Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis

Johnson, Don H.; DeGraaf, S.

doi:10.1109/tassp.1982.1163915

Cited by 224 publications

(60 citation statements)

References 9 publications

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“…Viberg and Ottersten found that a suitable weight for each eigenvector's fitting can be used to minimize the asymptotic estimation error of DOA parameters. The weighting mentioned here is different from Johnson and DeGraaf's noise eigenvector weighting [25], because here signal eigenvector weighting is involved. The optimal WSF method for parametric array processing has (dominant) signal eigenvalues appearing in the weight expressions in the cost function.…”

Section: In Parametric Signal Subspace Fitting Methodsmentioning

confidence: 92%

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Eigenvalues of Covariance Matrix for Two-Source Array Processing

Chou¹

1991

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SummaryWe begin this report with a survey of direction-finding algorithms restricted to the narrowband case in element space. We then set out to search for a simple satisfactory stress measure to direction-finding algorithmns applied to scenarios with two sources. The word "stress" for a scenario is used to indicate the difficulty that an algorithm has in determining the direction of arrival of each of the two sources. A scenario is said to be "stressful" to an algorithm if it causes difficulty in resolving the sources or in determining their directions of arrival. The apparent lack of understanding of the effect of phase difference between two signals in direction-finding made such an ideal stress measure illusive. Regardless of all its deficiencies, eigenvalue ratio is still a useful measu~c in summarizing stressing factors in many aspects for two-arrival direcion-finding scenario.Eigenvalue weighting appears in some noise subspace methods, in parametric signal subspace fitting methods, and in nonparametric subspace adaptive nulliiig beamforming. For a two-source array-processing scenario, normalized largc and small eigenvalues A, and A 2 are reduced to forms depending only on a real triplet: phase-dependent variable , phase-independent variable 77, and power ratio 21. The pairs ( , /) are conined to an isosceles-like region. We characterize * this isoscelks-like region and the many-to-one mapping from the Caitesian product of the temporal and spatial correlation unit-disks onto this region, * the behavior of the eigenvalues and their ratios as functions of the real triplet both analytically and graphically with respect to direction-finding.The main contribution of this work is a manageable presentation of a compact map showing Al, A 2 , and A as functions of , r, and 11 over all possible scenarios. This enables one to see A 2Ir 2 the relative positions among different scenarios. We also present some easy-to-remember formulas that enable one to exercise "back-of-envelope" assessment of scenarios. The small eigenvalue is shown to diminish qualitatively and quantitatively for two-arrival scenarios increasingly stressed with high temporal and/or spatial correlations. The special case of equal-strength signal arrivals (a = 1), also important in low-angle radar tracking, shares many rich structures of general a. The equal-strength case also has several additional unique features for signal eigenvalue ratio '\, which is important in direction-finding: e an extra 6 dB over the vertical axis =0 as compared to the general E, case, r 2 * a 6-dB increase for equipower arrivals highly correlated both temporally and spatially from changing the angle difference between the two unit-disk vectors from 90°(orthogonal waveforms) to 0°(in-phase waveforms), * the lower left corner of the isosceles-like triangle is a point of discontinuity for the eigenvalue ratio -'The developed results are used to assess some scenarios used by Cadzow and Ottersten.

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Section: In Parametric Signal Subspace Fitting Methodsmentioning

confidence: 92%

“…Johnson and DeGraaf [25] proposed to modify the original noise subspace MUSIC algorithm by weighting the noise eigenvectors with the noise eigenvalues. The modification was derived in a somewhat ad hoc fashion.…”

Section: In Noise Subspace Methodsmentioning

confidence: 99%

Eigenvalues of Covariance Matrix for Two-Source Array Processing

Chou¹

1991

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“…Note that the frequency estimator is a pseudo spectrum estimator because the autocorrelation sequence cannot be recovered by Fourier transforming the frequency estimator. A detailed discussion about the frequency estimator can be found in Schmidt (1986) and Johnson and Degraaf (1982). This method also has been used-in fracture scattering studies and discussed in Shen and Toksoz (1998).…”

Section: Estimation Of Avo and Fvo Attributesmentioning

confidence: 99%

Azimuthal offset‐dependent attributes (AVO and FVO) applied to fracture detection

Shen¹,

Sierra²,

Burns³

et al. 1999

SEG Technical Program Expanded Abstracts 1999

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Using the amplitude versus offset (AVO) and the frequency versus offset (FVO) information, the diagnostic ability of P-wave seismic data in fracture detection is investigated. The offset-dependent attributes (AVO and FVO) are estimated by using an eigenvector based estimation technique, the multiple signal classification frequency estimator. These attributes are applied to the determination of principal orientation of fractures in carbonate fractured reservoirs located in the Maporal field in the Barinas basin of southwestern Venezuela. Our studies show that, in the crack normal direction, P-wave reflectivity is characterized by a large increase of amplitude with offset (large positive AVO gradient) and a large frequency decay with offset (large negative FVO gradient). In the crack strike direction, P-wave reflectivity is characterized by a wide range of AVO gradients but a small variation of FVO gradients. The analyses of inverted offsetdependent velocities and theoretical calculations show that the lateral heterogeneity in the reservoir zone can lead to large variations of AVO signatures. The offset-dependent frequency attribute can help lessen the ambiguity in fracture detection.. The combination of the offset-dependent frequency attribute is more beneficial than using the offset-dependent amplitude attribute alone.

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“…Some of the most popular ones in recent years continue to be matched-field processing (Bucker, 1976;Jensen et al, 1994), MUSIC (MUltiple SIgnal Classification) (Schmidt, 1979;Johnson, 1982;Schmidt, 1986;Biondi and Kostov, 1989), and other linear subspace methods (Johnson, 1982;Johnson and DeGraaf, 1982;Cheney, 2001). When the targets are imbedded in heterogeneous media so that significant multiple scattering occurs in the background medium during wave propagation between array and target, the randomness has a different character than that usually envisioned in these traditional analyses.…”

Section: Introductionmentioning

confidence: 99%

Statistical Stability and Time-Reversal Imaging in Random Media

Berryman

Borcea

Papanicolaou

et al. 2004

Geometric Methods in Inverse Problems and PDE Control

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Localization of targets imbedded in a heterogeneous background medium is a common problem in seismic, ultrasonic, and electromagnetic imaging problems. The best imaging techniques make direct use of the eigenfunctions and eigenvalues of the array response matrix, as recent work on time-reversal acoustics has shown. Of the various imaging functionals studied, one that is representative of a preferred class is a time-domain generalization of MUSIC (MUltiple SIgnal Classification), which is a well-known linear subspace method normally applied only in the frequency domain. Since statistical stability is not characteristic of the frequency domain, a transform back to the time domain after first diagonalizing the array data in the frequency domain takes optimum advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.

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Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis

Cited by 224 publications

References 9 publications

Eigenvalues of Covariance Matrix for Two-Source Array Processing

Eigenvalues of Covariance Matrix for Two-Source Array Processing

Azimuthal offset‐dependent attributes (AVO and FVO) applied to fracture detection

Statistical Stability and Time-Reversal Imaging in Random Media

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