Abstract—We consider least squares (LS) approaches for locating a radiating source from range measurements (which we call R-LS) or from range-difference measurements (RD-LS) collected using an array of passive sensors. We also consider LS approaches based on squared range observations (SR-LS) and based on squared range-difference measurements (SRD-LS). Despite the fact that the resulting optimization problems are nonconvex, we provide exact solution procedures for efficiently computing the SR-LS and SRD-LS estimates. Numerical simulations suggest that the exact SR-LS and SRD-LS estimates outperform existing approximations of the SR-LS and SRD-LS solutions as well as approximations of the R-LS and RD-LS 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, range-difference measurements, single quadratic constraint, source localization, squared range observations. I.

Multidimensional scaling (MDS) is a class of methods used to find a low-dimensional 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 fixed-point 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

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 semi-precise 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.

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 partially-connected 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.

GNSS receivers compute its position by a two-steps 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 single-step procedure, obtaining the Maximum Likelihood estimate of position. We base on a recent result to show that the variance of the single-step estimator is lower than the variance of the conventional two-steps estimation of position. The result is validated by computer simulations, comparing the performances of both alternatives. 1.

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 phase-based 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.

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 range-based 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.