Distributed, simple and stable network localization

Soares, Cláudia; Gomes, João

doi:10.1109/globalsip.2014.7032222

Cited by 12 publications

(18 citation statements)

References 20 publications

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“…We also note that Soares, Xavier and Gomes developed two other important "simple" majorization methods, respectively referred to as SMLL (Stable Maximum-Likelihood Localization) [18] and diskRelax [15]. As pointed out in [18, Sect.…”

Section: Selection Of Benchmark Methodsmentioning

confidence: 99%

“…This is in addition to some computational techniques that exploit the sparsity properties in the linear equations encountered. Since our computation each iteration is dominated by Π K n + (r) (−D) in the construction of the majorization function g m in (18), the overall computational complexity of SQREDM is about O(rn 2 ) (we used MATLAB's built-in function eigs.m to compute PCA + r (A) in (15)). …”

Section: Selection Of Benchmark Methodsmentioning

confidence: 99%

“…This convex relaxation scheme is further enhanced by Piovesan and Erseghe [17] and it is solved by an Alternating Direction Method of Multipliers (ADMM). The convex relation with the majorization technique was considered in [18]. Another type of stress majorization was proposed in [9], resulting in the well-known ARAP (As Rigid As Possible) algorithm for SNL.…”

Section: A Literature Reviewmentioning

confidence: 99%

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A Fast Matrix Majorization-Projection Method for Penalized Stress Minimization With Box Constraints

Zhou

Xiu

2018

IEEE Trans. Signal Process.

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Abstract-Kruskal's stress minimization, though nonconvex and nonsmooth, has been a major computational model for dissimilarity data in multidimensional scaling. Semidefinite Programming (SDP) relaxation (by dropping the rank constraint) would lead to a high number of SDP cone constraints. This has rendered the SDP approach computationally challenging even for problems of small size. In this paper, we reformulate the stress optimization as an Euclidean Distance Matrix (EDM) optimization with box constraints. A key element in our approach is the conditional positive semidefinite cone with rank cut. Although nonconvex, this geometric object allows a fast computation of the projection onto it and it naturally leads to a majorization-minimization algorithm with the minimization step having a closed-form solution. Moreover, we prove that our EDM optimization follows a continuously differentiable path, which greatly facilitated the analysis of the convergence to a stationary point. The superior performance of the proposed algorithm is demonstrated against some of the state-of-the-art solvers in the field of sensor network localization and molecular conformation.

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Section: Selection Of Benchmark Methodsmentioning

confidence: 99%

Section: Selection Of Benchmark Methodsmentioning

confidence: 99%

Section: A Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

A Fast Matrix Majorization-Projection Method for Penalized Stress Minimization With Box Constraints

Zhou

Xiu

2018

IEEE Trans. Signal Process.

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“…H m were sufficiently stable. Here, H stands for an error, for example, E 1 in ( 10), E 2 in (11) or the angles θ ij and β ik in (12), computed from data of MC trial m.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…1, there is negligible error associated with the last relaxation. Whenever this is true, it is more illuminating to observe the approximation error in terms of the suboptimality angles θ ij (12) and β ik . Fig.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Range and Bearing Data Fusion for Precise Convex Network Localization

Soares

Valdeira

Gomes

2020

IEEE Signal Process. Lett.

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Hybrid localization in GNSS-challenged environments using measured ranges and angles is becoming increasingly popular, in particular with the advent of multimodal communication systems. Here, we address the hybrid network localization problem using ranges and bearings to jointly determine the positions of a number of agents through a single maximumlikelihood (ML) optimization problem that seamlessly fuses all the available pairwise range and angle measurements. We propose a tight convex surrogate to the ML estimator, we examine practical measures for the accuracy of the relaxation, and we comprehensively characterize its behavior in simulation. We found that our relaxation outperforms a state of the art SDP relaxation by one order of magnitude in terms of localization error, and is amenable to much more lightweight solution algorithms. I. INTRODUCTION Spatial awareness is a hallmark of contemporary real-world systems and applications, particularly when multiple agents collaborate to attain common goals. Location technologies are key for operation in GNSS-challenged environments, like underwater [1] or indoor [2] and city skyscraper areas [3], and also in many applications in wireless communications [4], sensor networks [5], IoT [6], medicine [7], [8], etc. Our work addresses the network localization problem [9], where multiple networked agents cooperate in sensing and computation to jointly estimate their unknown positions. Related work: There is a vast literature for range-based network localization, from multidimensional scaling [10], [11] to nonconvex ML estimation [12], [13], convexifications of ML problems [14]-[16], and other convex heuristics to match measured data to a data model [17], [18].Several current technologies not only give access to accurate distance measurements, but also provide angle information. These added measurements can improve the quality of estimates or reduce the amount of resources spent to obtain a reasonable localization precision. 5G is an especially noteworthy example where the value of hybrid measurements has been noted [4], [19], and information-theoretic bounds are available to characterize their impact [5], [20]. While the topic of single-source range/bearing localization is reasonably well covered in the technical literature, specific references addressing network localization algorithms for that data model

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STRONG: Synchronous and asynchronous robust network localization, under non-Gaussian noise

Soares

Gomes

2021

Signal Processing

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Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data -data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change the problem representation, to allow for distributed robust localization algorithms: a synchronous distributed method that has optimal convergence rate and an asynchronous one with proven convergence guarantees. A major highlight of our contribution lies on the fact that we pay no price for provable distributed computation neither in accuracy, nor in communication cost or convergence speed. Simulations showcase the superior performance of our algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of alternative approaches, distributed and centralized, even under heavy additive and multiplicative outlier noise.

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Distributed, simple and stable network localization

Cited by 12 publications

References 20 publications

A Fast Matrix Majorization-Projection Method for Penalized Stress Minimization With Box Constraints

A Fast Matrix Majorization-Projection Method for Penalized Stress Minimization With Box Constraints

Range and Bearing Data Fusion for Precise Convex Network Localization

STRONG: Synchronous and asynchronous robust network localization, under non-Gaussian noise

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