INSTRUCTIONS FOR PREPARATION OF CAMERA-READY MANUSCRIPTS FOR BULLETIN OF GRADUATE SCIENCE AND ENGINEERING, ENGINEERING STUDIES

In the field of autonomous mobile robotics, reliable localization performance is essential. However, there are real environments where localization is a failure. In this paper, we propose a method for estimating localizability based on occupancy grid maps. Localizability indicates the reliability of localization. There are several approaches to estimate localizability, and we propose a method using local map correlations. The covariance matrix of the Gaussian distribution from local map correlations is used to estimate localizability. In this way, we can estimate the magnitude of the localization error and the characteristics of the error. The experiment confirmed the characteristics of the distribution of correlations for each location on occupancy grid maps. And the localizability of the whole map was estimated using an occupancy grid map containing a vast and complex. The simulation experiment results showed that the proposed method could estimate localization error and the characteristics of the error on occupancy grid maps. The proposed method was confirmed to be effective in estimating localizability

On Sensor Network Localization Using SDP Relaxation

A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11]. In this paper, we analyze and determine new sufficient conditions and formulations that guarantee that the SDP relaxation is exact, i.e., gives the correct solution. These conditions can be useful for designing sensor networks and managing connectivities in practice. Our main contribution is twofold: We present the first non-asymptotic bound on the connectivity or radio range requirement of the sensors in order to ensure the network is uniquely localizable. Determining this range is a key component in the design of sensor networks, and we provide a result that leads to a correct localization of each sensor, for any number of sensors. Second, we introduce a new class of graphs that can always be correctly localized by an SDP relaxation. Specifically, we show that adding a simple objective function to the SDP relaxation model will ensure that the solution is correct when applied to a triangulation graph. Since triangulation graphs are very sparse, this is informationally efficient, requiring an almost minimal amount of distance information. We also analyze a number objective functions for the SDP relaxation to solve the localization problem for a general graph.Comment: 20 pages, 4 figures, submitted to the Fields Institute Communications Series on Discrete Geometry and Optimizatio

Robust Component-based Network Localization with Noisy Range Measurements

Accurate and robust localization is crucial for wireless ad-hoc and sensor networks. Among the localization techniques, component-based methods advance themselves for conquering network sparseness and anchor sparseness. But component-based methods are sensitive to ranging noises, which may cause a huge accumulated error either in component realization or merging process. This paper presents three results for robust component-based localization under ranging noises. (1) For a rigid graph component, a novel method is proposed to evaluate the graph's possible number of flip ambiguities under noises. In particular, graph's \emph{MInimal sepaRators that are neaRly cOllineaR (MIRROR)} is presented as the cause of flip ambiguity, and the number of MIRRORs indicates the possible number of flip ambiguities under noise. (2) Then the sensitivity of a graph's local deforming regarding ranging noises is investigated by perturbation analysis. A novel Ranging Sensitivity Matrix (RSM) is proposed to estimate the node location perturbations due to ranging noises. (3) By evaluating component robustness via the flipping and the local deforming risks, a Robust Component Generation and Realization (RCGR) algorithm is developed, which generates components based on the robustness metrics. RCGR was evaluated by simulations, which showed much better noise resistance and locating accuracy improvements than state-of-the-art of component-based localization algorithms.Comment: 9 pages, 15 figures, ICCCN 2018, Hangzhou, Chin

Localizability of Wireless Sensor Networks: Beyond Wheel Extension

A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in finite time. Therefore, identifying localizable networks is an important function. If the complete information about the network is available at a single place, localizability can be tested in polynomial time. In a distributed environment, networks with trilateration orderings (popular in real applications) and wheel extensions (a specific class of localizable networks) embedded in plane can be identified by existing techniques. We propose a distributed technique which efficiently identifies a larger class of localizable networks. This class covers both trilateration and wheel extensions. In reality, exact distance is almost impossible or costly. The proposed algorithm based only on connectivity information. It requires no distance information