Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization
This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using th...
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          | Published in | Entropy (Basel, Switzerland) Vol. 24; no. 9; p. 1259 | 
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| Main Authors | , , | 
| Format | Journal Article | 
| Language | English | 
| Published | 
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        07.09.2022
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| ISSN | 1099-4300 1099-4300  | 
| DOI | 10.3390/e24091259 | 
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| Abstract | This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp-norm with 0≤p<2 as the measurement error and the ℓ1-norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2. However, when 0≤p<1, the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise. | 
    
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| AbstractList | This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp-norm with 0≤p<2 as the measurement error and the ℓ1-norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2. However, when 0≤p<1, the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise.This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp-norm with 0≤p<2 as the measurement error and the ℓ1-norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2. However, when 0≤p<1, the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise. This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp -norm with 0≤p<2 as the measurement error and the ℓ1 -norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2 . However, when 0≤p<1 , the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise.  | 
    
| Author | Yan, Qingli Chen, Yanping Wang, Chunmei  | 
    
| AuthorAffiliation | 2 Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China 1 School of Computer Science and Technology, Xi’an University of Posts and Telecommunications, Xi’an 710121, China 3 Xi’an Key Laboratory of Big Data and Intelligent Computing, Xi’an 710121, China  | 
    
| AuthorAffiliation_xml | – name: 3 Xi’an Key Laboratory of Big Data and Intelligent Computing, Xi’an 710121, China – name: 1 School of Computer Science and Technology, Xi’an University of Posts and Telecommunications, Xi’an 710121, China – name: 2 Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China  | 
    
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| Copyright | 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2022 by the authors. 2022  | 
    
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| SubjectTerms | Accuracy Algorithms alternating direction method of multipliers Angle of arrival Computational geometry Convexity Error analysis Localization Methods Noise measurement Optimization algorithms Optimization models outliers Outliers (statistics) Parameter sensitivity Propagation Regularization Robustness (mathematics) Root-mean-square errors Sensors sparse regularization ℓp-norm  | 
    
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| Title | Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization | 
    
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