Asymptotic Eigenvalue Density of Noise Covariance Matrices

Menon, Ravi; Gerstoft, Peter; Hodgkiss, William S.

doi:10.1109/tsp.2012.2193573

Cited by 24 publications

(32 citation statements)

References 34 publications

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“…A new direction is taken in Menon [2012aMenon [ , 2012bMenon [ , 2012cMenon [ 2013 and where random matrix theory is used to analyze noise cross-spectral density matrices. A random matrix is a matrixvalued random variable, i.e., the elements are stochastic variables.…”

Section: Random Matrix Theorymentioning

confidence: 99%

“…For a line array of equidistant sensors in such a noise field, the true covariance matrix of the observations in the frequency domain is a symmetric Toeplitz sinc matrix. In Menon [2012a], we derive the eigenvalues of the true covariance matrix as the size of the matrix approaches infinity. For arrays spaced at less than half a wavelength apart, the covariance matrix is shown to be rank deficient and this has implications in techniques such as adaptive beamforming, which require the inverse covariance matrix.…”

Section: Random Matrix Theorymentioning

confidence: 99%

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Sequential Geoacoustic Filtering and Utilizing Ambient Noise for Geoacoustic Inversion

Gerstoft¹,

Yardim²,

Menon³

et al. 2013

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The development of new geoacoustic inversion methods, their use in the analysis of shallow water experimental data, and evaluation of geoacoustic model and parameter uncertainties including the mapping of these uncertainties through to system performance uncertainties. OBJECTIVESAnalysis of geoacoustic inversion data collected from various experiments. Of specific technical interest are: (1) development of methods to track the environmental parameters using sequential filtering, (2) use of ambient noise for estimation of seafloor structure parameters, and (3) the development of new inversion methods for use into the kHz frequency regime. In an ONR Graduate Traineeship Awards we address using Random Matrix Theory in ocean acoustics. APPROACH Sequential filteringA common feature of inverse problems in ocean acoustics is that estimates of underlying physical parameters are extracted from measured acoustic data. Geoacoustic inversion has been approached in the same framework, estimating, in addition to source location, ocean environment parameters and their uncertainty. Often, those parameters evolve in time or space, with acoustic data arriving at consecutive steps. Information on parameter values and uncertainty at preceding steps can be invaluable for the determination of future estimates but is often ignored.Sequential Bayesian filtering, tying together information on parameter evolution, a physical model relating acoustic field measurements to the unknown quantities, and a statistical model describing random perturbations in the field observations, offers a framework for the solution of such problems.

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Section: Random Matrix Theorymentioning

confidence: 99%

Section: Random Matrix Theorymentioning

confidence: 99%

Sequential Geoacoustic Filtering and Utilizing Ambient Noise for Geoacoustic Inversion

Gerstoft¹,

Yardim²,

Menon³

et al. 2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…It was shown in [14] that there are at most two distinct eigenvalues (with multiplicities) for all β, given by…”

Section: Asymptotic Eigenvalues Of the Isotropic Noise CMmentioning

confidence: 99%

“…The probability density of the eigenvalues of the noise SCM were derived in [14] in the limit N, M → ∞, N/M → ν, using Stieltjes transforms [16]. Here, we only consider ν ≤ 1, i.e.…”

Section: Eigenvalue Density Of the Isotropic Noise Scmmentioning

confidence: 99%

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Passive acoustic monitoring using random matrix theory

Menon

Gerstoft

Hodgkiss

2012

2012 IEEE Statistical Signal Processing Workshop (SSP)

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Cross-correlating ocean noise is a potential alternative to using active sources to monitor and study ocean environments. However, directional sources in the medium (usually ships) often introduce a bias in the cross-correlations, making the travel time estimates unreliable. Here, we use recent results in random matrix theory for the eigenvalue density of isotropic noise sample covariance matrices to separate the directional noise from the diffuse noise field. The eigenvalues obtained from ocean data agree well with the theoretical results. Beamforming on the diffuse noise components reveals a fairly spatially isotropic nature for the noise field, which fits the assumption. The cross-correlations using the diffuse noise field alone converge to the expected travel times (i.e., unbiased estimates) and are stable temporally.

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Spatial coherence of the seismic wavefield continuously recorded by the USArray

Seydoux

Shapiro

Rosny

et al. 2016

Geophysical Research Letters

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We use a method based on the array covariance matrix eigenvalues to study the level of spatial coherence and of isotropy of the seismic wavefield continuously recorded during 2010 by the USArray. First, we observe that the raw data are often dominated by local sources. To remove their influence, we apply spectral and temporal normalizations to the input signals. We notice that this widely used preprocessing in ambient‐noise seismology does not fully homogenize the seismic wavefield and that some strongly coherent arrivals persist. Among these persistent signals generated by teleseismic sources we detect (1) seismic waves emitted by strong earthquakes, (2) a nearly continuous quasi‐monochromatic signal at 26 s period, and (3) multiday coherent wave trends in the spectral band of oceanic microseisms (0.07–0.2 Hz). For the latter, beamforming analysis shows that while most of the signals are composed of surface waves, some are dominated by body waves likely generated in the deep ocean.

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Asymptotic Eigenvalue Density of Noise Covariance Matrices

Cited by 24 publications

References 34 publications

Sequential Geoacoustic Filtering and Utilizing Ambient Noise for Geoacoustic Inversion

Sequential Geoacoustic Filtering and Utilizing Ambient Noise for Geoacoustic Inversion

Passive acoustic monitoring using random matrix theory

Spatial coherence of the seismic wavefield continuously recorded by the USArray

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