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Stability and Super-Resolution of music and ESPRIT for Multi-Snapshot Spectral Estimation

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 4555-4570页

作者： Li, Weilin Zhu, Zengying Gao, Weiguo Liao, Wenjing CUNY City Coll New York NY 10031 USA Fudan Univ Sch Math Sci Shanghai 200437 Peoples R China Georgia Inst Technol Sch Math Atlanta GA 30332 USA

This paper studies the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a uniform array of sensors. We prove novel stability bounds for music and ESPRIT as a function of the noise standard deviation, number of snapshots, source amplitudes, and support. Our most general result is a perturbation bound of the signal space in terms of the minimum singular value of Fourier matrices. When the point sources are located in several separated clumps, we provide an explicit upper bound of the noise-space correlation perturbation error in music and the support error in ESPRIT in terms of a Super-Resolution Factor (SRF). The upper bound for ESPRIT is then compared with a new Cramer-Rao lower bound for the clumps model. As a result, we show that ESPRIT is comparable to that of the optimal unbiased estimator(s) in terms of the dependence on noise, number of snapshots and SRF. As a byproduct of our analysis, we discover several fundamental differences between the single-snapshot and multi-snapshot problems. Our theory is validated by numerical experiments.

关键词： Multiple signal classification Estimation Superresolution Sensor arrays Upper bound Perturbation methods Standards Multi-snapshot spectral estimation stability super-resolution music algorithm optimality of ESPRIT algorithm Cramer-Rao lower bound array imaging

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Underwater Acoustic DOA Estimation of Incoherent Signal Based on Improved GA-music

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IEEE ACCESS 2023年 11卷 69474-69485页

作者： Lan, Chaofeng Chen, Huan Zhang, Lei Guo, Rui Han, Chuang Luo, Dajun Harbin Univ Sci & Technol Sch Measurement & Commun Engn Harbin 150080 Peoples R China China Ship Dev & Design Ctr Wuhan 430064 Peoples R China Beidahuang Ind Grp Gen Hosp Harbin 150088 Peoples R China

The problem of poor real-time capability, a large number of traversals and the long operation time of the music algorithm bring great difficulties to the application of DOA estimation. For the above problems, this paper fuses music algorithm and genetic algorithm and proposes an improved genetic music algorithm (GA-music). Also, improvement strategies are proposed for the three operators of selection, crossover, and variation of the genetic algorithm. The GA-music was simulated for DOA estimation to verify the effectiveness of this algorithm. The research shows that the GA-music proposed in this paper has the best operational performance at different precisions and SNRs. This algorithm can effectively reduce the iterative computation of the algorithm with better real-time performance, and the search success rate is above 95% while ensuring accuracy. Furthermore, this paper corroborates that the proposed improved genetic music algorithm can achieve better performance in single signals and incoherent multi-signal sources. It can be seen that the algorithm in this paper can effectively solve the problems of low success rates of DOA estimation searches and poor real-time performance and has a significant reference value for practical engineering applications.

关键词： DOA estimation music algorithm genetic algorithm GA-music real-time

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DOA Estimation of Noncircular Signals Under Impulsive Noise Using a Novel Empirical Characteristic Function-Based music

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第6期42卷 3706-3743页

作者： Asghari, Mohsen Zareinejad, Mohammad Rezaei, Seyed Mehdi Amindavar, Hamidreza Amirkabir Univ Technol Mech Engn Dept Tehran Iran Amirkabir Univ Technol New Technol Res Ctr Tehran Iran Amirkabir Univ Technol Elect Engn Dept Tehran Iran

Noncircular (NC) signals constitute a significant class of signals that are frequently employed in communication systems. In the presence of extremely impulsive noises, determining the direction of these signals can present significant challenges. When the noise tail becomes heavier or the signal-to-noise ratio decreases, existing methods yield poor results. Recently, the authors have developed an empirical characteristic function (ECF)-based music algorithm. This method is called ECF-music. Despite its robustness and high precision, it only works with circular signals. This is a direct result of the covariance matrix of the ECF-music method containing a nonzero relation matrix. In this paper, a novel ECF-based music is developed to exploit the ECF in DOA estimation of NC signals. Using the CF of the output of the extended array, a new covariance-like matrix is introduced. Then, an analysis of eigen-decomposition is performed to develop a new music algorithm. Due to the unique properties of ECF, such as its ability to preserve information, this method yields precise results, particularly in the presence of heavy tail noise. Additionally, it doubles the maximum number of detectable sources. The Monte Carlo simulations demonstrate the excellent performance of the method, NC-ECF-music. This method outperforms existing methods in terms of estimation error and resolution, as demonstrated by these results.

关键词： DOA estimation Noncircular signal Empirical characteristic function Alpha stable noise music algorithm

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music Imaging Using Phase-Space Gaussian-Beams Processing

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2014年第3期62卷 1270-1281页

作者： Heilpern, Tal Heyman, Ehud Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

In a recent paper we presented a beam-based back-propagation and correlation imaging scheme for targets in a homogeneous medium. This beam-based approach is extended here for music-imaging algorithms. In the beam approach, the fields of the physical arrays of point-sources and point receivers are expanded using special sets of collimated beam-sources and beam-receivers. This converts the physical scattering data into a beam-domain data, describing the scattering amplitudes seen (synthetically) by receiver beams due to excitation by source beams. The image is then formed by applying the music algorithm directly in the beam domain. We derive a closed form expression for the data transformation to the beam domain and then derive multi-experiments music-imaging algorithms that accommodate the measurement noise. The beam approach enables local imaging of any given sub-domain of interest by retaining only the subset of beams that pass through that domain, thus reducing the overall computation complexity relative to the conventional Green function approach, and filtering out of data and noise that arrive from non-relevant directions. Numerical investigations reveal that the beam approach also provides a better resolution under low S/N conditions.

关键词： Beam summation method beam-based data processing Gaussian beams imaging inverse scattering music algorithm

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A music APPROACH FOR ESTIMATION OF DIRECTIONS OF ARRIVAL OF MULTIPLE NARROW-BAND AND BROAD-BAND SOURCES

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SIGNAL PROCESSING 1994年第2-3期40卷 319-323页

作者： NG, BP ER, MH [a]Singapore Polytechnic Department of Electronics Communication Engineering 500 Dover Road Singapore 0513 [b]Centre for Signal Processing Nanyang Technological University School of Electrical Electronic Engineering Nanyang Avenue Singapore 2263

In this paper, a high resolution technique is proposed, using a sensor array with arbitrary non-linear geometry (linear array can be used for spatial/temporal implementation), to handle the direction-of-arrival (DOA) estimation problem involving unknown narrowband and broadband sources. The technique basically uses the fundamental properties of the eigenvectors from the signal subspace to form an optimization problem with broadband response derivative constraints imposed, so as to achieve the broadband weight vector for the DOA estimator. Simulation results are presented to show the performance of the proposed technique.

关键词： music algorithm DIRECTION-OF-ARRIVAL ESTIMATION

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Impact energy level assessment of composite structures using music-ANN approach

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STRUCTURAL CONTROL & HEALTH MONITORING 2016年第5期23卷 825-837页

作者： Zhong, Yongteng Xiang, Jiawei Gao, Haifeng Zhou, Yuqing Wenzhou Univ Coll Mech & Elect Engn Wenzhou 325035 Peoples R China

Impact damage effects on the residual mechanical properties of the structure can be quite detrimental, and failure patterns depend strongly on the impact energy levels. This paper presents impact energy level assessment method using 2D multiple signal classification (music) and artificial neural network (ANN) approach for composite structures. Because uniform linear array has the shortcoming of the half-plane mirror effect, 2D music algorithm using a plum blossom sensor array is firstly applied to locate the position of impact and extract impact energy feature. Secondly, the relation impact energy feature, impact position, and impact energy level at different measurement points are established using ANN approach. Through the trained ANN, the impact energy level can be predicted when the position and impact energy feature results of unknown impact are given as input. Finally, the proposed method is applied to a quasi-isotropic epoxy laminate plate and a large stiffened carbon fiber composite structure showing its successful performance on composite structure. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： Impact energy level music algorithm ANN Plum blossom sensor array Composite structure

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A fast computation method for music spectrum function based on circular arrays

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INTERNATIONAL JOURNAL OF ELECTRONICS 2015年第2期102卷 260-268页

作者： Du, Zhengdong Wei, Ping Univ Elect Sci & Technol China Sch Elect Engn Chengdu 610054 Peoples R China Southwest Elect & Telecommun Technol Res Inst Chengdu 610041 Peoples R China

The large computation amount of multiple signal classification (music) spectrum function seriously affects the timeliness of direction finding system using music algorithm, especially in the two-dimensional directions of arrival (DOA) estimation of azimuth and elevation with a large antenna array. This paper proposes a fast computation method for music spectrum. It is suitable for any circular array. First, the circular array is transformed into a virtual uniform circular array, in the process of calculating music spectrum, for the cyclic characteristics of steering vector, the inner product in the calculation of spatial spectrum is realised by cyclic convolution. The computational amount of music spectrum is obviously less than that of the conventional method. It is a very practical way for music spectrum computation in circular arrays.

关键词： cyclic convolution computation amount DOA FFT circular arrays music algorithm

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music-like estimation of direction of arrival for noncircular sources

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第7期54卷 2678-2690页

作者： Abeida, Habti Delmas, Jean-Pierre Inst Natl Telecommun CNRS Dept CITI GETINTUMR 5157 F-91011 Evry France

This paper examines the asymptotic performance of music-like algorithms for estimating directions of arrival (DOA) of narrowband complex noncircalar sources. Using closed-form expressions of the covariance of the asymptotic distribution of different projection matrices, it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace-based algorithms valid for Gaussian or non-Gaussian and complex circular or noncircular sources. We also derive different robustness properties from the asymptotic covariance of the estimated DOA given by such algorithms. These results are successively applied to four algorithms: to two attractive music-like algorithms previously introduced in the literature, to an extension of these algorithms, and to an optimally weighted music algorithm proposed in this paper. Numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance (AMV) algorithms introduced as benchmarks.

关键词： asymptotically minimum variance (AMV) complex noncircular sources direction of arrival (DOA) estimation music algorithm subspace-based algorithms

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Recovery analysis of damped spectrally sparse signals and its relation to music

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INFORMATION AND INFERENCE-A JOURNAL OF THE IMA 2022年第1期11卷 355-383页

作者： Li, Shuang Mansour, Hassan Wakin, Michael B. Colorado Sch Mines Dept Elect Engn Golden CO 80401 USA Mitsubishi Elect Res Labs Cambridge MA 02139 USA

One of the classical approaches for estimating the frequencies and damping factors in a spectrally sparse signal is the MUltiple SIgnal Classification (music) algorithm, which exploits the low-rank structure of an autocorrelation matrix. Low-rank matrices have also received considerable attention recently in the context of optimization algorithms with partial observations, and nuclear norm minimization (NNM) has been widely used as a popular heuristic of rank minimization for low-rank matrix recovery problems. On the other hand, it has been shown that NNM can be viewed as a special case of atomic norm minimization (ANM), which has achieved great success in solving line spectrum estimation problems. However, as far as we know, the general ANM (not NNM) considered in many existing works can only handle frequency estimation in undamped sinusoids. In this work, we aim to fill this gap and deal with damped spectrally sparse signal recovery problems. In particular, inspired by the dual analysis used in ANM, we offer a novel optimization-based perspective on the classical music algorithm and propose an algorithm for spectral estimation that involves searching for the peaks of the dual polynomial corresponding to a certain NNM problem, and we show that this algorithm is in fact equivalent to music itself. Building on this connection, we also extend the classical music algorithm to the missing data case. We provide exact recovery guarantees for our proposed algorithms and quantify how the sample complexity depends on the true spectral parameters. In particular, we provide a parameter-specific recovery bound for low-rank matrix recovery of jointly sparse signals rather than use certain incoherence properties as in existing literature. Simulation results also indicate that the proposed algorithms significantly outperform some relevant existing methods (e.g., ANM) in frequency estimation of damped exponentials.

关键词： spectral estimation nuclear norm minimization atomic norm minimization music algorithm low-rank matrix completion

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On the resiliency of music direction finding against antenna sensor coupling

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2008年第2期56卷 371-380页

作者： Ye, Zhongfu Liu, Chao Univ Sci & Technol China Dept Elect Engn & Informat Sci Inst Stat Signal Proc Hefei 230027 Anhui Peoples R China

Many classical direction of arrival (DOA) estimation algorithms suffer from sensitivity to sensor coupling. By applying a group of auxiliary sensors in a uniform linear array (ULA), we prove the resiliency of the music direction finding algorithm against array sensor coupling. We show that the performance of music algorithm under antenna array with unknown coupling can be very close to the case with known coupling. We can also estimate the mutual coupling coefficients before refining the DOA estimates by utilizing an extended sensor array. Moreover, our analysis on the effect of mutual coupling in direction finding illustrates the existence of some blind angles which should be avoided when the array is designed. Our simulation results corroborate our analysis.

关键词： auxiliary sensor DOA estimation music algorithm mutual coupling ULA

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