In this paper, we propose new approaches based on convex optimization to address the received signal strength (RSS)-based noncooperative and cooperative localization problems in wireless sensor networks (WSNs). By using an array of passive anchor nodes, we collect the noisy RSS measurements from radiating source nodes in WSNs, which we use to estimate the source positions. We derive the maximum likelihood (ML) estimator, since the ML-based solutions have particular importance due to their asymptotically optimal performance. However, the ML estimator requires the minimization of a nonconvex objective function that may have multiple local optima, thus making the search for the globally optimal solution hard. To overcome this difficulty, we derive a new nonconvex estimator, which tightly approximates the ML estimator for small noise. Then, the new estimator is relaxed by applying efficient convex relaxations that are based on second-order cone programming and semidefinite programming in the case of noncooperative and cooperative localization, respectively, for both cases of known and unknown source transmit power. We also show that our approaches work well in the case when the source transmit power and the path loss exponent are simultaneously unknown at the anchor nodes. Moreover, we show that the generalization of the new approaches for the localization problem in indoor environments is straightforward. Simulation results show that the proposed approaches significantly improve the localization accuracy, reducing the estimation error between 15% and 20% on average, compared with the existing approaches.

This paper addresses target localization problems in both noncooperative and cooperative 3-D wireless sensor networks (WSNs), for both cases of known and unknown sensor transmit power, i.e., PT . We employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength and angle-of-arrival information, respectively. Based on range and angle measurement models, we derive a novel nonconvex estimator based on the least squares criterion. The derived nonconvex estimator tightly approximates the maximum-likelihood estimator for small noise. We then show that the developed estimator can be transformed into a generalized trust region subproblem framework, by following the squared range approach, for noncooperative WSNs. For cooperative WSNs, we show that the estimator can be transformed into a convex problem by applying appropriate semidefinite programming relaxation techniques. Moreover, we show that the generalization of the proposed estimators for known PT is straightforward to the case where PT is not known. Our simulation results show that the new estimators have excellent performance and are robust to not knowing PT . The new estimators for noncooperative localization significantly outperform the existing estimators, and our estimators for cooperative localization show exceptional performance in all considered settings.

This letter addresses the hybrid range/angle-based target localization problem in a cooperative 3-D wireless sensor network where no central processor is available. Due to battery exhaust over time, sensors' transmit powers are assumed different and unknown. Range and angle measurements are drawn from the received signal strength and angle-of-arrival models, respectively. By exploiting the measurement models, we derive a novel local-estimator by which each target updates its own estimate, based on the least squares criterion. Second-order cone relaxation technique is then applied to approximately solve the attained problem due to its non-convex nature. Our simulation results show that the proposed algorithm efficiently solves the localization problem.

This letter addresses the problem of target localization in a 3-D space, utilizing combined measurements of received signal strength and angle of arrival (AoA). By using the spherical coordinate conversion and available AoA observations to establish new relationships between the measurements and the unknown target location, we derive a simple closed-form solution method. We then show that the proposed method has straightforward adaptation to the case where the target’s transmit power is also not known. Simulation results validate the outstanding performance of the proposed method.

This letter addresses the problem of target localization in harsh indoor environments based on range measurements. To mitigate the non-line-of-sight (NLOS) bias, we propose a novel robust estimator by transforming the localization problem into a generalized trust region sub-problem framework. Although still non-convex in general, this class of problems can be readily solved exactly by means of bisection procedure. The new approach does not require to make any assumptions about the statistics of NLOS bias, nor to try to distinguish which links are NLOS and which are not. Unlike the existing algorithms, the computational complexity of the proposed algorithm is linear in the number of reference nodes. Our simulation results corroborate the effectiveness of the new algorithm in terms of NLOS bias mitigation and show that the performance of our estimator is highly competitive with the performance of the state-of-the-art algorithms. In fact, they show that the novel estimator outperforms slightly the existing ones in general, and that it always provides a feasible solution.