Browsing by Author "Gholami, M. R."

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Open Access
A concave-convex procedure for TDOA based positioning
(IEEE, 2013) Gholami, M. R.; Gezici, Sinan; Strom, E. G.
This letter investigates the time-difference-of-arrival based positioning problem in wireless sensor networks. We consider the least-mean absolute, i.e., the ℓ1 norm, minimization of the residual errors and formulate the positioning problem as a difference of convex functions (DC) programming. We then employ a concave-convex procedure to solve the corresponding DC programming. Simulation results illustrate the improved performance of the proposed approach compared to existing methods. © 1997-2012 IEEE.
Open Access
Cooperative positioning in wireless networks
(John Wiley & Sons, 2016) Gholami, M. R.; Keskin, M. F.; Gezici, Sinan; Jansson, M.; Webster, J. G.
In this article, we study cooperative positioning in wireless networks in which target nodes at unknown locations locally collaborate with each other to find their locations. We review different models available for positioning and categorize the model‐based algorithms in two groups: centralized and distributed. We then investigate a lower bound on the variance of unbiased estimators, namely the Cramer–Rao lower bound, which is a common benchmark in the positioning literature. We finally discuss some open problems and research topics in the area of positioning that are worth exploring in future studies.
Open Access
Distributed bounding of feasible sets in cooperative wireless network positioning
(IEEE, 2013) Gholami, M. R.; Wymeersch, H.; Gezici, Sinan; Ström, E. G.
Locations of target nodes in cooperative wireless sensor networks can be confined to a number of feasible sets in certain situations, e.g., when the estimated distances between sensors are larger than the actual distances. Quantifying feasible sets is often challenging in cooperative positioning. In this letter, we propose an iterative technique to cooperatively outer approximate the feasible sets containing the locations of the target nodes. We first outer approximate a feasible set including a target node location by an ellipsoid. Then, we extend the ellipsoid with the measured distances between sensor nodes and obtain larger ellipsoids. The larger ellipsoids are used to determine the intersections containing other targets. Simulation results show that the proposed technique converges after a small number of iterations.
Open Access
Improved position estimation using hybrid TW-TOA and TDOA in cooperative networks
(Institute of Electrical and Electronics Engineers, 2012-04-13) Gholami, M. R.; Gezici, Sinan; Ström, E. G.
This paper addresses the problem of positioning multiple target nodes in a cooperative wireless sensor network in the presence of unknown turn-around times. In this type of cooperative networks, two different reference sensors, namely, primary and secondary nodes, measure two-way time-of-arrival (TW-TOA) and time-difference-of-arrival (TDOA), respectively. Motivated by the role of secondary nodes, we extend the role of target nodes such that they can be considered as pseudo secondary nodes. By modeling turn-around times as nuisance parameters, we derive a maximum likelihood estimator (MLE) that poses a difficult global optimization problem due to its nonconvex objective function. To avoid drawbacks in solving the MLE, we linearize the measurements using two different techniques, namely, nonlinear processing and first-order Taylor series, and obtain linear models based on unknown parameters. The proposed linear estimator is implemented in three steps. In the first step, a coarse position estimate is obtained for each target node, and it is refined through steps two and three. To evaluate the performance of different methods, we derive the Cramér-Rao lower bound (CRLB). Simulation results show that the cooperation technique provides considerable improvements in positioning accuracy compared to the noncooperative scenario, especially for low signal-to-noise-ratios.
Open Access
Jamming of Wireless Localization Systems
(Institute of Electrical and Electronics Engineers Inc., 2016) Gezici, Sinan; Gholami, M. R.; Bayram, S.; Jansson M.
In this paper, the optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes, whereas in the second scheme, the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both the schemes are formulated as linear programs, and a closed-form solution is obtained for the first scheme. For the second scheme, under certain conditions, the property of full total power utilization is specified, and a closed-form solution is obtained when the total power is lower than a specific threshold. In addition, it is shown that non-zero power is allocated to at most NT jammer nodes according to the second scheme in the absence of peak power constraints, where NT is the number of target nodes. In the presence of parameter uncertainty, robust versions of the power allocation schemes are proposed. Simulation results are presented to investigate the performance of the proposed schemes and to illustrate the theoretical results. © 2016 IEEE.
Open Access
Optimal jammer placement in wireless localization networks
(IEEE, 2015-06-07) Gezici, Sinan; Bayram, S.; Gholami, M. R.; Jansson, M.
The optimal jammer placement problem is proposed for a wireless localization network, where the aim is to degrade the accuracy of locating target nodes as much as possible. In particular, the optimal location of a jammer node is obtained in order to maximize the minimum of the Cramér-Rao lower bounds for a number of target nodes under location related constraints for the jammer node. Theoretical results are derived to specify scenarios in which the jammer node should be located as close to a certain target node as possible, or the optimal location of the jammer node is determined by two or three of the target nodes. In addition, explicit expressions for the optimal location of the jammer node are derived in the presence of two target nodes. Numerical examples are presented to illustrate the theoretical results. © 2015 IEEE.
Open Access
Optimal jammer placement in wireless localization systems
(Institute of Electrical and Electronics Engineers Inc., 2016) Gezici, Sinan; Bayram, S.; Kurt, M. N.; Gholami, M. R.
In this study, the optimal jammer placement problem is proposed and analyzed for wireless localization systems. In particular, the optimal location of a jammer node is obtained by maximizing the minimum of the Cramér-Rao lower bounds (CRLBs) for a number of target nodes under location related constraints for the jammer node. For scenarios with more than two target nodes, theoretical results are derived to specify conditions under which the jammer node is located as close to a certain target node as possible, or the optimal location of the jammer node is determined by two of the target nodes. Also, explicit expressions are provided for the optimal location of the jammer node in the presence of two target nodes. In addition, in the absence of distance constraints for the jammer node, it is proved, for scenarios with more than two target nodes, that the optimal jammer location lies on the convex hull formed by the locations of the target nodes and is determined by two or three of the target nodes, which have equalized CRLBs. Numerical examples are presented to provide illustrations of the theoretical results in different scenarios. © 1991-2012 IEEE.
Open Access
TDOA based positioning in the presence of unknown clock skew
(IEEE, 2013-06) Gholami, M. R.; Gezici, Sinan; Strom, E. G.
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.
Open Access
TW-TOA based positioning in the presence of clock imperfections
(Elsevier Inc., 2016) Gholami, M. R.; Gezici, Sinan; Ström, E. G.
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 formulate 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. © 2016 Elsevier Inc.
Open Access
Upper bounds on position error of a single location estimate in wireless sensor networks
(Hindawi Publishing Corporation, 2014) Gholami, M. R.; Ström, E. G.; Wymeersch, H.; Gezici, Sinan
This paper studies upper bounds on the position error for a single estimate of an unknown target node position based on distance estimates in wireless sensor networks. In this study, we investigate a number of approaches to confine the target node position to bounded sets for different scenarios. Firstly, if at least one distance estimate error is positive, we derive a simple, but potentially loose upper bound, which is always valid. In addition assuming that the probability density of measurement noise is nonzero for positive values and a sufficiently large number of distance estimates are available, we propose an upper bound, which is valid with high probability. Secondly, if a reasonable lower bound on negative measurement errors is known a priori, we manipulate the distance estimates to obtain a new set with positive measurement errors. In general, we formulate bounds as nonconvex optimization problems. To solve the problems, we employ a relaxation technique and obtain semidefinite programs. We also propose a simple approach to find the bounds in closed forms. Simulation results show reasonable tightness for different bounds in various situations.