L1-Norm and Lp-Norm Optimization for Bearing-Only Positioning in Presence of Unreliable Measurements

Luo, Ji-An; Fang, Feng; Shi, Yueqin; Han, Song; Guo, Yunfei

doi:10.1109/ccdc49329.2020.9164285

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…This section illustrates the effectiveness and robustness of the POADMM estimator and the SPOADMM estimator through simulations in the uniformly distributed noise by comparing them with the PLE estimator [ 18 ], the

-norm minimization estimator [ 46 ], the

estimator [ 44 ], and the

-GMC estimator [ 32 ]. The

-norm minimization problem needs to be solved with CVX tools.…”

Section: Simulation Experimentsmentioning

confidence: 99%

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization

Chen

Wang

Yan

2022

Entropy

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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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-norm minimization estimator [ 46 ], the

estimator [ 44 ], and the

-GMC estimator [ 32 ]. The

-norm minimization problem needs to be solved with CVX tools.…”

Section: Simulation Experimentsmentioning

confidence: 99%

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization

Chen

Wang

Yan

2022

Entropy

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“…To further verify the effectiveness of the proposed algorithms, we examine the performance of the algorithms for different levels of noise impulsiveness. In the following figures drawing the simulation results, the value of the noise impulsiveness level α deviates from 1.9 to 1.1 and the corresponding optimum values of p are set as 1.546, 1.430, 1.348, 1.282, 1.225, 1.174, 1.127, 1.083, 1.041 from (17). In this example, γ 1/α is fixed at 4π/180 radian.…”

Section: Various Values Of Noise Impulsivenessmentioning

confidence: 99%

“…It is well known as the minimum dispersion criterion, which minimizes the Lp-norm of the estimation residuals. Unlike L2-norm minimization, the least Lp-norm estimator (

) does not have a closed-form solution and consequently needs to be solved in an iterative manner [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

A Total Lp-Norm Optimization for Bearing-Only Source Localization in Impulsive Noise with SαS Distribution

Luo

Xue

Rong

et al. 2021

Sensors

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This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric α-stable distribution based on the Lp-norm minimization criterion. The existing Iteratively Reweighted Pseudolinear Least-Squares (IRPLS) method can be used to solve the least LP-norm optimization problem. However, the IRPLS algorithm cannot reduce the bias attributed to the correlation between system matrices and noise vectors. To reduce this kind of bias, a Total Lp-norm Optimization (TLPO) method is proposed by minimizing the errors in all elements of system matrix and data vector based on the minimum dispersion criterion. Subsequently, an equivalent form of TLPO is obtained, and two algorithms are developed to solve the TLPO problem by using Iterative Generalized Eigenvalue Decomposition (IGED) and Generalized Lagrange Multiplier (GLM), respectively. Numerical examples demonstrate the performance advantage of the IGED and GLM algorithms over the IRPLS algorithm.

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Robust 3-D AOA Localization Against Malicious Attacks in Non-Gaussian Noise

Yan,

Wang,

Chen

et al. 2024

IEEE Sensors J.

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L1-Norm and Lp-Norm Optimization for Bearing-Only Positioning in Presence of Unreliable Measurements

Cited by 3 publications

References 15 publications

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization

A Total Lp-Norm Optimization for Bearing-Only Source Localization in Impulsive Noise with SαS Distribution

Robust 3-D AOA Localization Against Malicious Attacks in Non-Gaussian Noise

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