Localization using Distance Geometry : Minimal Solvers and Robust Methods for Sensor Network Self-Calibration

In this thesis, we focus on the problem of estimating receiver and sender node positions given some form of distance measurements between them. This kind of localization problem has several applications, e.g., global and indoor positioning, sensor network calibration, molecular conformations, data visualization, graph embedding, and robot kinematics. More concretely, this thesis makes contributions in three different areas.First, we present a method for simultaneously registering and merging maps. The merging problem occurs when multiple maps of an area have been constructed and need to be combined into a single representation. If there are no absolute references and the maps are in different coordinate systems, they also need to be registered. In the second part, we construct robust methods for sensor network self-calibration using both Time of Arrival (TOA) and Time Difference of Arrival (TDOA) measurements. One of the difficulties is that corrupt measurements, so-called outliers, are present and should be excluded from the model fitting. To achieve this, we use hypothesis-and-test frameworks together with minimal solvers, resulting in methods that are robust to noise, outliers, and missing data. Several new minimal solvers are introduced to accommodate a range of receiver and sender configurations in 2D and 3D space. These solvers are formulated as polynomial equation systems which are solvedusing methods from algebraic geometry.In the third part, we focus specifically on the problems of trilateration and multilateration, and we present a method that approximates the Maximum Likelihood (ML) estimator for different noise distributions. The proposed approach reduces to an eigendecomposition problem for which there are good solvers. This results in a method that is faster and more numerically stable than the state-of-the-art, while still being easy to implement. Furthermore, we present a robust trilateration method that incorporates a motion model. This enables the removal of outliers in the distance measurements at the same time as drift in the motion model is canceled

Localization and security algorithms for wireless sensor networks and the usage of signals of opportunity

In this dissertation we consider the problem of localization of wireless devices in environments and applications where GPS (Global Positioning System) is not a viable option. The _x000C_rst part of the dissertation studies a novel positioning system based on narrowband radio frequency (RF) signals of opportunity, and develops near optimum estimation algorithms for localization of a mobile receiver. It is assumed that a reference receiver (RR) with known position is available to aid with the positioning of the mobile receiver (MR). The new positioning system is reminiscent of GPS and involves two similar estimation problems. The _x000C_rst is localization using estimates of time-di_x000B_erence of arrival (TDOA). The second is TDOA estimation based on the received narrowband signals at the RR and the MR. In both cases near optimum estimation algorithms are developed in the sense of maximum likelihood estimation (MLE) under some mild assumptions, and both algorithms compute approximate MLEs in the form of a weighted least-squares (WLS) solution. The proposed positioning system is illustrated with simulation studies based on FM radio signals. The numerical results show that the position errors are comparable to those of other positioning systems, including GPS. Next, we present a novel algorithm for localization of wireless sensor networks (WSNs) called distributed randomized gradient descent (DRGD), and prove that in the case of noise-free distance measurements, the algorithm converges and provides the true location of the nodes. For noisy distance measurements, the convergence properties of DRGD are discussed and an error bound on the location estimation error is obtained. In contrast to several recently proposed methods, DRGD does not require that blind nodes be contained in the convex hull of the anchor nodes, and can accurately localize the network with only a few anchors. Performance of DRGD is evaluated through extensive simulations and compared with three other algorithms, namely the relaxation-based second order cone programming (SOCP), the simulated annealing (SA), and the semi-de_x000C_nite programing (SDP) procedures. Similar to DRGD, SOCP and SA are distributed algorithms, whereas SDP is centralized. The results show that DRGD successfully localizes the nodes in all the cases, whereas in many cases SOCP and SA fail. We also present a modi_x000C_cation of DRGD for mobile WSNs and demonstrate the e_x000E_cacy of DRGD for localization of mobile networks with several simulation results. We then extend this method for secure localization in the presence of outlier distance measurements or distance spoo_x000C_ng attacks. In this case we present a centralized algorithm to estimate the position of the nodes in WSNs, where outlier distance measurements may be present

TW-TOA based positioning in the presence of clock imperfections

This manuscript studies the positioning problem based on two-way time-of-arrival (TW-TOA) measurements in semi-asynchronous wireless sensor networks in which the clock of a target node is unsynchronized with the reference time. Since the optimal estimator for this problem involves difficult nonconvex optimization, two suboptimal estimators are proposed based on the squared-range least squares and the least absolute mean of residual errors. We formulated the former approach as an extended general trust region subproblem (EGTR) and propose a simple technique to solve it approximately. The latter approach is formulated as a difference of convex functions programming (DCP), which can be solved using a concave–convex procedure. Simulation results illustrate the high performance of the proposed techniques, especially for the DCP approach

ROLAX: LOCATION DETERMINATION TECHNIQUES IN 4G NETWORKS

In this dissertation, ROLAX location determination system in 4G networks is presented. ROLAX provides two primary solutions for the location determination in the 4G networks. First, it provides techniques to detect the error-prone wireless conditions in geometric approaches of Time of Arrival (ToA) and Time Difference of Arrival (TDoA). ROLAX provides techniques for a Mobile Station (MS) to determine the Dominant Line-of-Sight Path (DLP) condition given the measurements of the downlink signals from the Base Station (BS). Second, robust RF fingerprinting techniques for the 4G networks are designed. The causes for the signal measurement variation are identified, and the system is designed taking those into account, leading to a significant improvement in accuracy. ROLAX is organized in two phases: offline and online phases. During the offline phase, the radiomap is constructed by wardriving. In order to provide the portability of the techniques, standard radio measurements such as Received Signal Strength Indication (RSSI) and Carrier to Interference Noise Ratio(CINR) are used in constructing the radiomap. During the online phase, a MS performs the DLP condition test for each BS it can observe. If the number of the BSs under DLP is small, the MS attempts to determine its location by using the RF fingerprinting. In ROLAX, the DLP condition is determined from the RSSI, CINR, and RTD (Round Trip Delay) measurements. Features generated from the RSSI difference between two antennas of the MS were also used. The features, including the variance, the level crossing rate, the correlation between the RSSI and RTD, and Kullback-Leibler Divergence, were successfully used in detecting the DLP condition. We note that, compared to using a single feature, appropriately combined multiple features lead to a very accurate DLP condition detection. A number of pattern matching techniques are evaluated for the purpose of the DLP condition detection. Artificial neural networks, instance-based learning, and Rotation Forest are particularly used in the DLP detection. When the Rotation Forest is used, a detection accuracy of 94.8\% was achieved in the live 4G networks. It has been noted that features designed in the DLP detection can be useful in the RF fingerprinting. In ROLAX, in addition to the DLP detection features, mean of RSSI and mean of CINR are used to create unique RF fingerprints. ROLAX RF fingerprinting techniques include: (1) a number of gridding techniques, including overlapped gridding; (2) an automatic radiomap generation technique by the Delaunay triangulation-based interpolation; (3) the filtering of measurements based upon the power-capture relationship between BSs; and (4) algorithms dealing with the missing data. In this work, software was developed using the interfaces provided by Beceem/Broadcom chip-set based software. Signals were collected from both the home network (MAXWell 4G network) and the foreign network (Clear 4G network). By combining the techniques in ROLAX, a distance error in the order of 4 meters was achieved in the live 4G networks

A Geometrical-Statistical Approach to Outlier Removal for TDOA Measurements

The curse of outlier measurements in estimation problems is a well-known issue in a variety of fields. Therefore, outlier removal procedures, which enables the identification of spurious measurements within a set, have been developed for many different scenarios and applications. In this paper, we propose a statistically motivated outlier removal algorithm for time differences of arrival (TDOAs), or equivalently range differences (RD), acquired at sensor arrays. The method exploits the TDOA-space formalism and works by only knowing relative sensor positions. As the proposed method is completely independent from the application for which measurements are used, it can be reliably used to identify outliers within a set of TDOA/RD measurements in different fields (e.g., acoustic source localization, sensor synchronization, radar, remote sensing, etc.). The proposed outlier removal algorithm is validated by means of synthetic simulations and real experiments