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Estimator-correlator array processing: Theoretical underpinnings and adaptive implementation

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Abstract

We develop a generalized singular value decomposition methodology for implementing the estimator-correlator array processor. The usefulness of this structure stems from two key properties examined in this paper. First, the structure is canonical, in that it applies to a broad class of underwater signal processing problems. Second, it is robust, not critically dependent on a precise characterization of the medium in question. Numerical simulation experiments justifying this claim are presented.

Specific examples demonstrate the general implementation procedure. Although the results are computationally demanding, they can in large part be realized with parallel architectures. Hence, their implementation by dedicated processors is possible.

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References

  • D. Middleton,Introduction to Statistical Communication Theory, McGraw-Hill, New York, 1960.

    Google Scholar 

  • P.A. Flandrin, “A time-frequency formulation of optimum detection,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-36, pp. 1377–1384, 1988.

    Google Scholar 

  • Ed F. Deprettere (editor),SVD and Signal Processing: Algorithms, Applications and Architectures, North-Holland, Amsterdam, 1988.

    Google Scholar 

  • H.L. Van Trees, “A unified theory for optimum array processing,” Arthur D. Little, Inc. Report No. 4160866, August 1966.

  • T. Kailath, “A view of three decades of linear filtering theory,”IEEE Transactions on Information Theory, vol. IT-20, pp. 146–180, 1974.

    Article  Google Scholar 

  • R. Price, “Optimum detection of random signals in noise with applications to scatter-multipath communications, I,”IRE Transactions on Information Theory, vol. IT-2, pp. 125–135, 1956.

    Article  Google Scholar 

  • T. Kailath, “A note on least-squares estimates from likelihood ratios,”Information and Control, vol. 13, pp. 534–540, 1968.

    Article  Google Scholar 

  • T. Kailath, “A general likelihood-ratio formula for random signals in Gaussian noise,”IEEE Transactions on Information Theory, vol. IT-15, pp. 350–361, 1969.

    Article  Google Scholar 

  • R. Esposito, “A class of estimators for optimum adaptive detection,”Information and Control, vol. 10, pp. 137–148, 1967.

    Article  Google Scholar 

  • S.C. Schwartz, “Conditional mean estimates and Bayesian hypothesis testing,”IEEE Transactions on Information Theory, vol. IT-21, pp. 663–665, 1975.

    Article  Google Scholar 

  • S.C. Schwartz, “The estimator-correlator for discrete-time problems,”IEEE Transactions on Information Theory, vol. IT-23, pp. 93–100, 1977.

    Article  Google Scholar 

  • D. Middleton, “Channel modeling and threshold signal processing in underwater acoustics: an analytical overview,”IEEE Journal of Oceanic Engineering, vol. OE-12, pp. 4–27, 1987.

    Article  Google Scholar 

  • G.R.L. Sohie, “Applications of Hilbert space theory to optimal and adaptive space-time processing,” Ph.D. dissertation, The Pennsylvania State University, 1983.

  • L.H. Sibul and J.A. Tague, “Matrix representations of propagation and scattering operators,” Proceedings of the 20th Annual Conference on Information Sciences and Systems, Princeton University, Princeton, NJ, 1986.

    Google Scholar 

  • H.L. Van Trees,Detection, Estimation, and Modulation Theory (Parts One and Three), John Wiley, New York, 1968 and 1971.

    Google Scholar 

  • R.A. Monzingo and T.W. Miller,Introduction to Adaptive Arrays, John Wiley, New York, 1980.

    Google Scholar 

  • L.H. Sibul,Adaptive Signal Processing, IEEE Press, New York, 1987.

    Google Scholar 

  • G.H. Golub and C.F. Van Loan,Matrix Computations (Second Edition), The Johns Hopkins University Press, Baltimore, 1989.

    Google Scholar 

  • G.W. Stewart,Introduction to Matrix Computations, Academic Press, New York, 1973.

    Google Scholar 

  • H.C. Andrews and C.L. Patterson, “Singular value decomposition and digital image processing,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-24, pp. 26–53, 1976.

    Google Scholar 

  • C.F. Van Loan, “Generalizing the singular value decomposition,”SIAM Journal of Numerical Analysis, vol. 13, pp. 76–83, 1976.

    Article  Google Scholar 

  • C.F. Van Loan, “Computing the CS and the generalized singular value decompositions,”Numerische Mathematik, vol. 46, pp. 479–491, 1985.

    Article  Google Scholar 

  • C.F. Van Loan and J. Speiser, “Computation of the CS decomposition with application to signal processing,” SPIE volume 696—Advanced Algorithms and Architectures for Signal Processing, pp. 71–77, 1986.

  • F.T. Luk, “A parallel method for computing the generalized singular value decomposition,”Journal of Parallel and Distributed Computing, vol. 2, pp. 250–260, 1985.

    Article  Google Scholar 

  • M.S. Srivastava and C.G. Khatri,An Introduction to Multivariate Statistics, North-Holland, New York, 1979.

    Google Scholar 

  • J.A. Tague,Estimation-Correlation, Modeling, and Identification in Adaptive Array Processors, Ph.D. Dissertation, The Pennsylvania State University, 1987.

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Tague, J.A., Sibul, L.H. Estimator-correlator array processing: Theoretical underpinnings and adaptive implementation. Multidim Syst Sign Process 2, 55–68 (1991). https://doi.org/10.1007/BF01940472

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  • DOI: https://doi.org/10.1007/BF01940472

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