Beyond trilateration: On the localizability of wireless ad-hoc networks

Yang, Zheng; Liu, Y.; Li, X.-Y.

doi:10.1109/infcom.2009.5062166

Cited by 79 publications

(29 citation statements)

References 18 publications

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“…In general, (23) and (25) are over-determined and can be solved by using the well-known minimum mean square error (MMSE) method [1,2,3,20]. By applying the MMSE method, the solutions are:…”

Section: Comparisons With Mmse Methodsmentioning

confidence: 99%

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Range-Based Localization Algorithm for Next Generation Wireless Networks Using Radical Centers

2016

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Localization is an important issue in next generation wireless networks (NGWNs), such as 5G cellular networks, IEEE 802.11ax WiFi networks, and wireless ad hoc sensor network (WASNs). This paper proposes a 3-D localization algorithm for NGWNs by utilizing the concept of radical centers from analytic geometry, and takes WASNs as an example. Assume that an unknown node can measure its distances to four or more anchor nodes (reference nodes). By picking four distance measurements to four anchor nodes, a radical center is computed. Through analytic formulation, the radical center is shown to be able to be treated as an estimation of the unknown node location. Since every four distance measurements generates one radical center (in 3-D space), to further improve and fuse these estimations, effective filtering mechanisms are proposed to filter out the improper estimations. Afterward, the remaining radical centers are averaged, and the solution is the final estimation of the unknown node location. The location errors of the proposed algorithm and the conventional minimum mean square error (MMSE) method were analytically compared. It was shown that the proposed algorithm outperforms the conventional MMSE method both in accuracy and efficiency. Extensive computer simulations were carried out and the results verified the advantage of the proposed location algorithm over the MMSE approach.

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“…In general, (23) and (25) are over-determined and can be solved by using the well-known minimum mean square error (MMSE) method [1,2,3,20]. By applying the MMSE method, the solutions are:…”

Section: Comparisons With Mmse Methodsmentioning

confidence: 99%

“…To sum up, the Distance filtering scheme is to examine if the distance between the radical center and each of the four anchor nodes satisfy the constraints (17), (18), (19) and (20). If any of these constraints is not satisfied, the radical center is considered as being improper and is discarded.…”

Section: E Distance Filteringmentioning

confidence: 99%

Range-Based Localization Algorithm for Next Generation Wireless Networks Using Radical Centers

2016

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“…They showed that a network with a biconnected grounded graph is uniquely localizable if two-hop neighbors are connected and the complexity of network localization belongs to NP-hard. Zheng, et al [16] further proposed an optimal distributed algorithm to recognize all one-hop localizable nodes by using wheel graph.…”

Section: Network Localizationmentioning

confidence: 99%

Principles of the Complete Voronoi Diagram Localization

Lü

Ming-tian

Wang

et al. 2016

IEEE Trans. on Mobile Comput.

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This paper explores the rationale behind the Complete Voronoi Diagram (CVD) Localization, which is a computational geometry approach to the wireless network localization. Our work consists mainly of three parts. The first part focuses on the analysis of CVD's mathematical properties. We characterize CVD's central tendency as the mirror-image distribution and provide mathematical formula for its probability density function. We also provide a closed formula for the relationship between CVD's vertices, chords and faces, the average chord length, the average edge number of a CVD polygon. And the expressions for the average overall and local positioning error are also provided. Based upon these findings, we show that the convergence speed for a CVD based localization scheme is quadratic, and the optimal time and space complexities are (n 2 ) and n), respectively. The second part proposes a novel approach, called Polling, which utilizes the concept of the Error Region, to further improve the accuracy. Polling, in theory, enables us to make use of the topology information with the quantity up to O(n 4 ) provided by CVD for localization, while a conventional CVD scheme can use only O(1) such information. The third part, through simulations, shows how to use the qADC (quasi Analog-to-Digital Conversion) strategy to handle signal errors. Combined with Polling and qADC, a CVD scheme can provide a simple, robust and powerful solution to the wireless network localization. Some of our findings and methods may also contribute to the field of computational geometry its own.

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“…A diversity of approaches have been proposed for distance error minimization in order to determine the coordinates of sensors, with different localization accuracy and time complexity [15][16][17][18][19][20][21]. Generally, distance information is sufficient to localize sensor nodes on a 2D plane (except for non-rigid shapes [27]). For example, Fig.…”

Section: Challenges In 3d Surface Localizationmentioning

confidence: 99%

Cut-and-sew

Zhao

Jin

et al. 2013

Proceedings of the Fourteenth ACM International Symposium on Mobile Ad Hoc Networking and Computing

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Location awareness is imperative for a variety of sensing applications and network operations. Although a diversity of GPS-less and GPS-free solutions have been developed recently for autonomous localization in wireless sensor networks, they primarily target at 2D planar or 3D volumetric settings. There exists unique and fundamental hardness to extend them to 3D surface. The contributions of this work are twofold. First, it proposes a theoretically-proven algorithm for the 3D surface localization problem. Seeing the challenges to localize general 3D surface networks and the solvability of the localization problem on single-value (SV) surface, this work proposes the cut-and-sew algorithm that takes a divide-and-conquer approach by partitioning a general 3D surface network into SV patches, which are localized individually and then merged into a unified coordinates system. The algorithm is optimized by discovering the minimum SV partition, an optimal partition that creates a minimum set of SV patches. Second, it develops practically-viable solutions for real-world sensor network settings where the inputs are often noisy. The proposed algorithm is implemented and evaluated via simulations and experiments in an indoor testbed. The results demonstrate that the proposed cut-and-sew algorithm achieves perfect 100% localization rate and the desired robustness against measurement errors.

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Beyond trilateration: On the localizability of wireless ad-hoc networks

Cited by 79 publications

References 18 publications

Range-Based Localization Algorithm for Next Generation Wireless Networks Using Radical Centers

Range-Based Localization Algorithm for Next Generation Wireless Networks Using Radical Centers

Principles of the Complete Voronoi Diagram Localization

Cut-and-sew

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