Non-line-of-sight Node Localization based on Semi-Definite Programming in Wireless Sensor Networks

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, we propose a semi-definite programming (SDP) based node localization algorithm in NLOS environment for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of LOS paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy. And it is not easy to efficiently distinguish LOS from NLOS measurements. In this paper, an algorithm is proposed that achieves high location accuracy without the need of identifying NLOS and LOS measurement.Comment: submitted to IEEE ICC'1

Distributed Cooperative Localization in Wireless Sensor Networks without NLOS Identification

In this paper, a 2-stage robust distributed algorithm is proposed for cooperative sensor network localization using time of arrival (TOA) data without identification of non-line of sight (NLOS) links. In the first stage, to overcome the effect of outliers, a convex relaxation of the Huber loss function is applied so that by using iterative optimization techniques, good estimates of the true sensor locations can be obtained. In the second stage, the original (non-relaxed) Huber cost function is further optimized to obtain refined location estimates based on those obtained in the first stage. In both stages, a simple gradient descent technique is used to carry out the optimization. Through simulations and real data analysis, it is shown that the proposed convex relaxation generally achieves a lower root mean squared error (RMSE) compared to other convex relaxation techniques in the literature. Also by doing the second stage, the position estimates are improved and we can achieve an RMSE close to that of the other distributed algorithms which know \textit{a priori} which links are in NLOS.Comment: Accepted in WPNC 201

On geometric upper bounds for positioning algorithms in wireless sensor networks

This paper studies the possibility of upper bounding the position error for range-based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes have positive errors, e.g., in non-line-of-sight (NLOS) conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the position error can be upper bounded as the maximum distance between the estimate and any point in the feasible set (the first bound). Alternatively, if an estimate given by a positioning algorithm is always feasible, the maximum length of the feasible set is an upper bound on position error (the second bound). These bounds are formulated as nonconvex optimization problems. To progress, we relax the nonconvex problems and obtain convex problems, which can be efficiently solved. Simulation results show that the proposed bounds are reasonably tight in many situations, especially for NLOS conditions

Localization of Distributed Wireless Sensor Networks using Two Sage SDP Optimization

A wireless sensor network (WSN) may comprise a large distributed set of low cost, low power sensing nodes. In many applications, the location of sensors is a necessity to evaluate the sensed data and it is not energy and cost efficient to equip all sensors with global positioning systems such as GPS. In this paper, we focus on the localization of sensors in a WSN by solving an optimization problem. In WSN localization, some sensors (called anchors) are aware of their location. Then, the distance measurements between sensors and anchors locations are used to localize the whole sensors in the network. WSN localization is a non-convex optimization problem, however, relaxation techniques such as semi-definite programming (SDP) are used to relax the optimization. To solve the optimization problem, all constraints should be considered simultaneously and the solution complexity order is O(n2) where n is the number of sensors. The complexity of SDP prevents solving large size problems. Therefore, it would be beneficial to reduce the problem size in large and distributed WSNs. In this paper, we propose a two stage optimization to reduce the solution time, while provide better accuracy compared with original SDP method. We first select some sensors that have the maximum connection with anchors and perform the SDP localization. Then, we select some of these sensors as virtual anchors. By adding the virtual anchors, we add more reference points and decrease the number of constraints. We propose an algorithm to select and add virtual anchors so that the total solution complexity and time decrease considerably, while improving the localization accuracy

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks

Enabling optimization-based localization for IoT devices

In this paper, we propose an embedded optimization approach for the localization of Internet of Things (IoT) devices making use of range measurements from ultra-wideband (UWB) signals. Low-cost, low-power UWB radios provide time-of-arrival measurements with decimeter accuracy over large distances. UWB-based localization methods have been envisioned to enable feedback control in IoT applications, particularly, in GPS-denied environments, and large wireless sensor networks. In this paper, we formulate the localization task as a nonlinear least-squares optimization problem based on two-way time-of-arrival measurements between the IoT device and several UWB radios installed in a 3-D environment. For the practical implementation of large-scale IoT deployments we further assume only approximate knowledge of the UWB radio locations. We solve the resulting optimization problem directly on IoT devices equipped with off-the-shelf microcontrollers using state-of-the-art code generation techniques for plug-and-play deployment of the nonlinear-programming algorithms. This paper further provides practical implementation details to improve the localization accuracy for feedback control in experimental IoT applications. The experimental results finally show that subdecimeter localization accuracy can be achieved using the proposed optimization-based approach, even when the majority of the UWB radio locations are unknown