Cooperative and Distributed Localization for Wireless Sensor Networks in Multipath Environments

We consider the problem of sensor localization in a wireless network in a multipath environment, where time and angle of arrival information are available at each sensor. We propose a distributed algorithm based on belief propagation, which allows sensors to cooperatively self-localize with respect to one single anchor in a multihop network. The algorithm has low overhead and is scalable. Simulations show that although the network is loopy, the proposed algorithm converges, and achieves good localization accuracy

Indoor Cooperative Localization for Ultra Wideband Wireless Sensor Networks

In recent years there has been growing interest in ad-hoc and wireless sensor networks (WSNs) for a variety of indoor applications. Localization information in these networks is an enabling technology and in some applications it is the main sought after parameter. The cooperative localization performance of WSNs is ultimately constrained by the behavior of the utilized ranging technology in dense cluttered indoor environments. Recently, ultra-wideband (UWB) Time-of-Arrival (TOA) based ranging has exhibited potential due to its large bandwidth and high time resolution. However, the performance of its ranging and cooperative localization capabilities in dense indoor multipath environments needs to be further investigated. Of main concern is the high probability of non-line of sight (NLOS) and Direct Path (DP) blockage between sensor nodes, which biases the TOA estimation and degrades the localization performance. In this dissertation, we first present the results of measurement and modeling of UWB TOA-based ranging in different indoor multipath environments. We provide detailed characterization of the spatial behavior of ranging, where we focus on the statistics of the ranging error in the presence and absence of the DP and evaluate the pathloss behavior in the former case which is important for indoor geolocation coverage characterization. Parameters of the ranging error probability distributions and pathloss models are provided for different environments: traditional office, modern office, residential and manufacturing floor; and different ranging scenarios: indoor-to-indoor (ITI), outdoor-to-indoor (OTI) and roof-to-indoor (RTI). Based on the developed empirical models of UWB TOA-based OTI and ITI ranging, we derive and analyze cooperative localization bounds for WSNs in the different indoor multipath environments. First, we highlight the need for cooperative localization in indoor applications. Then we provide comprehensive analysis of the factors affecting localization accuracy such as network and ranging model parameters. Finally we introduce a novel distributed cooperative localization algorithm for indoor WSNs. The Cooperative LOcalization with Quality of estimation (CLOQ) algorithm integrates and disseminates the quality of the TOA ranging and position information in order to improve the localization performance for the entire WSN. The algorithm has the ability to reduce the effects of the cluttered indoor environments by identifying and mitigating the associated ranging errors. In addition the information regarding the integrity of the position estimate is further incorporated in the iterative distributed localization process which further reduces error escalation in the network. The simulation results of CLOQ algorithm are then compared against the derived G-CRLB, which shows substantial improvements in the localization performance

Distributed Algorithms for Target Localization in Wireless Sensor Networks Using Hybrid Measurements

This dissertation addresses the target localization problem in wireless sensor networks (WSNs). WSNs is now a widely applicable technology which can have numerous practical applications and offer the possibility to improve people’s lives. A required feature to many functions of a WSN, is the ability to indicate where the data reported by each sensor was measured. For this reason, locating each sensor node in a WSN is an essential issue that should be considered. In this dissertation, a performance analysis of two recently proposed distributed localization algorithms for cooperative 3-D wireless sensor networks (WSNs) is presented. The tested algorithms rely on distance and angle measurements obtained from received signal strength (RSS) and angle-of-arrival (AoA) information, respectively. The measurements are then used to derive a convex estimator, based on second-order cone programming (SOCP) relaxation techniques, and a non-convex one that can be formulated as a generalized trust region sub-problem (GTRS). Both estimators have shown excellent performance assuming a static network scenario, giving accurate location estimates in addition to converging in few iterations. The results obtained in this dissertation confirm the novel algorithms’ performance and accuracy. Additionally, a change to the algorithms is proposed, allowing the study of a more realistic and challenging scenario where different probabilities of communication failure between neighbor nodes at the broadcast phase are considered. Computational simulations performed in the scope of this dissertation, show that the algorithms’ performance holds for high probability of communication failure and that convergence is still achieved in a reasonable number of iterations

Tight Two-Dimensional Outer-Approximations of Feasible Sets in Wireless Sensor Networks

Finding a tight ellipsoid that contains the intersection of a finite number of ellipsoids is of interest in positioning applications for wireless sensor networks (WSNs). To this end, we propose a novel geometrical method in 2-dimensional (2-D) space. Specifically, we first find a tight polygon, which contains the desired region and then obtain the tightest ellipse containing the polygon by solving a convex optimization problem. For demonstrating the usefulness of this method, we employ it in a distributed algorithm for elliptical outer-approximation of feasible sets in co-operative WSNs. Through simulations, we show that the proposed method gives a tighter bounding ellipse than conventional methods, while having similar computational cost

Localization Of Sensors In Presence Of Fading And Mobility

The objective of this dissertation is to estimate the location of a sensor through analysis of signal strengths of messages received from a collection of mobile anchors. In particular, a sensor node determines its location from distance measurements to mobile anchors of known locations. We take into account the uncertainty and fluctuation of the RSS as a result of fading and take into account the decay of the RSS which is proportional to the transmitter-receiver distance power raised to the PLE. The objective is to characterize the channel in order to derive accurate distance estimates from RSS measurements and then utilize the distance estimates in locating the sensors. To characterize the channel, two techniques are presented for the mobile anchors to periodically estimate the channel\u27s PLE and fading parameter. Both techniques estimate the PLE by solving an equation via successive approximations. The formula in the first is stated directly from MLE analysis whereas in the second is derived from a simple probability analysis. Then two distance estimates are proposed, one based on a derived formula and the other based on the MLE analysis. Then a location technique is proposed where two anchors are sufficient to uniquely locate a sensor. That is, the sensor narrows down its possible locations to two when collects RSS measurements transmitted by a mobile anchor, then uniquely determines its location when given a distance to the second anchor. Analysis shows the PLE has no effect on the accuracy of the channel characterization, the normalized error in the distance estimation is invariant to the estimated distance, and accurate location estimates can be achieved from a moderate sample of RSS measurements

Error bounds for wireless localization in NLOS environments

An efficient and accurate method to evaluate the fundamental error bounds for wireless sen-sor localization is proposed. While there already exist efficient tools like Cram`er-Rao lower bound (CRLB) and position error bound (PEB) to estimate error limits, in their standard formulation they all need an accurate knowledge of the statistic of the ranging error. This requirement, under Non-Line-of-Sight (NLOS) environments, is impossible to be met a priori. Therefore, it is shown that collecting a small number of samples from each link and applying them to a non-parametric estimator, like the Gaussian kernel (GK), could lead to a quite accurate reconstruction of the error distribution. A proposed Edgeworth Expansion method is employed to reconstruct the error statistic in a much more efficient way with respect to the GK. It is shown that with this method, it is possible to get fundamental error bounds almost as accurate as the theoretical case, i.e. when a priori knowledge of the error distribution is available. Therein, a technique to determine fundamental error limits – CRLB and PEB – onsite without knowledge of the statistics of the ranging errors is proposed

Distributed Local Linear Parameter Estimation using Gaussian SPAWN

We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. Sensors exchange messages and cooperate with each other to estimate their own local parameters iteratively. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief propagation, but uses fixed size broadcast messages at each sensor instead. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, the gSPAWN algorithm allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that the gSPAWN algorithm converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of the gSPAWN algorithm to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs, with comparable root mean square errors