Range based sensor node localization in the presence of unknown clock skews

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

TW-TOA based positioning in the presence of clock imperfections

This manuscript studies the positioning problem based on two-way time-of-arrival (TW-TOA) measurements in semi-asynchronous wireless sensor networks in which the clock of a target node is unsynchronized with the reference time. Since the optimal estimator for this problem involves difficult nonconvex optimization, two suboptimal estimators are proposed based on the squared-range least squares and the least absolute mean of residual errors. We formulated the former approach as an extended general trust region subproblem (EGTR) and propose a simple technique to solve it approximately. The latter approach is formulated as a difference of convex functions programming (DCP), which can be solved using a concave–convex procedure. Simulation results illustrate the high performance of the proposed techniques, especially for the DCP approach

TDOA based positioning in the presence of unknown clock skew

Cataloged from PDF version of article.This paper studies the positioning problem of a single target node based on time-difference-of-arrival (TDOA) measurements in the presence of clock imperfections. Employing an affine model for the behaviour of a local clock, it is observed that TDOA based approaches suffer from a parameter of the model, called the clock skew. Modeling the clock skew as a nuisance parameter, this paper investigates joint clock skew and position estimation. The maximum likelihood estimator (MLE) is derived for this problem, which is highly nonconvex and difficult to solve. To avoid the difficulty in solving the MLE, we employ suitable approximations and relaxations and propose two suboptimal estimators based on semidefinite programming and linear estimation. To further improve the estimation accuracy, we also propose a refining step. In addition, the Cramer-Rao ´ lower bound (CRLB) is derived for this problem as a benchmark. Simulation results show that the proposed suboptimal estimators can attain the CRLB for sufficiently high signal-to-noise ratios

TDOA Based Positioning in the Presence of Unknown Clock Skew

This paper studies the positioning problem of a single target node based on time-difference-of-arrival (TDOA) measurements in the presence of clock imperfections. Employing an affine model for the behaviour of a local clock, it is observed that TDOA based approaches suffer from a parameter of the model, called the clock skew. Modeling the clock skew as a nuisance parameter, this paper investigates joint clock skew and position estimation. The maximum likelihood estimator (MLE) is derived for this problem, which is highly nonconvex and difficult to solve. To avoid the difficulty in solving the MLE, we employ suitable approximations and relaxations and propose two suboptimal estimators based on semidefinite programming and linear estimation. To further improve the estimation accuracy, we also propose a refining step. In addition, the Cramér-Rao lower bound (CRLB) is derived for this problem as a benchmark. Simulation results show that the proposed suboptimal estimators can attain the CRLB for sufficiently high signal-to-noise ratios