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Estimation of structured covariances with application to array beamforming

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Abstract

The estimation of covariance matrices which are structured, for example, of Toeplitz type, from measurement data is considered. The problem is considered in the context of array beamforming, and various methods of estimation are derived and compared, such comparison including consideration of the behavior of the estimate in beamforming applications.

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References

  1. R. A. Mozingo and T. W. Miller,Introduction to Adaptive Arrays, Wiley-Interscience, New York, 1980.

    Google Scholar 

  2. J. E. Hudson,Adaptive Array Principles, Peter Peregrinus, 1981.

  3. D. A. Gray, Theoretical and experimental comparisons of the formulation of optimum processors in element, beam and eigenspaces, inAdaptive Methods in Underwater Acoustics (H. G. Urban, ed.), Reidel, Dordrecht.

  4. R. N. McDonaugh, Application of the maximum-likelihood and maximum-entropy method to array processing, inNonlinear Methods of Spectral Analysis (S. Haykin ed.), Chap. 6, Springer-Verlag, New York, 1979.

    Google Scholar 

  5. D. H. Johnson, The application of spectral estimation methods to bearing estimaton problems,Proc. IEEE,70, 1018–1028, 1982.

    Google Scholar 

  6. N. Levinson, The Wiener RMS (root mean square) error in filter design,J. Math. Phys.,25, 261–278, 1947.

    Google Scholar 

  7. W. F. Trench, An algorithm for the inversion of finite Toeplitz matrices,J. Soc. Indust. Appl. Math.,12, 515–522, 1964.

    Google Scholar 

  8. I. S. Iohvidov,Hankel and Toeplitz Matrices and Forms, Birkhauser, Boston, 1982.

    Google Scholar 

  9. J. P. Burg, D. G. Luenberger, and D. L. Wenger, Estimation of structured covariances,Proc. IEEE,70, 963–974, 1982.

    Google Scholar 

  10. A. T. Moffett, Minimum redundancy linear arrays,IEEE Trans. Antennas and Propogation,16, 172–175, 1968.

    Google Scholar 

  11. D. H. Johnson and S. De Graaf, Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis,IEEE Trans. Acoust. Speech Signal Process.,30, 638–647, 1982.

    Google Scholar 

  12. G. Bienvenu and L. Kopp, Source power estimation associated with high resolution bearing estimation,Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Atlanta, GA, 153–156, 1981.

  13. A. Cantoni and L. C. Godara, Resolving the directions of sources in a correlated field incident on an array,J. Acoust. Soc. Amer.,67, 1247–1255, 1980.

    Google Scholar 

  14. C. L. Byrne and A. K. Steele, Stable nonlinear methods for sensor array processing,IEEE J. Oceanic Engng,10, 255–259, 1985.

    Google Scholar 

  15. D. A. Gray, Maximum entropy estimates of the frequency wavenumber power spectrum using a linear array of equispaced receivers, Technical Report WSRL-0196, Defence Research Centre, Salisbury, Adelaide, South Australia, 1981.

    Google Scholar 

  16. N. Q. A., On the uniqueness of the maximum-likelihood estimate of structured covariance matrices,IEEE Trans. Acoust. Speech Signal Process.,32, 1249–1251, 1984.

    Google Scholar 

  17. T. Kailath, The divergence and Bhattacharyya distance measures in signal selection,IEEE Trans. Comm.,15, 52–60, 1967.

    Google Scholar 

  18. N. R. Goodman, Statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,34, 152–176, 1963.

    Google Scholar 

  19. J. Aczél and Z. Daróczy,On Measures of Information and Their Characterizations, Academic Press, New York, 1975.

    Google Scholar 

  20. J. E. Shore and R. W. Johnson, Automatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy,IEEE Trans. Inform. Theory,26, 26–27, 1980.

    Google Scholar 

  21. J. E. Shore, On a relation between maximum likelihood classification and minimum relative entropy classification,IEEE Trans. Inform. Theory,30, 851–854, 1984.

    Google Scholar 

  22. S. Kullback,Information Theory and Statistics, Dover, New York, 1968.

    Google Scholar 

  23. H. A. d'Assumpaco, Some new signal processors for arrays of sensors,IEEE Trans. Inform. Theory,26, 441–453, 1982.

    Google Scholar 

  24. J. Capon and J. R. Goodman, Probability distributions for estimators of the frequency-wavenumber spectrum,Proc. IEEE,58, 1785–1786, 1970.

    Google Scholar 

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Authors and Affiliations

  1. Weapons System Research Laboratory, G.P.O. Box 2151, 5001, Adelaide, SA, Australia

    D. A. Gray

  2. Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, 2601, Canberra, ACT, Australia

    B. D. O. Anderson

  3. Department of Electronic and Communication Science, La Trobe University, 3083, Bundoora, Victoria, Australia

    P. K. Sim

Authors
  1. D. A. Gray
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  2. B. D. O. Anderson
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  3. P. K. Sim
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Additional information

The work of the first author was carried out as a Defence Fellow on leave from the Australian Department of Defence, whose support is gratefully acknowledged. The other two authors were also supported by the Department of Defence.

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Gray, D.A., Anderson, B.D.O. & Sim, P.K. Estimation of structured covariances with application to array beamforming. Circuits Systems and Signal Process 6, 421–447 (1987). https://doi.org/10.1007/BF01600233

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  • DOI: https://doi.org/10.1007/BF01600233

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