Browsing by Subject "Linear estimators"
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Item Unknown Hybrid TW-TOA/TDOA positioning algorithms for cooperative wireless networks(IEEE, 2011) Gholami, M.R.; Gezici, Sinan; Ström, E.G.; Rydström, M.The problem of positioning an unknown target is studied for a cooperative wireless sensor network using hybrid two-way time-of-arrival and time-difference-of-arrival measurements. A maximum likelihood estimator (MLE) can be employed to solve the problem. Due to the non-linear nature of the cost function in the MLE, a numerical method, e.g., an iterative search algorithm with a good initial point, should be taken to accurately estimate the target. To avoid drawbacks in a numerical method, we instead linearize the measurements and obtain a new two-step estimator that has a closed-form solution in each step. Simulation results confirm that the proposed linear estimator can attain Cramer-Rao lower bound for sufficiently high SNR. © 2011 IEEE.Item 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.Item Open Access Positioning algorithms for cooperative networks in the presence of an unknown turn-around time(IEEE, 2011) Gholami, M.R.; Gezici, Sinan; Ström, E.G.; Rydström, M.This paper addresses the problem of single node positioning in cooperative network using hybrid two-way time-of-arrival and time-difference-of-arrival where, the turn-around time at the target node is unknown. Considering the turn-around time as a nuisance parameter, the derived maximum likelihood estimator (MLE) brings a difficult global optimization problem due to local minima in the cost function of the MLE. To avoid drawbacks in solving the MLE, we obtain a linear two-step estimator using non-linear pre-processing which is algebraic and closed-form in each step. To compare different methods, Cramér-Rao lower bound (CRLB) is derived. Simulation results confirm that the proposed linear estimator attains the CRLB for sufficiently high signal-to-noise ratios. © 2011 IEEE.