Distributed on-line multidimensional scaling for self-localization in wireless sensor networks

The present work considers the localization problem in wireless sensor networks formed by fixed nodes. Each node seeks to estimate its own position based on noisy measurements of the relative distance to other nodes. In a centralized batch mode, positions can be retrieved (up to a rigid transformation) by applying Principal Component Analysis (PCA) on a so-called similarity matrix built from the relative distances. In this paper, we propose a distributed on-line algorithm allowing each node to estimate its own position based on limited exchange of information in the network. Our framework encompasses the case of sporadic measurements and random link failures. We prove the consistency of our algorithm in the case of fixed sensors. Finally, we provide numerical and experimental results from both simulated and real data. Simulations issued to real data are conducted on a wireless sensor network testbed.Comment: 32 pages, 5 figures, 1 tabl

Range-Only Node Localization: The Arbitrary Anchor Case In D-Dimensions

This work is situated at the intersection of two large fields of research the Localization problem and applications in Wireless Networks. We are interested in providing good estimations for network node locations in a defined space based on sensor measurements. Many methods have being created for the localization problem, in special we have the classical Triangulation and Trilateration procedures and MultiDimensional Scaling. A more recent method, DILOC, utilizes barycentric coordinates in order to simplify part of the non-linearities inherent to this problem. Except for Triangulation in which we require angle measurements between nodes, the other cited methodologies require, typically only, range measurements. Off course, there exists variants which allow the use of range and angle measurements. We specialize our interest in range only methods utilizing barycentric coordinates by first providing a novel way to compute barycentric coordinates for any possible node-neighbor spatial configuration in any given dimension. Which, we use as basis for our experiments with averaging processes and the development of our centralized and distributed gradient descent algorithms. Our distributed algorithm is able to receive range measurements with noise of uncharacterized distributions as it inputs. Using simulations in Matlab, we provide comparisons of our algorithms with Matlab\u27s MDS function. Lastly, we show our efforts on providing a physical network implementation utilizing existing small form factor computers, wireless communication modules and range sensors

Robust Localization Using Range Measurements With Unknown and Bounded Errors

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in practice. Compared with the statistical knowledge of measurement errors, it can often be easier to obtain the measurement error bound. This paper investigates a localization problem assuming unknown measurement error distribution except for a bound on the error. We first formulate this localization problem as an optimization problem to minimize the worst case estimation error, which is shown to be a nonconvex optimization problem. Then, relaxation is applied to transform it into a convex one. Furthermore, we propose a distributed algorithm to solve the problem, which will converge in a few iterations. Simulation results show that the proposed algorithms are more robust to large measurement errors than existing algorithms in the literature. Geometrical analysis providing additional insights is also provided.This work was supported in part by 973 Program under Grant 2015CB352503, in part by National Program for Special Support of Top-Notch Young Professionals, in part by NSFC under Grant 61371159, in part by the Fundamental Research Funds for the Central Universities (2017XZZX009-01), in part by scholarship funded by China Scholarship Council, in part by National ICT Australia Ltd., and in part by the Australian Research Council under Grant DP-110100538, Grant DP-130103610 and Grant DP16010450

A Nystr\"om method with missing distances

We study the problem of determining the configuration of $n$ points, referred to as mobile nodes, by utilizing pairwise distances to $m$ fixed points known as anchor nodes. In the standard setting, we have information about the distances between anchors (anchor-anchor) and between anchors and mobile nodes (anchor-mobile), but the distances between mobile nodes (mobile-mobile) are not known. For this setup, the Nystr\"om method is a viable technique for estimating the positions of the mobile nodes. This study focuses on the setting where the anchor-mobile block of the distance matrix contains only partial distance information. First, we establish a relationship between the columns of the anchor-mobile block in the distance matrix and the columns of the corresponding block in the Gram matrix via a graph Laplacian. Exploiting this connection, we introduce a novel sampling model that frames the position estimation problem as low-rank recovery of an inner product matrix, given a subset of its expansion coefficients in a special non-orthogonal basis. This basis and its dual basis--the central elements of our model--are explicitly derived. Our analysis is grounded in a specific centering of the points that is unique to the Nystr\"om method. With this in mind, we extend previous work in Euclidean distance geometry by providing a general dual basis approach for points centered anywhere.Comment: 11 page

Global solution to sensor network localization: A non-convex potential game approach and its distributed implementation

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem.Comment: arXiv admin note: text overlap with arXiv:2311.0332

Localization Context-Aware Models for Wireless Sensor Network

Wireless sensor networks (WSNs) are emerging as the key technology to support the Internet of Things (IoT) and smart objects. Small devices with low energy consumption and limited computing resources have wide use in many applications and different fields. Nodes are deployed randomly without a priori knowledge of their location. However, location context is a fundamental feature necessary to provide a context-aware framework to information gathered from sensors in many services such as intrusion detection, surveillance, geographic routing/forwarding, and coverage area management. Nevertheless, only a little number of nodes called anchors are equipped with localization components, such as Global Positioning System (GPS) chips. Worse still, when sensors are deployed in an indoor environment, GPS serves no purpose. This chapter surveys a variety of state-of-the-art existing localization techniques and compares their characteristics by detailing their applications, strengths, and challenges. The specificities and enhancements of the most popular and effective techniques are as well reported. Besides, current research directions in localization are discussed