A simple efficient anchor-free node localization algorithm for wireless sensor networks

Du, Tao; Qu, Shouning; Guo, Qingbei; Zhu, Lei

doi:10.1177/1550147717705784

Cited by 11 publications

(9 citation statements)

References 29 publications

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“…Note that the angles are often measured in a coordinate system that is local and different for each node. Distributed algorithms such as [25] can convert these relative angles to a common coordinate system.…”

Section: D Case With \Bfitk > \Bfitdmentioning

confidence: 99%

“…o \sim \scrN (\bfitx , \Sigma \widehat \bfitx o ), where \Sigma \widehat \bfitx o = \sigma 2 \bfitJ D (\bfitB \Phi ) \dagger ((\bfitB \Phi ) \dagger ) \top (\bfitJ D ) \top , \widehat \bfitx s \sim \scrN (\bfitx , \Sigma \widehat \bfitx s ), where \Sigma \widehat \bfitx s = \sigma 2 \bfitJ D \Phi \dagger \bfitB \dagger (\bfitB \dagger ) \top (\Phi \dagger ) \top (\bfitJ D ) \top .For a less cluttered notation, in(25) and the rest of the section, we omit the prime symbol \prime on \bfitJ D , \bfitB , \Phi .…”

mentioning

confidence: 99%

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Coordinate Difference Matrices

Baechler¹,

Dümbgen²,

Elhami³

et al. 2020

SIAM J. Matrix Anal. Appl.

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In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called vector geometry problems (VGPs). A closely related field studies distance geometry problems (DGPs), where only the Euclidean distance between pairs of points is available. This has been extensively studied in the literature and is often associated with Euclidean distance matrices (EDMs). Although similar to DGPs, VGPs have received little attention in the literature; our goal is to fill in this gap and introduce a framework to solve VGPs. Inspired by EDM-related approaches, we arrange the differences in what we call a coordinate difference matrix (CDM) and introduce a methodology to reconstruct a set of points from CDM entries. We first propose a reconstruction scheme in 1D and then generalize it to higher dimensions. We show that our algorithm is optimal in the least-squares sense, even when we have only access to partial measurements. In addition, we provide necessary and sufficient conditions on the number and structure of measurements needed for a successful reconstruction, as well as a comparison with EDMs. In particular we show that compared to EDMs, CDMs are simpler objects, both from an algorithmic and a theoretical point of view. Therefore, CDMs should be favored over EDMs whenever vector differences are available. In the presence of noise, we provide a statistical analysis of the reconstruction error. Finally, we apply the established knowledge to five practical problems to demonstrate the versatility of this theory and showcase the wide range of applications covered by the CDM framework.

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Section: D Case With \Bfitk > \Bfitdmentioning

confidence: 99%

mentioning

confidence: 99%

Coordinate Difference Matrices

Baechler¹,

Dümbgen²,

Elhami³

et al. 2020

SIAM J. Matrix Anal. Appl.

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show abstract

“…A WSN is a network where assorted nodes work together and feel the phenomena around them to achieve a common objective [1,2]. After the phenomenon has been detected, all sensors forward this information to the base station (BS), where the BS investigates all the occurrences in the environment and takes appropriate action [3].…”

Section: Introductionmentioning

confidence: 99%

“…A WSN has several characteristics-such as being self-organized, fault-tolerant, and scalable-but the most challenging part is the BS' awareness of the location of the event. That is, if a BS has the details that a particular operation is taking place, and a sensor transfers these attributes to the BS and the location of the BS is not known, then the BS cannot take the best possible action depending on the event [2]. To gather the location of sensor nodes, localization comes into the picture, through which the coordinates of the sensor node are determined.…”

Section: Introductionmentioning

confidence: 99%

SDSWSN—A Secure Approach for a Hop-Based Localization Algorithm Using a Digital Signature in the Wireless Sensor Network

Prashar

Rashid²,

Siddiqui

et al. 2021

Electronics

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Localization and security are among the most dominant tasks of wireless sensor networks (WSN). For applications containing sensitive information on the location parameters of the event, secure localization is mandatory and must not be compromised at any cost. The main task, as if any node is malicious, is to authenticate nodes that are involved in the localization process. In this paper, we propose a secure hop-based algorithm that provides a better localization accuracy. In addition, to maintain the security of the localization process, the digital signature approach is used. Moreover, the impact of malicious nodes on the proposed scheme has also been observed. The proposed approach is also contrasted with the basic DV-Hop and improved DV-Hop based on error correction. From the simulation outcomes, we infer that this secure digital-signature-based localization strategy is quite robust against any node compromise attacks, thereby boosting its precision. Comparisons between the proposed algorithm and the state of the art were made on the grounds of different parameters such as the node quantity, ratio of anchor nodes, and range value towards the localization error.

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“…5 There are two papers relevant to the localization and the positioning systems. One paper proposes anchor-free localization algorithm to achieve high localization accuracy with flexible structure, low cost, and high stability, 6 while the other paper, 7 rather than focusing on indoor positioning accuracy, studied store layout optimization by linking the customers' positioning data with the transaction data, rather than focusing on the indoor positioning accuracy. The following paragraphs summarize these papers in more detail.…”

Section: Technological Advances In Wireless Sensor Network Enabling mentioning

confidence: 99%

Technological advances in wireless sensor networks enabling diverse Internet of Things applications

Yoo

Cheng

Chong³

et al. 2018

International Journal of Distributed Sensor Networks

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A simple efficient anchor-free node localization algorithm for wireless sensor networks

Cited by 11 publications

References 29 publications

Coordinate Difference Matrices

Coordinate Difference Matrices

SDSWSN—A Secure Approach for a Hop-Based Localization Algorithm Using a Digital Signature in the Wireless Sensor Network

Technological advances in wireless sensor networks enabling diverse Internet of Things applications

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