Browsing by Subject "Least Square"
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Item Open Access Fundamental limits and improved algorithms for linear least-squares wireless position estimation(John Wiley & Sons, 2010-09-22) Guvenc, I.; Gezici, Sinan; Sahinoglu Z.In this paper, theoretical lower bounds on performance of linear least-squares (LLS) position estimators are obtained, and performance differences between LLS and nonlinear least-squares (NLS) position estimators are quantified. In addition, two techniques are proposed in order to improve the performance of the LLS approach. First, a reference selection algorithm is proposed to optimally select the measurement that is used for linearizing the other measurements in an LLS estimator. Then, a maximum likelihood approach is proposed, which takes correlations between different measurements into account in order to reduce average position estimation errors. Simulations are performed to evaluate the theoretical limits and to compare performance of various LLS estimators.Item Open Access Range based sensor node localization in the presence of unknown clock skews(IEEE, 2013) Gholami, M.R.; Gezici, Sinan; Strom, E.G.We deal with the positioning problem based on two-way time-of-arrival (TW-TOA) measurements in asynchronous wireless sensor networks. The optimal estimator for this problem poses a difficult global optimization problem. To avoid the drawbacks in solving the optimal estimator, we use approximations and derive linear models, which facilitate efficient solutions. In particular, we employ the least squares method and solve a general trust region subproblem to find a coarse estimate. To further refine the estimate, we linearize the measurements and obtain a linear model which can be solved using regularized least squares. Simulation results illustrate that the proposed approaches asymptotically attain the Cramér-Rao lower bound. © 2013 IEEE.Item Open Access Static positioning using UWB range measurements(IEEE, 2010) Gholami, M.R.; Ström, E.G.; Sottile F.; Dardari, D.; Conti, A.; Gezici, Sinan; Rydström, M.; Spirito, M.A.The performance of several existing and partly new algorithms for positioning of sensor node based on distance estimate is compared when the distance estimates are obtained from a measurement campaign. The distance estimates are based on time-of-arrival measurements done by ultrawideband devices in an indoor office environment. Two different positioning techniques are compared: statistical and geometrical. In statistical category, distributed weighted-multidimensional scaling (dwMDS), least squares, and sum product algorithm are evaluated and in geometrical technique projections approach and outer approximation (OA) method are investigated. No method shows the best performance in all cases, while in many situations, sum product algorithm, dwMDS, nonlinear least square, projection approach, OA, and weighted least square work well. Copyright © The authors.Item Open Access Structured least squares problems and robust estimators(IEEE, 2010-10-22) Pilanci, M.; Arıkan, Orhan; Pinar, M. C.A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.Item Open Access Structured least squares with bounded data uncertainties(IEEE, 2009) Pilanci, Mert; Arıkan, Orhan; Oguz, B.; Pınar, Mustafa C.In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise.