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29
Exact and approximate solution of source localization problems
 IEEE Trans. Signal Processing
, 2007
"... Abstract—We consider least squares (LS) approaches for locating a radiating source from range measurements (which we call RLS) or from rangedifference measurements (RDLS) collected using an array of passive sensors. We also consider LS approaches based on squared range observations (SRLS) and ba ..."
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Cited by 46 (1 self)
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Abstract—We consider least squares (LS) approaches for locating a radiating source from range measurements (which we call RLS) or from rangedifference measurements (RDLS) collected using an array of passive sensors. We also consider LS approaches based on squared range observations (SRLS) and based on squared rangedifference measurements (SRDLS). Despite the fact that the resulting optimization problems are nonconvex, we provide exact solution procedures for efficiently computing the SRLS and SRDLS estimates. Numerical simulations suggest that the exact SRLS and SRDLS estimates outperform existing approximations of the SRLS and SRDLS solutions as well as approximations of the RLS and RDLS solutions which are based on a semidefinite relaxation. Index Terms—Efficiently and globally optimal solution, generalized trust region subproblems (GTRS), least squares, nonconvex, quadratic function minimization, range measurements, rangedifference measurements, single quadratic constraint, source localization, squared range observations. I.
Ranging energy optimization for robust sensor positioning based on semidefinite programming
 IEEE Trans. Signal Process
, 2009
"... Abstract—Sensor positioning is an important task of locationaware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribe ..."
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Cited by 12 (4 self)
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Abstract—Sensor positioning is an important task of locationaware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribed accuracy requirements. This motivates us to investigate ranging energy optimization problems. We address ranging energy optimization for an unsynchronized positioning system, which features robust sensor positioning (RSP) in the sense that a specific accuracy requirement is fulfilled within a prescribed service area. We assume a lineofsight (LOS) channel exists between the sensor and each beacon. The positioning is implemented by timeofarrival (TOA) based twoway ranging between a sensor and beacons, followed by a location estimation at a central processing unit. To establish a dependency between positioning accuracy and ranging energy, we assume the adopted TOA and location estimators are unbiased and attain the associated Cramér–Rao bound. The accuracy requirement has the same form as the one defined by the Federal Communication Commission (FCC), and we present two constraints with linearmatrixinequality form for the RSP. Ranging energy optimization problems, as well as a practical algorithm based on semidefinite programming are proposed. The effectiveness of the algorithm is illustrated by numerical experiments. Index Terms—Cramér–Rao bound, localization, semidefinite programming, wireless sensor networks.
Distributed Maximum Likelihood Sensor Network Localization
 IEEE Transactions on Signal Processing
, 2014
"... Abstract—We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements.We deri ..."
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Cited by 7 (3 self)
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Abstract—We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements.We derive a computational efficient edgebased version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edgebased convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation errorresilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for largescale networks. Index Terms—Distributed optimization, convex relaxations, sensor network localization, distributed algorithms, ADMM, distributed localization, sensor networks, maximum likelihood. I.
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.
Correspondence Efficient Weighted Multidimensional Scaling for Wireless Sensor Network Localization
"... Abstract—Localization of sensor nodes is a fundamental and important problem in wireless sensor networks. Although classical multidimensional scaling (MDS) is a computationally attractive positioning method, it is statistically inefficient and cannot be applied in partiallyconnected sensor networks ..."
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Cited by 6 (0 self)
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Abstract—Localization of sensor nodes is a fundamental and important problem in wireless sensor networks. Although classical multidimensional scaling (MDS) is a computationally attractive positioning method, it is statistically inefficient and cannot be applied in partiallyconnected sensor networks. In this correspondence, a weighted MDS algorithm is devised to circumvent these limitations. It is proved that the estimation performance of the proposed algorithm can attain Cramér–Rao lower bound (CRLB) for sufficiently small noise conditions. Computer simulations are included to contrast the performance of the proposed algorithm with the classical MDS and distributed weighted MDS algorithms as well as CRLB. Index Terms—Localization, multidimensional scaling, wireless sensor networks. I.
Fast Multidimensional Scaling using Vector Extrapolation
, 2008
"... Multidimensional scaling (MDS) is a class of methods used to find a lowdimensional representation of a set of points given a matrix of pairwise distances between them. Problems of this kind arise in various applications, from dimensionality reduction of image manifolds to psychology and statistics. ..."
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Cited by 5 (2 self)
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Multidimensional scaling (MDS) is a class of methods used to find a lowdimensional representation of a set of points given a matrix of pairwise distances between them. Problems of this kind arise in various applications, from dimensionality reduction of image manifolds to psychology and statistics. In many of these applications, efficient and accurate solution of an MDS problem is required. In this paper, we propose using vector extrapolation techniques to accelerate the numerical solution of MDS problems. Vector extrapolation is used to accelerate the convergence of fixedpoint iterative algorithms. We review the problem of multidimensional scaling and vector extrapolation techniques, and show several examples of our accelerated solver for multidimensional scaling problems in various applications. 1
Correspondence Subspace Approach for Fast and Accurate SingleTone Frequency Estimation
"... Abstract—A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this m ..."
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Cited by 4 (3 self)
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Abstract—A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this matrix for frequency estimation. It is proved that for small error conditions, the frequency estimate is approximately unbiased and its variance is equal to Cramér–Rao lower bound. Computer simulations are included to compare the proposed approach with the generalized weighted linear predictor, periodogram, and phasebased maximum likelihood estimators in terms of estimation accuracy, computational complexity, and threshold performance. Index Terms—Frequency estimation, linear prediction, singular value decomposition, subspace method, weighted least squares. I.
Anchorless cooperative localization for mobile wireless sensor networks
 Proc. of WICSP
, 2011
"... Weproposetwoalgorithmsforanchorlesscooperativenetworklocalizationinmobile wireless sensor networks (WSNs). In order to continuously localize the mobilenetwork, giventhepairwisedistancemeasurementsbetweendifferentwireless sensor nodes, we propose to use subspace tracking to track the variations in si ..."
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Cited by 3 (1 self)
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Weproposetwoalgorithmsforanchorlesscooperativenetworklocalizationinmobile wireless sensor networks (WSNs). In order to continuously localize the mobilenetwork, giventhepairwisedistancemeasurementsbetweendifferentwireless sensor nodes, we propose to use subspace tracking to track the variations in signal eigenvectors and corresponding eigenvalues of the doublecentered distance matrix. We compare the computational complexity of the proposed algorithms with a recently developed anchorless algorithm exploiting the extended Kalman filter (EKF) as well as an anchored algorithm exploiting ordinary least squares (LS). We show that our proposed algorithms are computationally efficient, and hence, are appropriate for practical implementations. Simulation results further illustrate that the proposed algorithms have an acceptable accuracy in comparison with the aforementioned algorithms and are more robust to an increasing sampling period of the measurements. 1
TOA Based Robust Wireless Geolocation and CramérRao Lower Bound Analysis in Harsh LOS/NLOS Environments
"... N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to ..."
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Cited by 2 (1 self)
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N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
COOPERATIVE MOBILE NETWORK LOCALIZATION VIA SUBSPACE TRACKING
"... Two novel cooperative localization algorithms for mobile wireless networks are proposed. To continuously localize the mobile network, given the pairwise distance measurements between different wireless sensor nodes, we propose to use subspace tracking to track the variations in signal eigenvectors ..."
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Cited by 2 (2 self)
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Two novel cooperative localization algorithms for mobile wireless networks are proposed. To continuously localize the mobile network, given the pairwise distance measurements between different wireless sensor nodes, we propose to use subspace tracking to track the variations in signal eigenvectors and corresponding eigenvalues of the doublecentered distance matrix. We compare the computational complexity of the new algorithms with a recently developed algorithm exploiting the extended Kalman filter (EKF) and show that our proposed algorithms are computationally efficient, and hence, appropriate for practical implementations compared to the EKF. Simulation results further illustrate that the proposed algorithms are more accurate when the distance errors are small (low noise scenarios) in comparison with the EKF, while being more robust to the sampling period in high noise scenarios. Index Terms — Wireless sensor networks, cooperative mobile localization, multidimensional scaling, subspace tracking. 1.