Mohammad Reza Gholami

Cooperative Received Signal Strength-Based Sensor Localization With Unknown Transmit Powers

Cooperative localization (also known as sensor network localization) using received signal strength (RSS) measurements when the source transmit powers are different and unknown is investigated. Previous studies were based on the assumption that the transmit powers of source nodes are the same and perfectly known which is not practical. In this paper, the source transmit powers are considered as nuisance parameters and estimated along with the source locations. The corresponding Cramér-Rao lower bound (CRLB) of the problem is derived. To find the maximum likelihood (ML) estimator, it is necessary to solve a nonlinear and nonconvex optimization problem, which is computationally complex. To avoid the difficulty in solving the ML estimator, we derive a novel semidefinite programming (SDP) relaxation technique by converting the ML minimization problem into a convex problem which can be solved efficiently. The algorithm requires only an estimate of the path loss exponent (PLE). We initially assume that perfect knowledge of the PLE is available, but we then examine the effect of imperfect knowledge of the PLE on the proposed SDP algorithm. The complexity analyses of the proposed algorithms are also studied in detail. Computer simulations showing the remarkable performance of the proposed SDP algorithm are presented.

Improved Position Estimation Using Hybrid TW-TOA and TDOA in Cooperative Networks

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.

RSS-based sensor localization with unknown transmit power

Received signal strength (RSS)-based single source localization when there is not a prior knowledge about the transmit power of the source is investigated. Because of nonconvex behavior of maximum likelihood (ML) estimator, convoluted computations are required to achieve its global minimum. Therefore, we propose a novel semidefinite programming (SDP) approach by approximating ML problem to a convex optimization problem which can be solved very efficiently. Computer simulations show that our proposed SDP has a remarkable performance very close to ML estimator. Linearizing RSS model, we also derive the partly novel least squares (LS) and weighted total least squares (WTLS) algorithms for this problem. Simulations illustrate that WTLS improves the performance of LS considerably.

A new method of phase noise compensation in OFDM

The local oscillator phase noise can severely affect the performance of OFDM systems. In this paper a new method is presented for compensation of this phase noise. The method is based on the fact that the scattered pilots, which are used for channel estimation, are subject to the same phase error as the OFDM symbols. Least square approach is used to exploit the phase noise information that exists in the scattered pilots and compensate the phase noise on the OFDM symbols. Simulation results show that the method is very effective, especially in high SNR.

Bearing-only target localization with uncertainties in observer position

In this paper, the bearing-only target localization problem when the observer positions are subject to error is investigated. In this problem, the angle of arrival of the transmitted signal between target and observer are used to estimate the target position. It is assumed that not only the bearing measurements are corrupted by noise but also the exact position of observer is not available to the estimator. The accuracy of estimated location of target depends on the reliability of information from the observer position. Therefore, the previously published algorithms considering only the bearing measurement noise do not meet the expected performance when the observer positions are subject to error. The maximum likelihood, the least squares and total least square algorithms and a new method of localization based on weighted total least squares approach are developed for this problem. The corresponding Crame´r-Rao lower bound (CRLB) is derived for this problem. Computer simulations are performed to evaluate the performance of the proposed algorithms. Simulation results show that the new method can attain the CRLB for sufficiently high SNR.

RSS-Based Sensor Localization in the Presence of Unknown Channel Parameters

This correspondence studies the received signal strength-based localization problem when the transmit power or path-loss exponent is unknown. The corresponding maximum-likelihood estimator (MLE) poses a difficult nonconvex optimization problem. To avoid the difficulty in solving the MLE, we use suitable approximations and formulate the localization problem as a general trust region subproblem, which can be solved exactly under mild conditions. Simulation results show a promising performance for the proposed methods, which also have reasonable complexities compared to existing approaches.

Wireless network positioning as a convex feasibility problem

In this semi-tutorial paper, the positioning problem is formulated as a convex feasibility problem (CFP). To solve the CFP for non-cooperative networks, we consider the well-known projection onto convex sets (POCS) technique and study its properties for positioning. We also study outer-approximation (OA) methods to solve CFP problems. We then show how the POCS estimate can be upper bounded by solving a non-convex optimization problem. Moreover, we introduce two techniques based on OA and POCS to solve the CFP for cooperative networks and obtain two new distributed algorithms. Simulation results show that the proposed algorithms are robust against non-line-of-sight conditions.

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.

Cooperative Wireless Sensor Network Positioning via Implicit Convex Feasibility

We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions. Based on a geometric interpretation, we formulate the positioning problem as an implicit convex feasibility problem in which some of the sets depend on the unknown target positions and apply a parallel projection onto convex sets approach to estimate the unknown target node positions. The proposed technique is suitable for parallel implementation in which every target node in parallel can update its position and share the estimate of its location with other targets. We mathematically prove convergence of the proposed algorithm. Simulation results reveal enhanced performance for the proposed approach compared to available techniques based on projections, especially for sparse networks.

A Concave-Convex Procedure for TDOA Based Positioning

This letter investigates the time-difference-of-arrival based positioning problem in wireless sensor networks. We consider the least-mean absolute, i.e., the \ell_1 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.