization based on short intersensor distances and fully decentralized computation. The algorithm computes local coordinates of small “patches ” of sensors and glues them together using a distributed global optimization process. Thanks to the global ..."
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Cited by 6 (3 self)
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We describe a new algorithm for sensor network localization based on short intersensor distances and fully decentralized computation. The algorithm computes local coordinates of small “patches ” of sensors and glues them together using a distributed global optimization process. Thanks to the global optimization, our method is more robust in the presence of noisy measurements than existing incremental methods. Most notably, and unlike some other global optimization techniques, our method cannot be fooled by local minima that might lead to foldovers in the network layout. The method is anchorfree, so advance knowledge about locations of some sensors is not required. Nonetheless, we provide a way to take advantage of known locations of any number of anchors. An experimental study shows the effectiveness of the new algorithm in noisy environments where the sensors are distributed over regions with a variety of geometric shapes. 1.