The Spatial Representation

  • Dennis W. Ricker
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 725)


In addition to the estimation of Doppler and delay, bearing or angle with respect to the sonar’s orientation is crucial for scatterer localization. Acoustic energy at the transmitter is usually introduced into the medium by a distributed source (projector array) and echo energy is received via a distributed array of individual transducer elements that convert the acoustic energy back into an electrical signal. Sonar arrays are spatially distributed and when in a line, plane, on the surface of a body, or when distributed throughout a volume, they are called line, planar, conformal, and volumetric arrays respectively. The process of summing the weighted responses of the individual receive array elements or more generally integrating the response over a continuous array is called beam formation. The integrated receive array response to acoustic energy depends upon the direction from which the energy arrives and is described by a beam or pattern function. Likewise the transmit pattern function describes the directional distribution of transmitted intensity from a projector array.


Spatial Representation Beam Pattern Pattern Function Array Processor Array Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    S.C. Clay and H. Medwin. Acoustical Oceanography. Wiley Interscience, 1977.Google Scholar
  2. [2]
    L.J. Ziomek. Underwater Acoustics, A Linear Systems Approach. Academic Press, Orlando, FL, 1985.Google Scholar
  3. [3]
    D.C. Swanson. Signal Processing for Intelligent Sensor Systems. Marcel Dekker, New York, NY, 2000.CrossRefGoogle Scholar
  4. [4]
    R.J. Urick. Principles of Underwater Sound. McGraw-Hill, 1975.Google Scholar
  5. [5]
    W.S. Burdic. Underwater Acoustic System Analysis. Prentice-Hall, 1984.Google Scholar
  6. [6]
    L.S. Bendat and A.G. Piersol. Random Data Analysis and Measurement Procedures. John Wiley & Sons, 1986.MATHGoogle Scholar
  7. [7]
    F.J. Harris. On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proceedings of the IEEE, 66(1):51–83, Jan. 1978.CrossRefGoogle Scholar
  8. [8]
    D.C. Rife and G.A. Vincent. Use of Discrete Fourier Transform in the Measurement of Frequencies and Levels of Tones. Bell Sytem Tech. Journ., 49(2):197–228, Feb. 1970.MathSciNetGoogle Scholar
  9. [9]
    H. Rohling and J. Schuerman. Discrete Time Window Functions With Arbitrarily Low Sidelobe Level. Signal Processing, 5(2): 127–138, Mar. 1983.CrossRefGoogle Scholar
  10. [10]
    D.W. Ricker. Small Aperture Angle Measurement for Active Echo Location Systems. IEEE Trans, on Aerosp. and Elect. Systs., 22(4):380–388, 1986.CrossRefGoogle Scholar
  11. [11]
    S.D. Stearns. Digital signal Analysis. Hayden, Rochelle Park, NJ, 1975.Google Scholar
  12. [12]
    H. Cox. Interrelated Problems in Estimation and Detection II. In Proc. NATO Advanced Study Inst on Sig. Proc., Enschede, Netherlands, Aug. 1968. NATO.Google Scholar
  13. [13]
    A.D. Whalen. Detection of Signals in Noise. Academic Press, 1971.Google Scholar
  14. [14]
    W.B. Davenport and W.L. Root. An Introduction to the Theory of Random Signals and Noise. McGraw-Hill, 1958.MATHGoogle Scholar
  15. [15]
    H. Cox. Interrelated Problems in Estimation and Detection I. In Proc. NATO Advanced Study Inst on Sig. Proc., Enschede, Netherlands, Aug. 1968. NATO.Google Scholar
  16. [16]
    C.F. Van Loan G.H. Golub. Matrix Computations, volume 6. Johns Hopkins Press, Baltimore, MD, 1983.MATHGoogle Scholar
  17. [17]
    M.S. Bartlett. An Inverse Matrix Adjustment Arising in Discriminant Analysis. Annals of Mathematical Statistics, 22:107–111, 1951.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    W. J. Bangs II. Array Processing with Generalized Beamformers. PhD Thesis in Statistics, Yale Univ., New Haven, CT, Sept. 1971.Google Scholar
  19. [19]
    W. J. Bangs and P. M. Schultheiss. Space-Time Processing for Optimal Parameter Estimation, pages 577–589. Academic Press, 1973. in NATO edited book “Signal Processing”.Google Scholar
  20. [20]
    Altes R.A. Cross Correlation and Energy Detection in Multiarray Processing. IEEE Trans. Acoust, Speech, and Signal Proc., 33(3):493–504, 1985.CrossRefGoogle Scholar
  21. [21]
    R.C. Burkhardt. Robust Adaptive Processing for Application to Underwater Acoustic Arrays. PhD Thesis in Acoustics, Penna. State Univ., Dec. 1992.Google Scholar
  22. [22]
    H. Cox, R.M. Zeskind and M.W. Owen. Robust Adaptive Beamforming. IEEE Trans. Acoust,Speech, and Signal Proc., 35(10):1365–1376, Oct. 1987.CrossRefGoogle Scholar
  23. [23]
    L.H. Sibul and L.J. Ziomek. Generalized Wideband Cross- Ambiguity Function. In Proc. IEEE Intl. Conf. on Acoust. Spch. and Sig. Proc., Atlanta GA, 1981.Google Scholar
  24. [24]
    R.A. Monzingo and T.W. Miller. Introduction to Adaptive Arrays. Wiley Interscience, New York, 1980.Google Scholar
  25. [25]
    Altes R.A. Target Position Estimation in Radar and Sonar, and Generalized Ambiguity Analysis for Maximum Likelihood Parameter Estimation. Proceedings of the IEEE, 67(6):920–930, June 1979.CrossRefGoogle Scholar
  26. [26]
    A.N. Mirkin and L.H. Sibul. Cramér-Rao Bounds on Angle Estimation with a Two-Dimensional Array. IEEE Trans. Sig. Proc., 39(2):515–517, Feb. 1991.CrossRefGoogle Scholar
  27. [27]
    A.I. Leonov and K.I. Fomichev. Monopulse Radar. Artech House, Norwood MA, 1986. translated by W.F. Barton.Google Scholar
  28. [28]
    B.R. Mahafza. Introduction to Radar Analysis. CRC Press LLC, Boca Raton Fla, 1998.Google Scholar
  29. [29]
    D.R. Rhodes. Introduction to Monopulse. McGraw-Hill, 1959.Google Scholar
  30. [30]
    S.M. Sherman. Monopulse Principles and Techniques. Artech House, 1984.Google Scholar
  31. [31]
    A.J. Rainal. Monopulse Radars Excited by Gaussian Signals. IEEE Trans, on Aerosp. and Elect. Systs., 2(3):337–345, May 1966.CrossRefGoogle Scholar
  32. [32]
    C.C. Merchant. Detection of a Dual Channel Differential Phase Modulated Signal in Correlated Noise. MS Thesis in Electrical Engineering, Penna. State Univ., Univ. Park, PA, Aug. 1982.Google Scholar
  33. [33]
    R.A. Schmidt. A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation. PhD Thesis in Electrical Engineering, Stanford Univ., Nov. 1981.Google Scholar
  34. [34]
    B. Priedlander. The root-MUSIC Algorithm for Direction finding with Interpolated Arrays. Signal Processing, 30(1):15–29, 1993.CrossRefGoogle Scholar
  35. [35]
    L.L. Sharf. Statistical Signal Processing. Addison-Wesley, 1991.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Dennis W. Ricker
    • 1
  1. 1.The Pennsylvania State UniversityUSA

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