Davide Macagnano

MAC Performances for Localization and Tracking in Wireless Sensor Networks

Time delay rather then throughput, is a constraint of greater importance in tracking systems. In particular, the maximum accces delay permissible by the application ins strongly related to the dynamics of theracked objects. The purpose of this article is to study the performance of a new media access control (MAC) technology specifically suited for LDR UWB systems [3] under the point of view of a tracking application. Specifically, the time delay necessary to collect the ranging information in both, star and meshed topology networks, have been studied as function of the number of mobiles in the network. More importantly, we propose two new ranging packet to be used inside the aforementioned MAC, in order to achieve in both the network topologies, a clear advantage compared to the current solution.

Indoor positioning: A key enabling technology for IoT applications

Motivated by the recent advances on internet of things (IoT) and the importance that location information has on many application scenarios, this article offers references to theoretical and localization-algorithmic tools that can be utilised in connection with IoT. We develop this discussion from basic to sophisticated localization techniques covering also some less-intuitive notions of localization, e.g. semantic positioning, for which we provide a novel solution which overcome the problem of privacy. We analyze the localization problem from a mathematical perspective; reviewing the most common and best-performing class of localization methods based on optimization and algebraic approaches and we discuss benefits of location information in a wireless system. In this regard we discuss few concrete applications scenario currently under investigation in the largest EU project on IoT, namely the FP-7 Butler project, how location information is one of the key enabling technology in the IoT. In addition to the theoretical aspect, this article provides references to the pervasive localization system architecture using the smart sensors developed within the Butler project.

Adaptive Gating for Multitarget Tracking With Gaussian Mixture Filters

In this correspondence, we use a generalization of the Bayesian approach to the multitarget problem that goes under the name of cardinalized probability hypothesis density (CPHD) filter to jointly estimate a time varying number of targets and their locations from sets of noisy range measurements. While in the case of Gaussian linear models a closed-form solution for the CPHD recursion exists in the form of a Gaussian mixture (GM), the more general case of nonlinear systems suboptimal solutions becomes necessary. Due to the Gaussianity assumption in the the GM-CPHD filter, we propose to integrate the square-root cubature Kalman filter (S-CKF) into the GM-CPHD recursion. A novel weighted gating strategy, which exploits the GM implementation of the proposed S-CKF-GM-CPHD filter, is offered to lower the computational time by adaptively increasing the gate sizes in proportion to the likelihood of the single GM components. The results reveal that the proposed gating yields considerable savings in processing requirements compared to no gating, without any significant degradation in performance. In addition, although the run time improvement achieved with elliptical or adaptive gating is equivalent, the latter does not degrade the results.

Gershgorin Analysis of Random Gramian Matrices With Application to MDS Tracking

We offer a redesigned form of the multidimensional scaling (MDS) algorithm suitable to the simultaneous tracking of a large number of targets with no a priori mobility models. First, we employ an extreme-value and asymptotic take on the theory of Gershgorin spectrum bounds to perform a detailed statistical analysis of the spectrum of random N × N Gramian matrices which arise from dynamic constructions of MDS kernels where the diagonalizer of a previous kernel is used to construct the next one. The analysis reveals that even if the subspace distance between consecutive kernels is relatively large, the dominant eigenspace of dynamic MDS kernels are, with a high probability quantified analytically, associated with its first rows. This feature is exploited further to design a statistically optimized and truncated variation of the Jacobi algorithm, which converges to the dominant eigenspace of a dynamic MDS kernel as fast as the overall optimal Jacobian, but without the exhaustive search for the elements to be annihilated at each rotation as required in the latter. Under the fact that the Euclidean double-centered kernels of the classic MDS method are asymptotically Gramian, and the knowledge of Nyström-inspired methods to compensate for data erasures, the technique presented yields a very efficient (fast) MDS-based multitarget tracking algorithm which achieves a remarkably low complexity of order O(√(N)), and which is robust to arbitrary statistics of the targets dynamics.

Localization and Tracking for LDR-UWB Systems

Localization and tracking (LT) algorithms for low data rate (LDR) ultra wideband (UWB) systems developed within the Integrated Project PULSERS Phase II are reviewed and compared. In particular, two localization algorithms, designed for static networks with mesh topologies, and one Tracking Algorithm, designed for dynamic network with star topologies are described and/or compared. Each of the localization algorithms adopts a different approach, namely, a centralized non-parametric weighted least squares approach (WLS), and a distributed Bayesian approach that relies on the cooperative maximization of the log-likelihood of range measurements (DMLL). The performance of these two alternatives are compared in a 3D indoor scenario under realistic ranging errors. The tracking algorithm is a fast non-parametric technique based on multidimensional scaling (MDS) and its performance is tested in a dynamic scenario. The proposed algorithms are practical and robust solutions addressing distinct network topologies and/or service requirements related to LDR-LT applications.

Tracking Multiple Dynamic Targets with Multidimensional Scaling

We consider the problem of tracking multiple targets in the presence of imperfect and incomplete ranging information, focusing on the impact of target dynamics. The targets are assumed to describe independent, continuous and differentiable trajectories with non-stationary (dynamic) statistics, i.e., with variable velocities and accelerations. The impact of such dynamics onto the performance, computational complexity and memory requirements of two tracking techniques, namely, the Kalman filter (KF) and multidimensional scaling (MDS), is investigated. The main feature of the MDS-based tracking algorithm, which we proposed in an earlier work, is that tracking is performed over the eigenspace of a Nystrom-Gram kernel matrix constructed with no a-priori knowledge of the statistics of target trajectories. Consequently, tracking becomes a problem of updating the eigenspace given new input data, which is achieved with an iterative Jacobian eigen-decomposition technique. An advantage of this technique over the KF is that tracking accuracy is independent on target dynamics. Furthermore, the number of iterations required to update the eigenspace, is shown to grow only logarithmically with the target dynamics and with the number of simultaneously tracked targets. As a result, the MDS-based tracking algorithm with Jacobian eigenspace updating becomes more efficient than the KF as soon as a relatively small number of targets are simultaneously tracked, and/or target dynamics exceeds a certain threshold.

Algebraic Approach for Robust Localization with Heterogeneous Information

We offer a redesigned form of the classical multidimensional scaling (C-MDS) algorithm suitable to handle the localization of multiple sources under line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. To do so we propose to modify the kernel matrix used in the MDS algorithm to allow for both distance and angle information to be processed algebraically (without iteration) and simultaneously. In so doing we also show that the new formulation overcomes two well known limitations of the C-MDS approach, namely the propagation error problem and the possibility to weight the dissimilarities used as measurement information, including, for the case of binary weights, the data erasure problem. Due to the increased size of the proposed edge kernel matrix KE used in the algorithm, the Nystrom approximation is applied to reduce the overall computational complexity to few matrix multiplications. Range only scenarios are also dealt with by approximating the matrix KE. Simulations in range-angle as well as range-only scenarios demonstrate the superiority of our solution under both LOS and NLOS conditions versus semidefinite programming (SDP) formulations of the problem specifically designed to exploit the heterogeneity of the information available.

A Comprehensive Tutorial on Localization: Algorithms and Performance Analysis Tools

This tutorial offers a comprehensive view of technological solutions and theoretical fundamentals of localization and tracking (LT) systems for wireless networks. We start with a brief classification of the most common types of LT systems, e.g. active versus passive technologies, centralized versus distributed solutions and so forth. To continue, we categorize the LT techniques based on the elementary types of position-related information, namely, connectivity, angle, distance and power-profile. The attention is then turned to the difference between active and passive LT systems, highlighting the evolution of the localization techniques. Motivated by the interests of industry and academia on distance-based active localization system, a deep review of the most common algorithms used in these systems is provided. Non-Bayesian and Bayesian techniques will be tackled and compared with numerical simulations. To list some of the proposed approaches, we mention the multidimensional scaling (MDS), the semidefinite programming (SDP) and the Kalman filter (KF) methods. To conclude the tutorial, we address the fundamental limits of the accuracy of range-based positioning. Based on the unifying framework proposed by Abel, we derive the closed-form expressions for the Cramér–Rao lower bound (CRLB), the Battacharyya Bound (BB), the Hammersley–Chapmann–Robbins Bound (HCRB) and the Abel Hybrid Bound (AHB) in a source localization scenario. We show a comparison of the aforementioned bounds with respect to a Maximum-Likelihood estimator and explore the difference between random and regular (equi-spaced anchors) network topologies. Finally, extensions to cooperative scenarios are also discussed in connection with the concept of information-coupling existing in multitarget networks.

Hypothesis Testing and Iterative WLS Minimization for WSN Localization under LOS/NLOS Conditions

We propose a novel non-parametric solution for accurate distance-based source localization in wireless sensor networks (WSNs). The proposed technique includes a method to detect whether or not ranging is affected by bias due to non- line-of-sight (NLOS) conditions, requiring no a-priori knowledge of distance estimate statistics. Instead, we exploit the triangular inequality property of the Euclidean space and employ hypothesis testing (HT) in order to derive confidence levels on the observations and classify each link in the network as LOS or NLOS. These confidence levels are then incorporated in the formulation of an iterative WLS (IWLS) algorithm for WSN localization. The combination of the two contributions proves a powerful WSN localization algorithm, that is robust to noise, bias and erasure (incompleteness) over ranging data.

Localization with heterogeneous information

Although during the last decade considerable efforts have been invested in the integration of different wireless technologies, a new surge of interest is arising due to the upcoming internet of things (IoT) in which many relevant application scenarios rely on location information. However, due to the heterogeneity of the devices, ergo the heterogeneity of information available, novel indoor positioning algorithms capable to account for different types of information must be designed. Differently from the vast majority of localization solutions currently available which rely on one specific type of observation, e.g. range information only, in this article we consider the localization problem of multiple sources from range and angle measurements. To this end we first study the benefit of heterogeneous information via the rigidity theory and the Cramèr-Rao Lower Bound (CRLB) and then we show how to utilize an extension of the Euclidean-kernel, i.e. the Edge-kernel, to perform robust positioning under Non-Line-of-Sight (NLOS) conditions. In particular with reference to the latter contribution it is shown how to exploit the robust principal component analysis theory to improve the edge-kernel recovery and in turn the estimated targets locations.