Statistical Methods in Sonar

I. Introductory Remarks.- x1. Some Definitions.- x2. The Sonar Model.- x3. Sonar and Radar.- x4. Statistical Problems of Sonar.- II. Procedural Fundamentals of Experimental Research in Sonar.- x5. Principal Tasks of Experimental Research.- x6. The Structural Diagram of Quantitative Experimental Research.- x7. Discrimination Functional of the Probability Characteristic and Its Statistical Estimate.- x8. The Base Model.- x9. Interpretation of Experimental Results.- x10. Objects of Experimental Research in Sonar.- III. Probability Models of Hydroacoustic Signals.- x11. Varieties of Models.- x12. A Priori Information and Probability Models.- x13. Methods for Describing Hydroacoustic Signals in Terms of Probability.- x14. Classification of Hydroacoustic Signals.- x15. Canonical Models.- x16. Parametrical Models.- x17. Additive-Multiplicative Constructive Models.- x18. Models in the Form of Oscillations with Random Amplitude and Phase.- x19. Complex Representation of Signals.- IV. The Emitted Signals.- x20. Signal Classification.- x21. Complex Representation of Emitted Signals.- x22. Ambiguity Function and Diagrams.- x23. Signals with Sinusoidal Occupation.- x24. Frequency-Modulating Signals.- x25. Noiselike Signals.- V. Echo Signals.- x26. Classification of Objects of Research and the Conditions under Which They Are Observed.- x27. Representation of Echo Signals and Their Probability Characteristics.- x28. The Model of an Echo Signal of Known Form with Constant Lag and Change in Time Scale.- x29. Echo Signal with Fluctuating Amplitude.- x30. Echo Signal Consisting of an Additive Mixture of a Signal of Known Form and a Random Component.- x31. Echo Signal with Random Amplitude Modulation.- x32. Echo Signal with Random Phase Modulation.- x33. Echo Signal with Random Frequency Modulation.- x34. Model of an Echo Signal in the Form of a Sum of Elementary Signals.- VI. Marine Reverberation.- x35. Classification of Reverberatory Signals.- x36. Discrete Canonical Model of Reverberation.- x37. Complex Representations.- x38. Characteristics of the Random Parameters of Elementary Scattered Signals.- x39. Average Value of Reverberation.- x40. Autocorrelation Function for the Complex Envelope of Reverberation.- x41. Energy Spectrum of the Complex Envelope of Reverberation.- x42. Evaluation of the Frequency-Time Cross-Correlation Function for the Complex Envelopes of the Emitted Signal and Reverberation.- x43. Generalization for the Case of Elementary Scattered Signals of Different Forms.- x44. Space-Time Correlation of Reverberation when Wideband Signals Are Emitted.- x45. One-Dimensional Semi-invariants.- x46. Probability Distributions for Instantaneous Values of Reverberation and Its Envelope.- VII. Problems of Detecting Echo Signals in the Presence of Interference.- x47. Specific Features of Detecting Echo Signals in Sonar.- x48. Probability Characteristics of Detection.- x49. Typical Probability Distributions of the Output Effect.- x50. Incoherent Detection of Simple Echo Signals with a Linear Detector.- x51. Incoherent Detection of a Noiselike Echo Signal with Quadratic Detection and Smoothing ("Energy Detection").- x52. Coherent Detection of a Noiselike Echo Signal Using Cross-Correlation Processing.- x53. The Effect of Reverberation Interference on Echo Signal Detection.- x54. Detection with Multichannel Systems, and Discussion of Results.- VIII. Elements of the Theory of Statistical Measurement.- x55. Basic Stages of Statistical Measurements.- x56. Statistical Measurement Errors.- x57. Formation of a Statistical Estimate.- x58. Statistical Measurement Errors of the Characteristics of Nonstationary Homogeneous Random Processes.- x59. Optimization of the Parameters of the Statistical Measuring System.- x60. Adaptive Optimization.- IX. Inverse Probability Problems in Sonar.- x61. Direct and Inverse Problems.- x62. Correctness Conditions.- x63. Determination of the Probability Density for the Rates of Movement of Scatterers.- x64. Determination of the Spectrum of the Fluctuations in the Rate of Movement of Scatterers.- x65. Determination of the Relative Level of Coherent Scattering.- x66. Determination of the Average Number of Scatterers.- x67. Determination of the Frequency Properties of Scatterers.- x68. Determination of the Spatial Distribution of Scatterers.- Conclusion.