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