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.

Emerging communication network applications including 5G cellular and the Internet-of-Things (IoT) will almost certainly require location information at as many network nodes as possible. Given the energy requirements and lack of indoor coverage of GPS, collaborative localization appears to be a powerful tool for such networks. In this paper, we survey the state of the art in collaborative localization with an eye towards 5G cellular and IoT applications. In particular, we discuss theoretical limits, algorithms, and practical challenges associated with collaborative localization based on range-based as well as range-angle-based techniques.

In this paper, cooperative source localization using range-based measurements in severe non-line-of-sight (NLOS) environments is studied. The accuracy of localization can degrade significantly in indoor and dense environments where the majority of connections are NLOS. Cooperative localization is highly beneficial in such environments by improving localization performance considerably. However, NLOS connections still must be handled properly. In this work, a novel cooperative localization algorithm with the ability to mitigate NLOS propagation based on semidefinite programming (SDP) is derived. It is assumed that the algorithm knows neither which connections are NLOS nor the distribution of NLOS propagation. The performance of the proposed SDP method is compared with that of the optimal maximum likelihood estimator and several previously considered methods through computer simulations. It will be shown that the proposed SDP method substantially outperforms other methods in NLOS environments.Index Terms-Cooperative localization, non-line-of-sight (NLOS), semidefinite programming (SDP). 1089-7798 (c)

In this paper, asynchronous wireless source localization using timeof-arrival (TOA) measurements is studied. In TOA localization, the travel time of the signal between the source node and anchor nodes is measured and used to estimate range. In synchronous networks, the anchor nodes know when the source node starts transmission. In asynchronous networks, however, the source transmit time is unknown and TOA measurements have a positive bias due to the synchronization error which could lead to a large localization error. One way to tackle this problem is to use time-difference-of-arrival (TDOA) measurements which do not depend on the source transmission time. However, in this work, applying an alternative approach, we estimate the source transmit time as a nuisance parameter jointly with the source location. The optimal maximum likelihood (ML) estimator is derived. To avoid the ML convergence problem, a novel semidefinite programming (SDP) technique is proposed by converting the noncovex ML problem into a convex one. Computer simulations showing superior performance of the proposed SDP estimator are conducted.Index Terms-time-of-arrival (TOA), source localization, semidefinite programming (SDP), asynchronous networks.

This paper 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.

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.

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