Slavisa Tomic

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

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.

Distributed RSS-based localization in wireless sensor networks based on second-order cone programming.

In this paper, we propose a new approach based on convex optimization to address the received signal strength (RSS)-based cooperative localization problem in wireless sensor networks (WSNs). By using iterative procedures and measurements between two adjacent nodes in the network exclusively, each target node determines its own position locally. The localization problem is formulated using the maximum likelihood (ML) criterion, since ML-based solutions have the property of being asymptotically efficient. To overcome the non-convexity of the ML optimization problem, we employ the appropriate convex relaxation technique leading to second-order cone programming (SOCP). Additionally, a simple heuristic approach for improving the convergence of the proposed scheme for the case when the transmit power is known is introduced. Furthermore, we provide details about the computational complexity and energy consumption of the considered approaches. Our simulation results show that the proposed approach outperforms the existing ones in terms of the estimation accuracy for more than 1.5 m. Moreover, the new approach requires a lower number of iterations to converge, and consequently, it is likely to preserve energy in all presented scenarios, in comparison to the state-of-the-art approaches.

A Closed-Form Solution for RSS/AoA Target Localization by Spherical Coordinates Conversion

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 targets transmit power is also not known. Simulation results validate the outstanding performance of the proposed method.

Distributed algorithm for target localization in wireless sensor networks using RSS and AoA measurements

This paper addresses target localization problem in a cooperative 3-D wireless sensor network (WSN). We employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength (RSS) and angle-of-arrival (AoA) information, respectively. Based on range measurement model and simple geometry, we derive a novel non-convex estimator based on the least squares (LS) criterion. The derived non-convex estimator tightly approximates the maximum likelihood (ML) one for small noise levels. We show that the developed non-convex estimator is suitable for distributed implementation, and that it can be transformed into a convex one by applying a second-order cone programming (SOCP) relaxation technique. We also show that the developed non-convex estimator can be transformed into a generalized trust region sub-problem (GTRS) framework, by following the squared range (SR) approach. The proposed SOCP algorithm for known transmit powers is then generalized to the case where the transmit powers are different and not known. Furthermore, we provide a detailed analysis of the computational complexity of the proposed algorithms. Our simulation results show that the new estimators have excellent performance in terms of the estimation accuracy and convergence, and they confirm the effectiveness of combining two radio measurements.

Hybrid RSS-AoA technique for 3-D node localization in wireless sensor networks

We consider 3-D target positioning in noncooperative wireless sensor network (WSN) by employing received signal strength (RSS) and angle-of-arrival (AoA) measurements. Based on the least squares (LS) criterion, we derive a novel objective function for solving the hybrid localization problem. Despite the fact that the resulting optimization problem is non-convex, we show that it can be approximated into a convex problem by applying second-order cone programming (SOCP) relaxation. Moreover, we show that the objective function can be written in the form that belongs to the generalized trust region subproblems (GTRS), which can be solved exactly. Our numerical results exhibit remarkable performance of the new approaches, reducing the estimation error for more than 5 m and 3 m, in comparison to the state-of-the-art approach.

A bisection-based approach for exact target localization in NLOS environments

Abstract This work addresses the range-based target localization problem in adverse non-line-of-sight (NLOS) environments. We start by deriving the maximum likelihood (ML) estimator from the measurement model, since it is asymptotically efficient. However, this estimator is highly non-convex and difficult to solve directly. Hence, we convert the localization problem into a generalized trust region sub-problem (GTRS) framework. Although still non-convex in general, the derived estimator is strictly decreasing over a readily obtained interval, and thus, can be solved exactly by a bisection procedure. In huge contrast to existing algorithms, which either require the knowledge about the magnitude of the NLOS bias or to a priori distinguish between line-of-sight (LOS) and NLOS links, the new one does not require such prerequisites. Also, the computational complexity of the proposed algorithm is linear in the number of reference nodes, unlike the majority of existing ones. Our simulation results show that the new algorithm possesses a steady NLOS bias mitigation capacity and that it represents an excellent alternative in the sense of the trade off between accuracy and complexity. To be more specific, it not only matches the performance of existing methods (majority of which significantly more computationally complex) but outperforms them in general. Moreover, the performance of the proposed algorithm is validated through real-indoor experimental data.

A Robust Bisection-Based Estimator for TOA-Based Target Localization in NLOS Environments

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.

Distributed RSS-Based Localization in Wireless Sensor Networks with Node Selection Mechanism

In this work, we address the target localization problem in large-scale cooperative wireless sensor networks (WSNs). Using the noisy range measurements, extracted from the received signal strength (RSS) information, we formulate the localization problem based on the maximum likelihood (ML) criterion. ML-based solutions are particularly important due to their asymptotically optimal performance, but the localization problem is highly non-convex. To overcome this difficulty, we propose a convex relaxation leading to second-order cone programming (SOCP), which can be efficiently solved by interior-point algorithms. Furthermore, we investigate the case where target nodes limit the number of cooperating nodes by selecting only those neighbors with the highest RSS measurements. This simple procedure may decrease the energy consumption of an algorithm in both communication and computation phase. Our simulation results show that the proposed approach outperforms the existing ones in terms of the estimation accuracy. Moreover, they show that the new approach does not suffer significant degradation in its performance when the number of cooperating nodes is reduced.

RSS-based localization in wireless sensor networks using SOCP relaxation

This paper addresses the problem of locating a single source from noisy received signal-strength (RSS) measurements in wireless sensor networks (WSNs). To overcome the non-convexity of the maximum likelihood (ML) optimization problem, we provide an efficient convex relaxation that is based on the second order cone programming (SOCP), for both cases of known and unknown source transmit power, and we use a simple iterative procedure to solve the problem when the transmit power and the path loss exponent (PLE) are simultaneously unknown. Simulation results demonstrate that the new approach outperforms the existing ones in terms of the estimation accuracy, while in terms of the complexity, it represents a good balance when compared to the existing approaches.

Bayesian methodology for target tracking using combined RSS and AoA measurements

Abstract This work addresses the target tracking problem based on received signal strength (RSS) and angle of arrival (AoA) measurements. The Bayesian methodology, which integrates the information given by observations with prior knowledge extracted from target motion model in order to enhance the estimation accuracy was employed. First, by converting the considered highly non-linear measurement model into a linear one, i.e., a novel linearization technique of the measurement model is proposed. The derived model is then merged with the prior knowledge, and a novel maximum a posteriori (MAP) estimator whose solution is given in closed-form is proposed. It is also shown that the Kalman filter (KF) can be directly applied on top of the linearized observation model, which results in a proposal of a novel KF algorithm. Furthermore, to the best of authors’ knowledge, this paper premierly presents the application of the extended KF (EKF) and the unscented KF (UKF) to the considered tracking problem, by applying first-order linearization technique to the original non-linear model, and by applying the unscented transformation to carefully selected sample points, respectively. Finally, importance weights are computed for a large number of randomly selected sample points to render a well-known particle filter (PF) solution. Simulation results show that the proposed algorithms perform better than a naive one which uses only information from observations. They also confirm the effectiveness of the proposed linearization technique in comparison with the existing one, reducing the estimation error for about 25%.