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.

/pdf/rss-based-localization-in-wireless-sensor-networks-using-3j47w55mtj.pdf

RSS-Based Localization in Wireless Sensor Networks Using Convex Relaxation: Noncooperative and Cooperative Schemes

Network localization and navigation (NLN) is a promising paradigm, in which mobile nodes exploit spatiotemporal cooperation, to provide reliable location information for a diverse range of wireless applications. This paper presents a theoretical foundation of NLN, including a mathematical formulation for NLN, an introduction of equivalent Fisher information analysis, and determination of the fundamental limits of localization accuracy. Key ingredients such as spatiotemporal cooperation, array signal processing, and map exploitation are then studied. We also develop a geometric interpretation to provide insights into the essence of NLN for network design. Finally, the paper highlights the connection between the theoretical foundation and algorithm development for NLN, guiding the design and operation of practical localization systems.

A Theoretical Foundation of Network Localization and Navigation

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., $P_{T}$ . 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 $P_{T}$ is straightforward to the case where $P_{T}$ is not known. Our simulation results show that the new estimators have excellent performance and are robust to not knowing $P_{T}$ . The new estimators for noncooperative localization significantly outperform the existing estimators, and our estimators for cooperative localization show exceptional performance in all considered settings.

/pdf/3-d-target-localization-in-wireless-sensor-networks-using-4zunbyo1oq.pdf

3-D Target Localization in Wireless Sensor Networks Using RSS and AoA Measurements

Emerging communication network applications including fifth-generation (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 Global Positioning System (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 toward 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.

https://research.chalmers.se/publication/503903/file/503903_Fulltext.pdf

Collaborative Sensor Network Localization: Algorithms and Practical Issues

Range based localization often relies on TOA that creates a circular contour or TDOA that yields hyperbolic surface to determine the position of an emitting object. Another approach that has gained attention recently is elliptic localization. Elliptic localization uses an active transmitter to send out a signal and several receivers to acquire the reflected or relayed signal from an object to obtain its location. This paper performs a fundamental investigation on the performance of elliptic localization, for both the synchronous and asynchronous cases between the transmitter and the receivers. Their performance is also characterized with respect to the hyperbolic localization. The study is based on the Cramer-Rao lower bound (CRLB) for the object location under Gaussian measurement noise as well as Gaussian errors in the transmitter and receiver positions. When the receiver positions are controllable, we derive the optimum receiver placement for elliptic positioning to improve the localization accuracy. We conclude the study with simulation results to demonstrate the elliptic localization performance using the CRLBs and the Maximum Likelihood estimators.

Elliptic Localization: Performance Study and Optimum Receiver Placement

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 Cramer-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.

https://publications.lib.chalmers.se/records/fulltext/local_164545.pdf

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

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