Advertisement

A Common Framework for Acoustic Signal Analysis in the Ocean Environment

  • J. C. Hassab
Part of the NATO ASI Series book series (volume 1)

Abstract

Estimates of arrival time intervals and their variation in time constitute basic measurement in a signal processor for undersea applications. Those measurements are then mapped in the data processor into the desired estimate of emitting source range, direction, depth and velocity. The integration of the signal and data processing stages within the signal analysis function (see Fig. 1) form the subject of this paper. Figure 2 gives the three basic types of channels with the pertinent time intervals and processing functions. The processor structure has a spectral type formulation for its stationary elements and a state space formulation for its nonstationary ones.

Though varied, the basic signal processing elements have a common set of issues that can be addressed simultaneously (Fig. 3,4). Each signal processing stage has a set of linear and non linear operations, i.e. Fourier transform, absolute value, log, tan−1. . . that map the embedded time interval in the input function into a recognizable clue denoting the value of that time interval. The clue may be a dominant peak or a slope. To enhance a deteriorating clue in the presence of varied interferences, windowing has been incorporated into the basic signal processing stage. Gating is added to limit the search for the clue to the most probable region in the signal processor output. The detected time intervals could then be passed through a linear weighed least square filter to improve and assess the quality of the estimates. Those estimates are fed back in a loose couple to adapt the parameters of the gate and in turn those of the window, for instance. The same estimates are also fed forward through a linearized or nonlinear weighted least square filter to map the time interval estimates into smoothed source position and velocity estimates (Fig. 5). The source parameter estimates are also fed back for use in adaptive design of gate, window…

An interactive system is depicted in Figure (6) that utilizes to best advantage all available information in a synergistic way. The motivation for the described approach lies in the desire to accommodate the widest variety of practical situations with a priori information generally lacking. Too often sub-systems are compartmented and there is little or haphazard communication from one to another. Each sub-system by itself has natural performance limits which can be enhanced through sub-system interactions. The coupling provides guidance for localized search and adaptation, not direction to the local processor.

Directive information may lead to system instability.

Keywords

Time Delay Unwrap Phase Time Delay Estimation Source Track Complex Demodulation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

List of References

I. Multipath With Single Sensing Point Signal Processing

  1. 1.
    B. P. Bogert, J. J. Healy, and J. W. Tukey, “The Frequency Analysis of Time Series for Echoes; Cepstrum Pseudo—Autocovariance, Cross—Cepstrum, and Saphe Cracking,” in Time Series Analysis, M. Rosenblatt, Ed. Chap. 15 pp. 209–243, New York: Wiley, 1963.Google Scholar
  2. 2.
    A. Noll, “Short—Time Spectrum and ‘Cepstrum’ Techniques for Vocal—Pitch Detection,” J. Acoust. Soc. Amer., Vol. 36, pp. 296–302, Feb. 1964.MathSciNetCrossRefGoogle Scholar
  3. 3.
    B. P. Bogert and J. F. Ossanna, “The Heuristics of Cepstrum Analysis of a Stationary Complex Echoed Gaussian Signal in Stationary Gaussian Noise,” IEEE Trans. Inform. Theory, Vol. IT-12, pp. 373–380, July 1966.CrossRefGoogle Scholar
  4. 4.
    A. V. Oppenheim, “Generalized Superposition,” Inform. Contr., Vol. 11, pp. 528–536, Nov. — Dec. 1967.MATHCrossRefGoogle Scholar
  5. 5.
    A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Jr., “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE, Vol. 56, pp. 1264–1291, Aug. 1968.CrossRefGoogle Scholar
  6. 6.
    J. Prabhakar and S. C. Gupta, “Separation of Rayleigh and Poisson Density Functions Through Homomorphie Filtering,” Nat. Elec. Conf., pp. 605–610, Dec. 1970.Google Scholar
  7. 7.
    T. Cohen, “Source—Depth Determination Using Spectral, Pseudo—Autocorrelation and Cepstral Analysis,” Geophys. J. Roy. Astron. Soc., Vol. 20, pp. 223–231, 1970.Google Scholar
  8. 8.
    T. Ulrych, “Application of Homomorphie Deconvolution to Seismology,” Geophysics, Vol. 36, No. 4, pp. 650–660, Aug. 1971.CrossRefGoogle Scholar
  9. 9.
    S. Senmoto and D. G. Childers, “Decomposition of a Composite Signal of Unknown Wavelets in Noise,” in Int. Conf. Comm. (ICC), 71C 28—COM, Montreal, Canada, pp. 514–519, 1971.Google Scholar
  10. 10.
    R. Kemerait and D. G. Childers, “Signal Detection and Extraction by Cepstrum Techniques,” IEEE Trans. on Inform. Theory, Vol. IT-18, pp. 745–759, Nov 1972.Google Scholar
  11. 11.
    T. Ulrych, O. G. Jensen, R. M. Ellis, and P. G. Sommervile, “Homomorphie Deconvolution of Some Teleseismic Events,” Bull. Seismological Soc. Amer., Vol. 62, No. 5, pp. 1253–1265, Mar. 1972.Google Scholar
  12. 12.
    P. Buhl, P. L. Stoffa, and G. M. Bryan, “The Application of Homomorphie — Part II; Real Data,” Geophyiscs, Deconvolution to Shallow Water Marine Seismology Vol. 39, No. 4, pp. 417–426, Aug. 1974.Google Scholar
  13. 13.
    P. L. Stoffa, P. Buhl, and G. M. Bryan, “The Application of Homomorphie Deconvolution to Shallow Water Marine Seismology — Part I: Models,” Geophysics, Vol. 39, No. 4, pp. 401–416, Aug. 1974.CrossRefGoogle Scholar
  14. 14.
    J. F. Bohme, “The Cepstrum as a Generalized Function,” IEEE Trans. on Inform. Theory, Vol. IT-20, pp. 650–653, Sept. 1974.CrossRefGoogle Scholar
  15. 15.
    J. C. Hassab, “Time Delay Processing Near the Ocean Surface,” Journal of Sound Vibration, Vol. 35, (4), PP. 489–501, 1974.Google Scholar
  16. 16.
    J. C. Hassab, “On the Convergence Interval of the Power Cepstrum,” IEEE Transaction on Information Theory, Vol. IT-20, No. 1, pp. 111–112, 1974.CrossRefGoogle Scholar
  17. 17.
    P. O. Fjell, Decomposition of Signal Arrival Times Due to Multipath Conditions in Shallow Waters, Norwegian Defense Research Establishment Report N-U-319, 1975.Google Scholar
  18. 18.
    R. Rom, “On the Cepstrum of Two—Dimensional Functions,” IEEE Trans. on Inform. Theory, pp. 214–217, Mar. 1975.Google Scholar
  19. 19.
    T. G. Stockham, Jr., T. M. Cannon, R. B. Ingebretsen, “Blind Deconvolution Through Digital Signal Processing,” Proc. IEEE, vol. 63, pp. 678–692, Apr. 1975.CrossRefGoogle Scholar
  20. 20.
    H. Schwazlander, B. Silverman, R. Hohensee, “Use of the Cepstrum for Processing Multipath Signals — II,” Rome Air Development Center TR-75–117, May 1975.Google Scholar
  21. 21.
    R. G. Smith, “Cepstrum Discrimination Functions,” IEEE Trans. Inform. Theory, Vol. IT-21, pp. 332–334, May 1975.CrossRefGoogle Scholar
  22. 22.
    J. C. Hassab and R. E. Boucher, “Analysis of Signal Extraction, Echo Detection and Removal by Complex Cepstrum in Presence of Distortion and Noise,” Journal of Sound and Vibration, Vol. 40, No. 3, pp. 321–335, 1975.CrossRefGoogle Scholar
  23. 23.
    J. C. Hassab, “Network Function Theory and Complex Cepstrum,” Journal of Sound and Vibration, Vol. 41, No. 1, 1975.CrossRefGoogle Scholar
  24. 24.
    D. P. Skinner and D. G. Childers, “Real—time Composite Signal Decomposition,” IEEE Trans. on Acoust., Speech, and Signal Processing, Vol. ASSP-24, pp. 267–270, June 1976.CrossRefGoogle Scholar
  25. 25.
    J. C. Hassab, “The Probability Density Functions at the Output of the Complex Cepstrum,” Proceedings IEEE International Symposium on Information Theory, Ronneby, Sweeden, June 1976.Google Scholar
  26. 26.
    J. C. Hassab, R. E. Boucher, “A Probalistic Analysis of Time Delay Extraction in Stationary Gaussian Noise,” IEEE Transactions on Information Theory, Vol. IT22, pp. 444–454, Jul. 1976.CrossRefGoogle Scholar
  27. 27.
    J. K. Hammond and L. G. Peardon, “The Power Cepstrum Applied to Multi—Peaked Wavelets,” J. Sound and Vibration, Vol. 48, pp. 537–541, 1976.CrossRefGoogle Scholar
  28. 28.
    J. C. Hassab, “Further Statistical Measures in the Cepstrum,” IEEE Transactions on Information Theory, Vol. IT23, No. 4, pp. 540–544, July 1977.CrossRefGoogle Scholar
  29. 29.
    L. B. Poche, Jr., “Complex Cepstrum Processing of Digitized Transient Calibration Data for Removal of Echos,” Naval Research Lab Report 8143, Sept. 1977.Google Scholar
  30. 30.
    D. G. Childers, D. P. Skinner, and R. C. Kemerait, “The Cepstrum; a Guide to Processing,” Proc. IEEE. Vol. 65, No. 10. pp. 1428–1443, Oct. 1977.CrossRefGoogle Scholar
  31. 31.
    M. H. Loew, R. Shankar, A. Mucciardi, “Experiments with Echo Detection in the Presence of Noise Using the Power Cepstrum and a Modification,” IEEE Int’l Conf. on Acoust., Speech, and Sig. Processing, pp. 307–310, 1977.Google Scholar
  32. 32.
    J. M. Tribolet, “Seismic Applications of Homomorphie Signal Processing,” Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1977.Google Scholar
  33. 33.
    J. C. Hassab, “The Smoothing of ‘Zero’ Singularities in the Cepstrum,” Journal of Sound and Vibration, Vol. 57, No. 2, pp. 299–301, 1978.MATHCrossRefGoogle Scholar
  34. 34.
    J. C. Hassab and R. E. Boucher, “Improved Cepstrum Performance Through Windowing of Log Spectrum,” Journal’ of Sound and Vibration, Vol. 58, No. 4, pp. 597–598, 1978.CrossRefGoogle Scholar
  35. 35.
    J. C. Hassab and R. E. Boucher, “Improved Time Delay Estimation Given a Composite Signal in Noise,” Proceedings IEEE Int’l Conference on Communications, pp. 1661–1667, Toronto, Canada, 1978.Google Scholar
  36. 36.
    J. C. Hassab, “Homomorphie Deconvolution in Reverberant and Distortional Channels: An Analysis,” Journal of Sound and Vibration, Vol. 58 (2), pp. 215–231, 1978.CrossRefGoogle Scholar
  37. 37.
    J. C. Hassab and R. E. Boucher, “Further Comments on Windowing in the Power Cepstrum,” Proceedings of the IEEE, Vol. 66, No. 10, pp. 1290–1291, October 1978.CrossRefGoogle Scholar
  38. 38.
    J. C. Hassab and R. E. Boucher, “The Effect of Dispersive and Non—Dispersive Channels on Time Delay Estimation,” Journal of Sound Vibration, Vol. 66 (2), pp. 247–253, 1979.MATHCrossRefGoogle Scholar

II. Single Path With Multiple Sensing Points Signal Processing

  1. 1.
    V. H. MacDonald and P. M. Schultheiss, “Optimum Passive Bearing Estimation,” J. Acoust. Soc. Am., 46, 37–43, 1969.CrossRefGoogle Scholar
  2. 2.
    H. J. Hannan and P. J. Thomson, “The Estimation of Coherence and Group Delay,” Biometrika, 58, 469–481, 1971.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Melvin J. Hinich and Paul Shaman, “Parameter Estimation for an R—Dimensional Plane Wave Observed with Additive Independent Gaussian Errors,” The Annals of Mathematical Statistics, Vol. 43, No. 1, 153–169, 1972.MATHCrossRefGoogle Scholar
  4. 4.
    W. R. Hahn and S. A. Tretter, “Optimum Processing for Delay—Vector Estimation in Passive Signal Arrays,” IEEE Trans. Inf. Theory IT-19, 608–614, September 1973.CrossRefGoogle Scholar
  5. 5.
    C. N. Pryor, “Minimum Detectable Signal for Spectrum Analyzer Systems,” Signal Processing, Academic Press London and New York, 1973.Google Scholar
  6. 6.
    E. J. Hannan and P. J. Thomson, “Estimating Group Delay,” Biometrika, Vol. 60, No. 2 pp. 241–253, 1973.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    B. V. Hamon and E. J. Hannan, “Spectral Estimation of Time Delay for Dispersive and Non—Dispersive Systems,” Appl. Statist., Vol. 23, No. 2, pp. 134–14CrossRefGoogle Scholar
  8. 8.
    C. H. Knapp and G. C. Carter, “The Generalized Correlation Method for Estimation of Time Delay,” IEEE Trans. Acoust., Speech, Signal Process., ASSP-24, pp. 320–327, Aug. 1976CrossRefGoogle Scholar
  9. 9.
    C. H. Knapp and G. C. Carter, “Estimation of Time Delay in the Presence of Source or Receiver Motion,” J. Acoust. Soc. Am., 61, 1545–1549, 1977.CrossRefGoogle Scholar
  10. 10.
    R. Kirlin, “Augmenting the Maximum Likelihood Delay Estimator to Give Maximum Likelihood Direction,” IEEE, Vol. ASSP-26, No. 1, February 1978.Google Scholar
  11. 11.
    Y. T. Chan, R. V. Hattin and J. B. Plant, “The Least Squares Estimation of Time Delay and Its Use in Signal Detection”, IEEE Trans Acoust., Speech Signal Processing, Vol. ASSP-26, No. 3, pp. 217–222, 1978.CrossRefGoogle Scholar
  12. 12.
    J. T. Patzewitsch, M. D. Srinath, and C. I. Black, “Nearfield Performance of Passive Correlation Processing Sonars,” J. Acoust. Soc. Am., Vol. 64, No. 5, pp. 1412–1423, 1978.CrossRefGoogle Scholar
  13. 13.
    R. Kirlin, “Improvement of Delay Measurements from Sonar Arrays via Sequential State Estimation,” Univ. of Wyoming, Laramie, WY, May 1979.Google Scholar
  14. 14.
    J. C. Hassab and R. E. Boucher, “Optimum Estimation of Time Delay by a Generalized Correlator,” IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 27, No. 4, pp. 373–380, August 1979.CrossRefGoogle Scholar
  15. 15.
    J. C. Hassab and R. E. Boucher, “A Quantitative Study of Optimum and Sub-Optimum Filters in the Generalized Correlator,” ICASS P-79 Conference Record, Catalog No. 79 CH 1379–7 ASSP, IEEE Press, Piscataway, NJ. pp. 124–127, 1979.Google Scholar
  16. 16.
    W. B. Adams, J. P. Kuhn, and W. P. Whyland, “Correlator Compensation Requirements for Passive Time Delay Estimation with Moving Source or Receivers,” IEEE Trans, Acoust,. Speech, Signal Processing, Vol. ASSP-28, No. 2, pp. 158–168, 1980.CrossRefGoogle Scholar
  17. 17.
    J. C. Hassab, R. E. Boucher, “An Experimental Comparison of Optimum and Sub—Optimum Filters Effectiveness in the Generalized Correlator,” Journal of Sound and Vibration, Vol. 76, pp. 117–128, May 1981.CrossRefGoogle Scholar
  18. 18.
    G. L. Sackman and S. C. Shelef, “The Use of Phase Difference Trace Functions for Bearing Estimation with Small Circular Arrays,” IEEE Transactions on Acoust., Speech, and Signal Processing, Vol. ASSP-29, No. 3, pp. 501–507, June 1981.CrossRefGoogle Scholar
  19. 19.
    R. L. Kirlin, D. F. Moore and R. F. Kubicheck, “Improvement of Delay Measurements from Sonar Arrays Via Sequential State Estimation,” IEEE Transactions on Acoust., Speech and Signal Processing, Vol. ASSP-29, No. 3, PP. 514–519, June 1981.CrossRefGoogle Scholar
  20. 20.
    D. M. Etter and S. D. Stearns, “Adaptive Estimation of Time Delays in Sampled Data Systems,” IEEE Transactions on Acoust., Speech and Signal Processing, Vol. ASSP-29, No. 3, PP. 582–587, June 1981.CrossRefGoogle Scholar
  21. 21.
    R. E. Boucher, J. C. Hassab, “Analysis of Discrete Implementation of Generalized Cross Correlator,” IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. 29, No. 3, Pp. 609–611, June 1981.CrossRefGoogle Scholar
  22. 22.
    J. C. Hassab, R. E. Boucher, “Performance of the Generalized Cross Correlator in the Presence of a Strong Spectral Peak in the Signal,” IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. 29, No. 3, pp. 549–555, June 1981.CrossRefGoogle Scholar
  23. 23.
    J. C. Hassab, “Signal Processing in Difficult Channels”, in Intl Symposium on Underwater Acoustics, Tel Aviv, Israel, June 15–18, 1981.Google Scholar
  24. 24.
    J. P. Ianniello, “Time Delay Estimation via Cross-Correlation in the Presence of Large Estimation Errors,” Oceans 81 Conference Record, Vol. 2, pp. 998–1001, Sept. 1981.Google Scholar
  25. 25.
    J. C. Hassab, “Generalized Window Synthesis for Optimum Time Delay Detection,” J. Acoustical Society of America, Supp. 1, Vol. 70, pp. 516, Dec 1981.CrossRefGoogle Scholar

III. Estimation of Source Location and Velocity

  1. 1.
    D. J. Murphy, “Noisy Bearings-Only Target Motion Analysis,” Ph.D. thesis, Department of Electrical Engineering, Northeastern Univ., 1970.Google Scholar
  2. 2.
    Per Heimdal and Finn Bryn, Passive Ranging Techniques, Signal Processing, edited by J. W. Griffiths, P. L. Stocklin, and C. Van Sehoonveld Academic Press London and New York, 1973.Google Scholar
  3. 3.
    Norman L. Owsley, A Recent Trend in Adaptive Spatial Processing for Sensor Arrays: Constrained Adaptation, Signal Processing, Academic Press London and New York, 1973.Google Scholar
  4. 4.
    Loren W. Nolte, Adaptive Processing: Time varying Parameters, Signal Processing, edited by J. W. Griffiths, P. L. Stocklin, and C. Van Schoonveld, Academic Press London and New York, 1973.Google Scholar
  5. 5.
    W. J. Bangs and P. M. Schultheiss, “Space—Time Processing for Optimal Parameter Estimation,” in Signal Processing, edited by J. W. Griffiths, P. L. Stocklin, and C. Van Schoonveld (Academic, New York), 1973.Google Scholar
  6. 6.
    J. C. Hassab and D. Watson, “Positioning and Navigation Under the Sea: An Acoustic Method,” Proceedings IEEE International Conference on Engineering in Ocean Environment, pp. 145–149, August 1974.Google Scholar
  7. 7.
    B. Widrow et al., Adaptive Noise Cancelling: Principles and Applications,: Proc. IEEE, Vol. 63. pp. 1692–1716, Dec. 1975.CrossRefGoogle Scholar
  8. 8.
    W. R. Hahn, “Optimum Signal Processing for Passive Sonar Range and Bearing Estimation,” J. Acoust. Soc. Amer., Vol. 58, No. 1, pp. 201–207, 1975.CrossRefGoogle Scholar
  9. 9.
    J. C. Hassab, “Passive Tracking of a Moving Source by Single Observer in Shallow Water,” Journal of Sound and Vibration, Vol. 44, No. 1, pp. 127–145, 1975.CrossRefGoogle Scholar
  10. 10.
    N. H. Gholson and R. L. Moose, “Maneuvering Target Tracking Using Adaptive State Estimation,” IEEE Trans. Aerosp. Electron. Syst., Vol. AES-13, May 1977.Google Scholar
  11. 11.
    G. C. Carter, “Variance Bounds for Passively Locating an Acoustic Source with a Symmetric Line Array,” J. Acoust. Soc. AM 62, 922–926, (1977).CrossRefGoogle Scholar
  12. 12.
    J. S. Davis and K. F. Gong, “Adaptive Filtering via Maximization of Residual Joint Density Functions,” Proc. IEEE Conf. on Decision and Control, New Orleans, LA, December 1977.Google Scholar
  13. 13.
    J. Billingsley, A Comparison of the Source Location Techniques of the Acoustic Telescope and Polar Correlation, Journal of Sound and Vibration 61 (3), 419–425, 1978.CrossRefGoogle Scholar
  14. 14.
    J. M. F. Moura and A. B. Baggeroer, “Passive Systems Theory with Narrow-Band and Linear Constraints: Part I-Spatial Diversity,” IEEE J. Oceanic Eng., Vol 0E-3, P. 5, 1978.CrossRefGoogle Scholar
  15. 15.
    P. M. Shultheiss and E. Weinstein, “Passive Localization of a Moving Source,” Eascon 78 Conference Record, No. CH1352, pp. 258–266, IEEE, Piscataway, NJ, 1978.Google Scholar
  16. 16.
    R. Moose, H. F. Vanlandingham and D. H. McCabe, “Modeling and Estimation of Tracking Maneuvering Targets,” IEEE Trans, Aerosp. Electron Syst., Vol 15,P.P. 448–456, 1979.CrossRefGoogle Scholar
  17. 17.
    P. M. Schultheiss, “Locating a Passive Source with Array Measurements: A Summary of Results”, ICASSP-79 Conference Record, Catalog No. 79CH1379–7ASSP, IEEE Press, Piscataway, NJ, pp. 967–970, 1979.Google Scholar
  18. 18.
    J. M. F. Moura, “Passive Systems Theory with Narrow-Band and Linear Constraints: Part II-Temporal Diversity,” IEEE J. Oceanic Eng., Vol. 0E-4, p. 19, 1979.CrossRefGoogle Scholar
  19. 19.
    J. M. F. Moura, “Passive Systems Theory with Narrow-Band and Linear Constraints: Part III-Spatial/Temporal Diversity,” IEEE J. Oceanic Eng., Vol. 0E-4, p. 113, 1979.CrossRefGoogle Scholar
  20. 20.
    J. C. Hassab and R. E. Boucher, “Passive Ranging Estimation from an Array of Sensors,” Journal of Sound and Vibration, Vol. 67 (1), 1979.CrossRefGoogle Scholar
  21. 21.
    E. J. Hilliard, Jr. and R. F. Pinkos, “An Analysis of Triangulation Ranging Using Beta Density Angular Errors,” J. Acoust. Soc. Amer., Vol. 65, pp. 1218–1228, May 1979.CrossRefGoogle Scholar
  22. 22.
    B. W. Guimond, “Joint Estimation and Adaptive Identification for Systems with Unknown Inputs,” 13th Asilomar Conf. on Circuits, Systems, and Computers, Monterey, CA, November 1979.Google Scholar
  23. 23.
    G. C. Carter and P. B. Abraham, “Estimation of Source Motion From Time Delay and Time Compression Measurements,” J. Acoust. Soc. Amer., Vol 67, No. 3, pp. 830–832, 1980.CrossRefGoogle Scholar
  24. 24.
    J. C. Hassab, B. W. Guimond, and S. C. Nardone, “A Structure for the Combined Reduction of Bias and Variance in Estimating Source Location and Motion,” Int. Conf. on Acoust. Speech and Signal Processing, Denver, CO, April 1980.Google Scholar
  25. 25.
    Peter M. Schultheiss, John P. Ianniello, “Optimum Range and Bearing Estimation with Randomly Perturbed Arrays,” J. Acoust. Soc. AM 68 (1), July 1980.CrossRefGoogle Scholar
  26. 26.
    N. L. Owsley, Model Decomposition of Data Adaptive Spectral Estimates, NUSC Technical Document 6479,p.p. 27–29, May 1981.Google Scholar
  27. 27.
    P. M. Schultheiss and E. Weinstein, “Lower Bounds on the Localization Errors of a Moving Source Observed by a Passive Array,” IEEE Transactions on Acoust., Speech, and Signal Processing, Vol. ASSP-29, No. 3, pp. 600–607, June 1981.CrossRefGoogle Scholar
  28. 28.
    D. H. McCabe and R. L. Moose, “Passive Source Tracking Using Sonar Time Delay Data,” IEEE Transactions on Acoust., Speech, and Signal Processing, Vol. ASSP-29, No. 3, pp. 614–617, June 1981.CrossRefGoogle Scholar
  29. 29.
    J. C. Hassab, B. Guimond, S. Nardone, “Estimation of Location and Motion Parameters of a Moving Source Observed from a Linear Array,” J. Acoustical Society of America, Vol. 70, No. 4, pp. 1054–1061, Oct 1981.CrossRefGoogle Scholar
  30. 30.
    M. J. Hinich and M. C. Bloom, “Statistical Approach to Passive Target Tracking,” J. Acoust. Soc. Am,. Vol. 69.,P.P. 738–743, 1981.CrossRefGoogle Scholar
  31. 31.
    J. C. Hassab, B. Guimond, S. Nardone, Comments on Inherent Bias in Wavefront Curvature Ranging, IEEE Transactions on Acoustic Speech and Signal Processing, Vol. ASSP 30, No. 1, p. 99, Feb 1982.CrossRefGoogle Scholar

IV. General References

  1. 1.
    E. J. Hannan, Mulitple Time Series, New York: Wiley 1970.CrossRefGoogle Scholar
  2. 2.
    C. H. Chen, Statistical Pattern Recognition, Hayden Book Company, Inc, Rochelle Park, New Jersey, 1973.Google Scholar
  3. 3.
    J. W. R. Griffiths, P. L. Stocklin and C. Van Schooneweld, Editors, Signal Processing, Academic Press London and New York, 1973.Google Scholar
  4. 4.
    J. C. Hassab, Editor, “Proceedings of the Time Delay Estimation and Applications Conference,” Vol. 1, DDC No. 9312068, Naval Postgraduate School, Monterey, CA July 1978.Google Scholar
  5. 5.
    J. C. Hassab, “Problems, Obstacles and Approaches in Naval Signal Analysis: A Sampling,” presented to the U.S. National Academy of Sciences Panel on Applied Mathematics Research Alternatives for the Navy, Washington, DC, November 2, 1979.Google Scholar
  6. 6.
    D. G. Childers and A. E. Burling, Digital Filtering and Signal Processing, St. Paul, MN: West Publishing, 1975.Google Scholar
  7. 7.
    G. C. Carter, Editor, IEEE Special Issue on Time Delay Estimation, IEEE Trans. Acoustics, Speech, and Signal Processing, Vol 29, No. 3, June 1981.Google Scholar
  8. 8.
    C. H. Chen, Editor, Digital Waveform Processing and Recognition, CRC Press, Inc, Boca Raton, Florida, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • J. C. Hassab
    • 1
  1. 1.Naval Underwater Systems CenterNewportUSA

Personalised recommendations