Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Ding, Chibiao; Qi, Houduo

doi:10.1007/s10589-016-9858-5

Cited by 18 publications

(31 citation statements)

References 49 publications

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“…We have already seen that D mds is the optimal solution under the semi-norm · J in (15). In this part, we will show that it is also an optimal solution under the Frobenius norm · .…”

Section: A Subspace Perspective Of Cmds and Over-denoisingmentioning

confidence: 75%

“…We note that the models behind those methods are non-convex optimization. 1 regularized methods also appeared in the field of sensor network localization with non-light-of-sight (NLOS) distance measurements, see e.g., [13]- [15]. NLOS measurements occur when the LOS (line-of-sight) path is blocked due to environmental limitations such as the indoor environment depicted in the example of locating Motorola facilities [16].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, such links can be treated as outliers. A dominating approach is the convex relaxation/optimization, which often involves semidefinite programming (SDP) with 1 regularization, see [13]- [15] and [17].…”

Section: Introductionmentioning

confidence: 99%

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Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Kong

2019

IEEE Trans. Signal Process.

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The classical Multi-Dimensional Scaling (cMDS) has become a cornerstone for analyzing metric dissimilarity data due to its simplicity in derivation, low computational complexity and its nice interpretation via the principle component analysis. This paper focuses on its capability of denoising and outlier detection. Our new interpretation shows that cMDS always overly denoises a sparsely perturbed data by subtracting a fully dense denoising matrix in a subspace from the given data matrix. This leads us to consider two types of sparsity-driven models: Subspace sparse MDS and Full-space sparse MDS, which respectively uses the 1 and 1−2 regularization to induce sparsity. We then develop fast majorization algorithms for both models and establish their convergence. In particular, we are able to control the sparsity level at every iterate provided that the sparsity control parameter is above a computable threshold. This is a desirable property that has not been enjoyed by any of existing sparse MDS methods.Our numerical experiments on both artificial and real data demonstrates that cMDS with appropriate regularization can perform the tasks of denoising and outlier detection, and inherits the efficiency of cMDS in comparison with several state-of-the-art sparsity-driven MDS methods.

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“…We have already seen that D mds is the optimal solution under the semi-norm · J in (15). In this part, we will show that it is also an optimal solution under the Frobenius norm · .…”

Section: A Subspace Perspective Of Cmds and Over-denoisingmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Kong

2019

IEEE Trans. Signal Process.

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“…In [15], the authors propose a centralized technique, which is a method for estimating unknown node positions via convex optimization. This technique is based on connectivity-induced constraints.…”

Section: Introductionmentioning

confidence: 99%

Cooperative Spatial Retreat for Resilient Drone Networks

Kang

Kwon

Park

2017

Sensors

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Drones are broadening their scope to various applications such as networking, package delivery, agriculture, rescue, and many more. For proper operation of drones, reliable communication should be guaranteed because drones are remotely controlled. When drones experience communication failure due to bad channel condition, interference, or jamming in a certain area, one existing solution is to exploit mobility or so-called spatial retreat to evacuate them from the communication failure area. However, the conventional spatial retreat scheme moves drones in random directions, which results in inefficient movement with significant evacuation time and waste of battery lifetime. In this paper, we propose a novel spatial retreat technique that takes advantage of cooperation between drones for resilient networking, which is called cooperative spatial retreat (CSR). Our performance evaluation shows that the proposed CSR significantly outperforms existing schemes.

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“…When ∆ is not far from a true EDM, cMDS works fairly well. This has been justified in various situations including [28] on manifold learning and [9] where the noises can be bounded. Instead of directly applying cMDS on ∆, one may also modify ∆ so as for it to be a true EDM.…”

Section: Introductionmentioning

confidence: 99%

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

Qi¹

2017

JCM

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When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling (MDS). In this paper, we consider the case where some of the distances are far from being accurate (containing large noises or even missing). In such a situation, the order of the known distances (i.e., some distances are larger than others) is valuable information that often yields far more accurate construction of the points than just using the magnitude of the known distances. The methods making use of the order information is collectively known as non-metric MDS. A challenging computational issue among all existing nonmetric MDS methods is that there are often a large number of ordinal constraints. In this paper, we cast this problem as a matrix optimization problem with ordinal constraints. We then adapt an existing smoothing Newton method to our matrix problem. Extensive numerical results demonstrate the efficiency of the algorithm, which can potentially handle a very large number of ordinal constraints.Mathematics subject classification: 90C30, 90C26, 90C90.

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Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Cited by 18 publications

References 49 publications

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Cooperative Spatial Retreat for Resilient Drone Networks

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

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