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Statistical Methods in Sonar
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I. Introductory Remarks.- 1. Some Definitions.- 2. The Sonar Model.- 3. Sonar and Radar.- 4. Statistical Problems of Sonar.- II. Procedural Fundamentals of Experimental Research in Sonar.- 5. Principal Tasks of Experimental Research.- 6. The Structural Diagram of Quantitative Experimental Research.- 7. Discrimination Functional of the Probability Characteristic and Its Statistical Estimate.- 8. The Base Model.- 9. Interpretation of Experimental Results.- 10. Objects of Experimental Research in Sonar.- III. Probability Models of Hydroacoustic Signals.- 11. Varieties of Models.- 12. A Priori Information and Probability Models.- 13. Methods for Describing Hydroacoustic Signals in Terms of Probability.- 14. Classification of Hydroacoustic Signals.- 15. Canonical Models.- 16. Parametrical Models.- 17. Additive-Multiplicative Constructive Models.- 18. Models in the Form of Oscillations with Random Amplitude and Phase.- 19. Complex Representation of Signals.- IV. The Emitted Signals.- 20. Signal Classification.- 21. Complex Representation of Emitted Signals.- 22. Ambiguity Function and Diagrams.- 23. Signals with Sinusoidal Occupation.- 24. Frequency-Modulating Signals.- 25. Noiselike Signals.- V. Echo Signals.- 26. Classification of Objects of Research and the Conditions under Which They Are Observed.- 27. Representation of Echo Signals and Their Probability Characteristics.- 28. The Model of an Echo Signal of Known Form with Constant Lag and Change in Time Scale.- 29. Echo Signal with Fluctuating Amplitude.- 30. Echo Signal Consisting of an Additive Mixture of a Signal of Known Form and a Random Component.- 31. Echo Signal with Random Amplitude Modulation.- 32. Echo Signal with Random Phase Modulation.- 33. Echo Signal with Random Frequency Modulation.- 34. Model of an Echo Signal in the Form of a Sum of Elementary Signals.- VI. Marine Reverberation.- 35. Classification of Reverberatory Signals.- 36. Discrete Canonical Model of Reverberation.- 37. Complex Representations.- 38. Characteristics of the Random Parameters of Elementary Scattered Signals.- 39. Average Value of Reverberation.- 40. Autocorrelation Function for the Complex Envelope of Reverberation.- 41. Energy Spectrum of the Complex Envelope of Reverberation.- 42. Evaluation of the Frequency-Time Cross-Correlation Function for the Complex Envelopes of the Emitted Signal and Reverberation.- 43. Generalization for the Case of Elementary Scattered Signals of Different Forms.- 44. Space-Time Correlation of Reverberation when Wideband Signals Are Emitted.- 45. One-Dimensional Semi-invariants.- 46. Probability Distributions for Instantaneous Values of Reverberation and Its Envelope.- VII. Problems of Detecting Echo Signals in the Presence of Interference.- 47. Specific Features of Detecting Echo Signals in Sonar.- 48. Probability Characteristics of Detection.- 49. Typical Probability Distributions of the Output Effect.- 50. Incoherent Detection of Simple Echo Signals with a Linear Detector.- 51. Incoherent Detection of a Noiselike Echo Signal with Quadratic Detection and Smoothing ("Energy Detection").- 52. Coherent Detection of a Noiselike Echo Signal Using Cross-Correlation Processing.- 53. The Effect of Reverberation Interference on Echo Signal Detection.- 54. Detection with Multichannel Systems, and Discussion of Results.- VIII. Elements of the Theory of Statistical Measurement.- 55. Basic Stages of Statistical Measurements.- 56. Statistical Measurement Errors.- 57. Formation of a Statistical Estimate.- 58. Statistical Measurement Errors of the Characteristics of Nonstationary Homogeneous Random Processes.- 59. Optimization of the Parameters of the Statistical Measuring System.- 60. Adaptive Optimization.- IX. Inverse Probability Problems in Sonar.- 61. Direct and Inverse Problems.- 62. Correctness Conditions.- 63. Determination of the Probability Density for the Rates of Movement of Scatterers.- 64. Determination of the Spectrum of the Fluctuations in the Rate of Movement of Scatterers.- 65. Determination of the Relative Level of Coherent Scattering.- 66. Determination of the Average Number of Scatterers.- 67. Determination of the Frequency Properties of Scatterers.- 68. Determination of the Spatial Distribution of Scatterers.- Conclusion.

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