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Application of the Maximum Entropy method to sonar signal processing

Application of the Maximum Entropy method to sonar signal processing. R. Lee Culver, H. John Camin, Jeffrey A. Ballard, Colin W. Jemmott, and Leon H. Sibul Applied Research Laboratory and Graduate Program in Acoustics The Pennsylvania State University, P.O. Box 30 State College, PA 16804

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Application of the Maximum Entropy method to sonar signal processing

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  1. Application of the Maximum Entropy method to sonar signal processing R. Lee Culver, H. John Camin, Jeffrey A. Ballard, Colin W. Jemmott, and Leon H. Sibul Applied Research Laboratory and Graduate Program in Acoustics The Pennsylvania State University, P.O. Box 30 State College, PA 16804 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering Saratoga Springs, NY, July 8-13, 2007 Work supported by Office of Naval Research MaxEnt 2007

  2. Outline • Sonar application description • Domain of existing solutions • A new Estimator-Correlator detector that makes use of the Maximum Entropy principal • An example: the 1996 Strait of Gibraltar Acoustic Monitoring Experiment (SGAME) • Planned extensions MaxEnt 2007

  3. Problem description time-frequency plot for a single beam detected lines successive FFTs of one beam Increasing time Fan of narrow beams Horizontal line array (plan view) frequency Problem: Many signals are detected, but what and where are the sources? MaxEnt 2007

  4. Matched Field Processing surface vertical line array (side view) acoustic rays source bottom MaxEnt 2007

  5. . . . . . . Matched field processing Sensors F F T 1 2 . . . J Bucker, H. P. (1976). “Use of calculated sound fields and matched-field detection to location sound sources in shallow water,” J. Acoust. Soc. Am. 59 (2), pp. 368-373. MaxEnt 2007

  6. Matched field processing MaxEnt 2007

  7. Matched field processing Depth, yd Bucker, H. P. (1976). J. Acoust. Soc. Am. 59 (2), pp. 368-373. Range, kyd MaxEnt 2007

  8. Optimum Uncertain Field Processor Richardson, A. M. and L. W. Nolte (1991). “A posteriori probability source localization in an uncertain sound speed, deep ocean environment,” J. Acoust. Soc. Am. 89, pp. 2280-2284. MaxEnt 2007

  9. Optimum Uncertain Field Processor MaxEnt 2007

  10. Optimum Uncertain Field Processor MaxEnt 2007

  11. Optimum Uncertain Field Processor • The optimum uncertain field processor cannot be applied to our problem for two reason. • Our array is horizontal, not vertical. With no vertical aperture, vertical structure (multipath) in the sound field is not observed. • The noise field is not necessarily Gaussian (See E. J. Wegman, S.C. Schwartz and J. B. Thomas eds., Topics in Non-Gaussian Signal Processing, Springer-Verlag, New York, 1988.). • Therefore, we take a different approach to obtain a processor that can be applied to our problem. • Use a propagation model to predict signal parameter statistics • Look for statistical clues in the observation (received signal) J. A. Ballard (2007). “The Estimated Signal Parameter Detector”, M.S Thesis (The Pennsylvania State University, State College, PA). MaxEnt 2007

  12. The Estimated Ocean Detector The underlying assumption is that sources at different locations will generate different received statistics Source near the surface pdf of signal from near-surface source (H1) p1(r) Receive array Source near the bottom pdf of signal from near-bottom source (H2) p2(r) MaxEnt 2007

  13. The Estimated Ocean Detector S.C. Schwartz, “The Estimator-Correlator for Discrete-Time Problems,” IEEE Trans. On Information Theory, Vol. 23, No. 1, January 1977, pp. 93-100. MaxEnt 2007

  14. The Estimated Ocean Detector MaxEnt 2007

  15. The Estimated Ocean Detector Bayes’ rule MaxEnt 2007

  16. The Estimated Ocean Detector MaxEnt 2007

  17. The Estimated Ocean Detector MaxEnt 2007

  18. The Estimated Ocean Detector Calculate signal parameter pdf Conditional Moment Functions H1 - - Calculate signal parameter pdf Received Signal, r H2 MaxEnt 2007

  19. The Estimated Ocean Detector J. A. Ballard (2007). “The Estimated Signal Parameter Detector”, M.S Thesis (The Pennsylvania State University, State College, PA). MaxEnt 2007

  20. The Estimated Ocean Detector MaxEnt 2007

  21. The Estimated Ocean Detector MaxEnt 2007

  22. p2(A) p1(A) The Estimated Ocean Detector performance improves MaxEnt 2007

  23. Applying the MaxEnt Method • We use the MaxEnt method in two ways: • Obtain by fitting an exponential (or MaxEnt) pdf to noise samples that do not contain signal, e.g. from another beam or at another frequency (or both). • Use an acoustic propagation model and Monte Carlo simulation to produce samples of A under H1 and H2, and use MaxEnt to estimate the prior pdfs p1(A) and p2(A). • In both cases, we compute sample moments from the data and apply the gradient method developed by Mohammad-Djarari (1991). (I think I need to spend some more time on this part of the approach). MaxEnt 2007

  24. P7 P6 P5 P4 P3 P2 P1 1996 Strait of Gibraltar Acoustic Measurement Experiment (SGAME) • Warm, fresh surface • layer of Atlantic • water moving east • over salty, cool layer of • Mediterranean water • moving west. • Strong internal tide • East-moving tidal bores • released after high tide. Tx = projector Rx = hydrophone Pn = groupings of CTD drops. • Worcester, Send, Curnuelle and Tiemann (1997), in Shallow-Water Acoustics, Bejing, China. • Tiemann, Worcester and Cornuelle (2001), JASA 109 and 110 (2 kHz data only). MaxEnt 2007

  25. 1996 Strait of Gibraltar Acoustic Measurement Experiment (SGAME) hydrophones range, km projector 12 Acoustic propagation paths depth, m. 1000 MaxEnt 2007

  26. 1996 Strait of Gibraltar Acoustic Measurement Experiment (SGAME) CTD drop times relative to tidal height CTD (conductivity and temperature vs. depth) measurements spanned the tidal cycle. P1, P2, etc. correspond to positions shown on Slide 3. Height, m. yearday 1996 Height, m. yearday 1996 MaxEnt 2007

  27. 1996 Strait of Gibraltar Acoustic Measurement Experiment (SGAME) Propagation loss predicted using RAM Collins, M. (1993). “A split-step Padá solution for the parabolic equation method,” J. Acoust. Soc. Am,93, pp. 1736-1742. MaxEnt 2007

  28. Applying the MaxEnt Method MaxEnt 2007

  29. Applying the MaxEnt Method Mohammad-Djafari, A. (1992). “Maximum Likelihood Estimate of the Lagrange parameters of the Maximum Entropy Distributions,” in Maximum Entropy and Bayesian Methods, Proc. 11th International Workshop on Maximum Entropy and Bayesian Methods of Statistical Analysis, Ed. C. R. Smith, G. J. Erickson, and P. O. Neudorfer (Kluwer Academic, Dordrecht, NL). MaxEnt 2007

  30. Applying the MaxEnt Method * Histogram of measured received pressure MaxEnt pdf fit to received pressure MaxEnt pdf fit to RAM predictions Relative occurrence Received pressure, dB re 1µPa MaxEnt 2007

  31. Applying the MaxEnt Method * Histogram of measured received pressure MaxEnt pdf fit to received pressure MaxEnt pdf fit to RAM predictions MaxEnt 2007

  32. Summary • We have used an Estimator-Correlator structure to develop a Maximum Likelihood detector that can accept any exponential class noise pdf (not just a Gaussian). • The MaxEnt method has been used to obtain exponential class pdfs. Example shown for 1996 Strait of Gibraltar Acoustic Monitoring Experiment (SGAME). • We are learning about the MaxEnt method. MaxEnt 2007

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