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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.
Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes
"... algorithm to locate sensors (with unknown locations) in 1, with respect to a minimal number of +1anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fu ..."
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Cited by 37 (6 self)
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algorithm to locate sensors (with unknown locations) in 1, with respect to a minimal number of +1anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors ’ locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley–Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors ’ locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions. Index Terms—Absorbing Markov chain, anchor, barycentric coordinates, Cayley–Menger determinant, distributed iterative
1 RobottoRobot Relative Pose Estimation from Range Measurements
"... Abstract—In this paper, we address the problem of determining the 2D relative pose of pairs of communicating robots from (i) robottorobot distance measurements and (ii) displacement estimates expressed in each robot’s reference frame. Specifically, we prove that for nonsingular configurations the ..."
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Cited by 29 (5 self)
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Abstract—In this paper, we address the problem of determining the 2D relative pose of pairs of communicating robots from (i) robottorobot distance measurements and (ii) displacement estimates expressed in each robot’s reference frame. Specifically, we prove that for nonsingular configurations the minimum number of distance measurements required for determining all 6 possible solutions for the 3 degreesoffreedom robottorobot transformation is 3. Additionally, we show that given 4 distance measurements the maximum number of solutions is 4, while 5 distance measurements are sufficient for uniquely determining the robottorobot transformation. Furthermore, we present an efficient algorithm for computing the unique solution in closed form and describe an iterative leastsquares process for improving its accuracy. Finally, we derive necessary and sufficient observability conditions based on Lie derivatives, and evaluate the performance of the proposed estimation algorithms both in simulation and experimentally.
Euclidean Distance Matrices and Applications
"... Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especia ..."
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Cited by 14 (0 self)
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Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially
Distributed Sensor Network Localization Using SOCP Relaxation
"... Abstract—The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a distributed localization algorithm based on secondorder cone programming ..."
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Cited by 11 (0 self)
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Abstract—The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a distributed localization algorithm based on secondorder cone programming relaxation. We show that the sensor nodes can estimate their positions based on local information. Unlike previous approaches, we also consider the effect of inaccurate anchor positions. In the presence of anchor position errors, the localization is performed in three steps. First, the sensor nodes estimate their positions using information from their neighbors. In the second step, the anchors refine their positions using relative distance information exchanged with their neighbors and finally, the sensors refine their position estimates. We demonstrate the convergence of the algorithm numerically. Simulation study, for both uniform and irregular network topologies, illustrates the robustness of the algorithm to anchor position and distance estimation errors, and the performance gains achievable in terms of localization accuracy, problem size reduction and computational efficiency. Index Terms—Distributed algorithms, convex optimization, relaxation methods, secondorder cone programming, positioning, localization, synchronous and asynchronous algorithms. I.
Interview by author
, 2008
"... Abstract—For a Hausdorff space X, we denote by 2X the collection of all closed subsets of X. In this paper, we discuss the connectedness and locally connectedness of hyperspace 2X endowed with the vietoris topology. Further path connectedness is investigated. The results generalize some theorems of ..."
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Cited by 11 (1 self)
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Abstract—For a Hausdorff space X, we denote by 2X the collection of all closed subsets of X. In this paper, we discuss the connectedness and locally connectedness of hyperspace 2X endowed with the vietoris topology. Further path connectedness is investigated. The results generalize some theorems of E. Micheal. Keywordsconnectedness; locally connectedness; path connectedness; vietoris topology; hyperspace I.
Robust Localization of Nodes and TimeRecursive Tracking in Sensor Networks Using Noisy Range Measurements
"... Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to it ..."
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Cited by 10 (3 self)
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Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to iteratively maximize a likelihood function (ML) of positions given the observed ranges, which requires initialization with an approximate solution to avoid convergence towards local extrema. This paper develops methods for handling both Gaussian and Laplacian noise, the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem is solved for a block of target range measurements to approximately set up initial sensor/target positions, and the likelihood function is then iteratively refined through MajorizationMinimization (MM). To avoid the computational burden of repeatedly solving increasingly large EDM problems in timerecursive operation, an incremental scheme is exploited whereby a new target/node position is estimated from previously available node/target locations to set up the iterative ML initial point for the full spatial configuration. The above methods are first derived under Gaussian noise assumptions, and modifications for Laplacian noise are then considered. Analytically, the main challenges to overcome in the Laplacian case stem from the nondifferentiability of ℓ1 norms that arise in the various cost functions. Simulation results Copyright (c) 2011 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubspermissions@ieee.org.
On the Global Optimum of Planar, Rangebased RobottoRobot Relative Pose Estimation
"... Abstract — In this paper, we address the problem of determining the relative position and orientation (pose) of two robots navigating in 2D, based on known egomotion and noisy robottorobot distance measurements. We formulate this as a weighted Least Squares (WLS) estimation problem, and determine ..."
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Cited by 9 (4 self)
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Abstract — In this paper, we address the problem of determining the relative position and orientation (pose) of two robots navigating in 2D, based on known egomotion and noisy robottorobot distance measurements. We formulate this as a weighted Least Squares (WLS) estimation problem, and determine the exact global optimum by directly solving the multivariate polynomial system resulting from the firstorder optimality conditions. Given the poor scalability of the original WLS problem, we propose an alternative formulation of the WLS problem in terms of squared distance measurements (squared distances WLS or SDWLS). Using a hybrid algebraicnumeric technique, we are able to solve the corresponding firstorder optimality conditions of the SDWLS in 125 ms in Matlab. Both methods solve the minimal (3 distance measurements) as well as the overdetermined problem (more than 3 measurements)
Determining the robottorobot relative pose using rangeonly measurements
, 2006
"... Abstract — In this paper we address the problem of determining the relative pose of pairs robots that move on a plane while measuring the distance to each other. We show that the minimum number of distance measurements required for the 3 degrees of freedom robottorobot transformation to become loc ..."
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Cited by 9 (3 self)
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Abstract — In this paper we address the problem of determining the relative pose of pairs robots that move on a plane while measuring the distance to each other. We show that the minimum number of distance measurements required for the 3 degrees of freedom robottorobot transformation to become locally observable is 3. Furthermore, we prove that the maximum number of possible solutions in this case is 6, while a minimum of 5 distance measurements is necessary in order to uniquely determine the robots ’ relative pose. Finally, we present efficient algorithms for computing all possible solutions and evaluate the validity of our theoretical results both in simulation and experimentally. I. INTRODUCTION AND RELATED WORK In order to solve distributed estimation problems such as cooperative localization, mapping, and tracking, robots
A Modified Multidimensional Scaling with Embedded Particle Filter Algorithm for Cooperative Positioning of Vehicular Networks
"... Abstract—Vehicular communication technologies are on their way to be recognized as icons of modern societies. One important scientific challenge to the safety related applications of vehicular communication is indeed semiprecise positioning. Cooperative positioning is an idea for that purpose, and ..."
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Cited by 7 (5 self)
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Abstract—Vehicular communication technologies are on their way to be recognized as icons of modern societies. One important scientific challenge to the safety related applications of vehicular communication is indeed semiprecise positioning. Cooperative positioning is an idea for that purpose, and of course from research point of view is very attractive. From the practical point of view the attractiveness of cooperative positioning lies in its independence from any major additional infrastructure other than the vehicular communication systems. This paper introduces a new positioning algorithm for localization of mobile networks, in general, that nicely applies to vehicular networks. The algorithm is based on the well known multidimensional algorithm and shows remarkable performance compared to its counterparts in the vehicular positioning literature.