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

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6471
Author(s):  
Ji-An Luo ◽  
Chang-Cheng Xue ◽  
Ying-Jiao Rong ◽  
Shen-Tu Han
Keyword(s):  
Source Localization ◽  
Stable Distribution ◽  
Impulsive Noise ◽  
Equivalent Form ◽  
Eigenvalue Decomposition ◽  
System Matrix ◽  
Lp Norm ◽  
Norm Minimization ◽  
Data Vector ◽  
Generalized Eigenvalue Decomposition

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.

scholarly journals Robust Bearing-Only Localization Using Total Least Absolute Residuals Optimization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ji-An Luo ◽  
Chang-Cheng Xue ◽  
Dong-Liang Peng
Keyword(s):  
Impulsive Noise ◽  
Equivalent Form ◽  
System Matrix ◽  
Noise Resistance ◽  
Robust Estimate ◽  
Localization Accuracy ◽  
Least Absolute Deviations ◽  
Data Vector ◽  
Absolute Residual ◽  
Robust Techniques

Robust techniques critically improve bearing-only target localization when the relevant measurements are being corrupted by impulsive noise. Resistance to isolated gross errors refers to the conventional least absolute residual (LAR) method, and its estimate can be determined by linear programming when pseudolinear equations are set. The LAR approach, however, cannot reduce the bias attributed to the correlation between system matrices and noise vectors. In the present study, perturbations are introduced into the elements of the system matrix and the data vector simultaneously, and the total optimization problem is formulated based on least absolute deviations. Subsequently, an equivalent form of total least absolute residuals (TLAR) is obtained, and an algorithm is developed to calculate the robust estimate by dual ascent algorithms. Moreover, the performance of the proposed method is verified through the numerical simulations by using two types of localization geometries, i.e., random and linear. As revealed from the results, the TLAR algorithm is capable of exhibiting significantly higher localization accuracy as compared with the LAR method.

Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization

2021 ◽  
Vol 140 ◽  
pp. 100-112
Author(s):  
You Zhao ◽  
Xiaofeng Liao ◽  
Xing He ◽  
Rongqiang Tang ◽  
Weiwei Deng
Keyword(s):  
Signal Reconstruction ◽  
Sparse Signal ◽  
Sparse Signal Reconstruction ◽  
Lp Norm ◽  
Norm Minimization

scholarly journals Adaptive Iterated Shrinkage Thresholding-Based Lp-Norm Sparse Representation for Hyperspectral Imagery Target Detection

2020 ◽  
Vol 12 (23) ◽  
pp. 3991
Author(s):  
Xiaobin Zhao ◽  
Wei Li ◽  
Mengmeng Zhang ◽  
Ran Tao ◽  
Pengge Ma
Keyword(s):  
Sparse Representation ◽  
Target Detection ◽  
Matched Filter ◽  
Hyperspectral Imagery ◽  
Low Rank ◽  
Collaborative Representation ◽  
Support Vector ◽  
L1 Norm ◽  
Lp Norm ◽  
Norm Minimization

In recent years, with the development of compressed sensing theory, sparse representation methods have been concerned by many researchers. Sparse representation can approximate the original image information with less space storage. Sparse representation has been investigated for hyperspectral imagery (HSI) detection, where approximation of testing pixel can be obtained by solving l1-norm minimization. However, l1-norm minimization does not always yield a sufficiently sparse solution when a dictionary is not large enough or atoms present a certain level of coherence. Comparatively, non-convex minimization problems, such as the lp penalties, need much weaker incoherence constraint conditions and may achieve more accurate approximation. Hence, we propose a novel detection algorithm utilizing sparse representation with lp-norm and propose adaptive iterated shrinkage thresholding method (AISTM) for lp-norm non-convex sparse coding. Target detection is implemented by representation of the all pixels employing homogeneous target dictionary (HTD), and the output is generated according to the representation residual. Experimental results for four real hyperspectral datasets show that the detection performance of the proposed method is improved by about 10% to 30% than methods mentioned in the paper, such as matched filter (MF), sparse and low-rank matrix decomposition (SLMD), adaptive cosine estimation (ACE), constrained energy minimization (CEM), one-class support vector machine (OC-SVM), the original sparse representation detector with l1-norm, and combined sparse and collaborative representation (CSCR).

Flux-normalized wavefield decomposition and migration of seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. S83-S92 ◽  
Author(s):  
Bjørge Ursin ◽  
Ørjan Pedersen ◽  
Børge Arntsen
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Transmission Loss ◽  
Correction Term ◽  
Eigenvalue Decomposition ◽  
System Matrix ◽  
Interaction Terms ◽  
Reflectivity Function ◽  
And Migration ◽  
Wavefield Decomposition

Separation of wavefields into directional components can be accomplished by an eigenvalue decomposition of the accompanying system matrix. In conventional pressure-normalized wavefield decomposition, the resulting one-way wave equations contain an interaction term which depends on the reflectivity function. Applying directional wavefield decomposition using flux-normalized eigenvalue decomposition, and disregarding interaction between up- and downgoing wavefields, these interaction terms were absent. By also applying a correction term for transmission loss, the result was an improved estimate of the up- and downgoing wavefields. In the wave equation angle transform, a crosscorrelation function in local offset coordinates was Fourier-transformed to produce an estimate of reflectivity as a function of slowness or angle. We normalized this wave equation angle transform with an estimate of the plane-wave reflection coefficient. The flux-normalized one-way wave-propagation scheme was applied to imaging and to the normalized wave equation angle-transform on synthetic and field data; this proved the effectiveness of the new methods.

Generalized Eigenvalue Decomposition in Time Domain Modal Parameter Identification

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Wenliang Zhou ◽  
David Chelidze
Keyword(s):  
Time Domain ◽  
Hankel Matrix ◽  
Eigenvalue Decomposition ◽  
Modal Parameter ◽  
Current Time ◽  
Modal Parameter Identification ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Decomposition ◽  
Single Input ◽  
Complex Exponential

This paper is intended to point out the relationship among current time domain modal analysis methods by employing generalized eigenvalue decomposition. Ibrahim time domain (ITD), least-squares complex exponential (LSCE) and eigensystem realization algorithm (ERA) methods are reviewed and chosen to do the comparison. Reformulation to their original forms shows these three methods can all be attributed to a generalized eigenvalue problem with different matrix pairs. With this general format, we can see that single-input multioutput (SIMO) methods can easily be extended to multi-input multioutput (MIMO) cases by taking advantage of a generalized Hankel matrix or a generalized Toeplitz matrix.

Group-Based Sparse Representation Based on lp-norm Minimization for Compressive Sensing

2020 ◽  
Vol 8 (1) ◽  
pp. 13-18
Author(s):  
Ruijing Li ◽  
◽  
Yechao Bai ◽  
Xinggan Zhang ◽  
Lan Tang ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Sparse Representation ◽  
Lp Norm ◽  
Norm Minimization

Noise-Robust MUSIC-Based Sound Source Localization Using Steering Vector Transformation for Small Humanoids

2017 ◽  
Vol 29 (1) ◽  
pp. 26-36 ◽  
Author(s):  
Ryu Takeda ◽  
◽  
Kazunori Komatani
Keyword(s):  
Source Localization ◽  
Sound Source ◽  
Computational Cost ◽  
Internal Noise ◽  
Humanoid Robots ◽  
Eigenvalue Decomposition ◽  
Sound Source Localization ◽  
Noise Robustness ◽  
Localization Accuracy ◽  
Steering Vector

[abstFig src='/00290001/03.jpg' width='300' text='Sound source localization and problem' ] We focus on the problem of localizing soft/weak voices recorded by small humanoid robots, such as NAO. Sound source localization (SSL) for such robots requires fast processing and noise robustness owing to the restricted resources and the internal noise close to the microphones. Multiple signal classification using generalized eigenvalue decomposition (GEVD-MUSIC) is a promising method for SSL. It achieves noise robustness by whitening robot internal noise using prior noise information. However, whitening increases the computational cost and creates a direction-dependent bias in the localization score, which degrades the localization accuracy. We have thus developed a new implementation of GEVD-MUSIC based on steering vector transformation (TSV-MUSIC). The application of a transformation equivalent to whitening to steering vectors in advance reduces the real-time computational cost of TSV-MUSIC. Moreover, normalization of the transformed vectors cancels the direction-dependent bias and improves the localization accuracy. Experiments using simulated data showed that TSV-MUSIC had the highest accuracy of the methods tested. An experiment using real recoded data showed that TSV-MUSIC outperformed GEVD-MUSIC and other MUSIC methods in terms of localization by about 4 points under low signal-to-noise-ratio conditions.

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