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16
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 23 (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.
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.
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 5 (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.
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
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 2 (1 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 2 (2 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.
Ranging energy optimization for robust sensor positioning
 2009 ” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '09
"... We address ranging energy optimization for an unsynchronized localization system, which features robust sensor positioning, in the sense that specific accuracy requirements are fulfilled within a prescribed service area. Optimization problems related to the ranging energy of a sensor and beacons are ..."
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Cited by 1 (0 self)
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We address ranging energy optimization for an unsynchronized localization system, which features robust sensor positioning, in the sense that specific accuracy requirements are fulfilled within a prescribed service area. Optimization problems related to the ranging energy of a sensor and beacons are proposed, after which a practical algorithm based on semidefinite programming is presented. The effectiveness of the algorithm is illustrated by a numerical experiment. Index Terms — CramérRao bound, semidefinite programming, localization
DIRECT POSITION ESTIMATION APPROACH OUTPERFORMS CONVENTIONAL TWOSTEPS POSITIONING
"... GNSS receivers compute its position by a twosteps procedure. First, synchronization parameters are estimated and, then, a geometrical problem is solved to obtain receiver’s position. This is the approach typically taken due to its simplicity and modularity. However, recent results pointed out the p ..."
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GNSS receivers compute its position by a twosteps procedure. First, synchronization parameters are estimated and, then, a geometrical problem is solved to obtain receiver’s position. This is the approach typically taken due to its simplicity and modularity. However, recent results pointed out the potential pitfalls of such approach. In that vein, Direct Position Estimation arise as a potential alternative, computing receiver’s position directly from the digitized GNSS signal. The latter is performed as a singlestep procedure, obtaining the Maximum Likelihood estimate of position. We base on a recent result to show that the variance of the singlestep estimator is lower than the variance of the conventional twosteps estimation of position. The result is validated by computer simulations, comparing the performances of both alternatives. 1.
NEW CONSTRAINED LEAST SQUARES APPROACH FOR RANGEBASED POSITIONING
, 2011
"... The problem of finding the location of a target based on range measurements from an array of receivers is addressed. In the linear least squares (LLS) approach for rangebased positioning, an extra range variable is usually introduced. In this paper, we derive a LLS algorithm with exploiting the kno ..."
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The problem of finding the location of a target based on range measurements from an array of receivers is addressed. In the linear least squares (LLS) approach for rangebased positioning, an extra range variable is usually introduced. In this paper, we derive a LLS algorithm with exploiting the known relation between the source position and range variable, which results in a simple constrained optimization problem. The optimality of the proposed algorithm at sufficiently small noise conditions is demonstrated by the theoretical analysis as well as computer simulations. 1.
Accurate and Simple Source Localization Using Differential Received Signal Strength
"... Locating an unknownposition source using received signal strength (RSS) measurements in an accurate and lowcomplexity manner is addressed in this paper. Given that the source transmit power is unknown, we employ the differential RSS information to devise two computationally attractive localization ..."
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Locating an unknownposition source using received signal strength (RSS) measurements in an accurate and lowcomplexity manner is addressed in this paper. Given that the source transmit power is unknown, we employ the differential RSS information to devise two computationally attractive localization methods based on the weighted least squares (WLS) approach. The main ingredients in the first algorithm development are to obtain the unbiased estimates of the squared ranges and introduce an extra variable. The second method improves the first version by implicitly exploiting the relationship between the extra variable and source location through a second WLS step. The performance of the two estimators is analyzed in the presence of zeromean white Gaussian disturbances. Numerical examples are also included to evaluate their localization accuracy by comparing with the maximum likelihood approach and CramérRao lower bound. Keywords: source localization, received signal strength, positioning algorithm, least squares 1.