Range-based Localization Problem Research Articles

Modified Zeroing Neurodynamics Models for Range-Based WSN Localization From AOA and TDOA Measurements

With the rise of the internet of things, wireless sensor network (WSN) technology has gained unprecedented development and has attracted increasing attention from researchers. Due to the inherent characteristics of WSN, such as interaction with the environment, WSN localization becomes an essential and attractive topic in academia and industry. In this paper, the range-based localization problem in a mobile WSN application scenario is considered to be time-varying and modeled as a dynamic matrix equation by introducing the time parameter. Two modified zeroing neurodynamics (ZND) models are proposed and investigated to deal with range-based WSN localization problems from angle of arrival (AOA) measurement and time difference of arrival (TDOA) measurement. In addition, the convergence of the proposed models is theoretically analyzed. Furthermore, computer simulations on WSN localization are carried out to prove the effectiveness of the proposed models in terms of accuracy and robustness to the dynamic environment. Additionally, the application to underwater sensor node localization of underwater acoustic network (UAN) testbed is provided to illustrate the feasibilities of the proposed models for solving UAN localization problem.

Global and Asymptotically Efficient Localization From Range Measurements

We consider the range-based localization problem, which involves estimating an object's position by using $m$ sensors, hoping that as the number $m$ of sensors increases, the estimate converges to the true position with the minimum variance. We show that under some conditions on the sensor deployment and measurement noises, the LS estimator is strongly consistent and asymptotically normal. However, the LS problem is nonsmooth and nonconvex, and therefore hard to solve. We then devise realizable estimators that possess the same asymptotic properties as the LS one. These estimators are based on a two-step estimation architecture, which says that any $\sqrt{m}$-consistent estimate followed by a one-step Gauss-Newton iteration can yield a solution that possesses the same asymptotic property as the LS one. The keypoint of the two-step scheme is to construct a $\sqrt{m}$-consistent estimate in the first step. In terms of whether the variance of measurement noises is known or not, we propose the Bias-Eli estimator (which involves solving a generalized trust region subproblem) and the Noise-Est estimator (which is obtained by solving a convex problem), respectively. Both of them are proved to be $\sqrt{m}$-consistent. Moreover, we show that by discarding the constraints in the above two optimization problems, the resulting closed-form estimators (called Bias-Eli-Lin and Noise-Est-Lin) are also $\sqrt{m}$-consistent. Plenty of simulations verify the correctness of our theoretical claims, showing that the proposed two-step estimators can asymptotically achieve the Cramer-Rao lower bound.

Gordian

Accurate localization from Cyber-Physical Systems (CPS) is a critical enabling technology for context-aware applications and control. As localization plays an increasingly safety-critical role, location systems must be able to identify and eliminate faulty measurements to prevent dangerously inaccurate localization. In this article, we consider the range-based localization problem and propose a method to detect coordinated adversarial corruption on anchor positions and distance measurements. Our algorithm, G ordian , rapidly finds attacks by identifying geometric inconsistencies at the graph level without requiring assumptions about hardware, ranging mechanisms, or cryptographic protocols. We give necessary conditions for which attack detection is guaranteed to be successful in the noiseless case, and we use that intuition to extend G ordian to the noisy case where fewer guarantees are possible. In simulations generated from real-world sensor noise, we empirically show that G ordian ’s trilateration counterexample generation procedure enables rapid attack detection even for combinatorially difficult problems.

An Extended Joint Spatial and Temporal Cooperation Model for the Range-Based Localization Problem

Location awareness is becoming essential for various wireless applications, and cooperation among nodes is highly beneficial for localization performance. However, the existing cooperative localization (CL) algorithms may suffer from major performance loss when applied to the mobile environments with fast changing network topologies. In this paper, we extend the joint spatial and temporal cooperation (JSTC) model to the range-based localization problem. Based on mobility constraints and the maximum likelihood estimation (MLE) criterion, we formulate the CL problems in both centralized and distributed cases. Different from the conventional distributed CL problems, the proposed one takes the transmission delay and the cooperation among multi-hop nodes into account, which is more practical. Moreover, the performance limits of the considered problems are investigated by the Cramer-Rao lower bound (CRLB). Finally, these two problems are solved by the Sequential Quadratic Programming (SQP) algorithm. Both simulation and experiment results show that the extended JSTC model can effectively improve the localization reliability and accuracy.

GROLO: Realistic Range-Based Localization for Mobile IoTs Through Global Rigidity

We study the realistic problem of range-based localization for mobile Internet of Things (IoT) without using GPS. This problem arises from the real-world applications and is characterized by the following three challenges: 1) inaccurate devices, such as the low cost motion sensors and moving parts in the mobile IoT nodes, make it infeasible to localize the nodes using their speed and direction; 2) when a team of IoT nodes keep moving, some nodes may get lost and be disconnected from the network due to the large accumulated errors in the distances; and 3) although the theory of global rigidity ensures the position uniqueness of nodes, there are still nonlocalizable nodes in a globally rigid graph. To address these challenges, we propose a distributed localization protocol, called GROLO. GROLO is able to perform efficient distributed localization through an adaptive global rigidity formation maintenance mechanism especially designed for the resource limited IoT nodes. GROLO is able to localize all of the nodes periodically in a mobile IoT by short distance adjustment. Furthermore, GROLO requires only necessary additional neighbor distance measurements. We evaluated GROLO and other localization protocols using both simulated nodes and ten real mobile nodes in an IoT. The results show that GROLO is promising for the localization and formation control with inaccurate mobile IoT in realistic environments.

Kernel Methods for Ill-Posed Range-Based Localization Problems

A kernel regression technique for the ill-posed range-based localization problem is proposed. We introduce a generic kernel design method which relies on a probabilistic modeling of the respective physical environment in terms of a class of stochastic differential equations. The combination of dynamic modeling with physical and stochastic interpretability leads to a unique solution in a Reproducing Kernel Hilbert Space and thus eliminates the need for a time-discrete representation of the localization solution. By design of the problem formulation, an extended Kalman filter naturally evolves as an iterative optimization method. As a practical example, we tackle an ill-posed localization problem that stems from a preinstalled sensor network of unknown geometry, providing nonsynchronous range information to a moving beacon. To obtain a unique solution for the beacon positions and the network geometry, we apply the proposed kernel regression technique and kernel design method. The proposed approach eventually leads to a least squares optimization problem that can be interpreted as a maximum a posteriori estimation problem. While the methodology is not restricted to localization problems only, its validity is shown by a demonstrator which is comprised of a mobile robot and a network of multiple nonmoving beacons that provide time-of-arrival measurements of ultra wide band signals.