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E-raamat: Underwater Acoustic Signal Processing: Modeling, Detection, and Estimation

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Underwater Acoustic Signal Processing: Modeling, Detection, and EstimationSuurem pilt
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This book provides comprehensive coverage of the detection and processing of signals in underwater acoustics. Background material on active and passive sonar systems, underwater acoustics, and statistical signal processing makes the book a self-contained and valuable resource for graduate students, researchers, and active practitioners alike. Signal detection topics span a range of common signal types including signals of known form such as active sonar or communications signals; signals of unknown form, including passive sonar and narrowband signals; and transient signals such as marine mammal vocalizations. This text, along with its companion volume on beamforming, provides a thorough treatment of underwater acoustic signal processing that speaks to its author’s broad experience in the field.

Part I Sonar and Underwater Acoustics
1 Introduction to Underwater Acoustic Signal Processing
3(30)
1.1 Overview of Underwater Acoustic Signal Processing
3(24)
1.1.1 Sonar Systems
4(2)
1.1.2 Common Applications
6(1)
1.1.3 Signal Processing in Underwater Acoustics
7(2)
1.1.4 Development Process for Novel Applications
9(1)
1.1.5 Example Signals of Interest
10(5)
1.1.6 Examples of Signal and Information Processing
15(18)
1.1.6.1 Detection
16(2)
1.1.6.2 Localization
18(3)
1.1.6.3 Tracking
21(3)
1.1.6.4 Classification
24(3)
1.2 Intended Use and Organization of This Book
27(4)
References
31(2)
2 Sonar Systems and the Sonar Equation
33(62)
2.1 Introduction
33(1)
2.2 Remote Sensing with Sonar Systems
33(23)
2.2.1 Components of a Sonar System
34(2)
2.2.2 Monostatic, Bistatic, and Distributed Sonar Systems
36(1)
2.2.3 Localization: Estimating the Position of a Sound or Scattering Source
37(8)
2.2.3.1 Active vs. Passive Localization
38(1)
2.2.3.2 Array Design and Angle Estimation
39(1)
2.2.3.3 Localization with Distributed and Moving Sonar Systems
40(3)
2.2.3.4 Localization and the Effects of Propagation
43(2)
2.2.4 Bistatic Active Sonar
45(3)
2.2.4.1 Active Sonar Resolution Cell
47(1)
2.2.5 Doppler Scale and Shift
48(6)
2.2.5.1 Doppler Effect via Waveform and Platform Trajectories
51(3)
2.2.6 Doppler Sensitive and Insensitive Waveforms
54(2)
2.3 The Sonar Equation
56(35)
2.3.1 Decibel Notation
58(2)
2.3.2 The Basic Passive Sonar Equation
60(7)
2.3.2.1 Example: Passive Submarine Radiated Noise Detection
66(1)
2.3.3 The Basic Active Sonar Equation
67(6)
2.3.3.1 Example: Reverberation- and Noise-Limited Active Sonar Detection
71(2)
2.3.4 Summary of Sonar Equation Terms
73(2)
2.3.5 Relating SNR to Detection Performance: Detection Threshold
75(10)
2.3.5.1 Gaussian-Fluctuating Signal
76(2)
2.3.5.2 Non-fluctuating or Deterministic Signal
78(1)
2.3.5.3 Extensions to Other Signal and Noise Models
79(1)
2.3.5.4 Example Signal-Model Performance Comparison
80(1)
2.3.5.5 Detection Threshold (DT)
81(4)
2.3.6 Relating SNR to Estimation Performance
85(2)
2.3.7 Other Applications of the Sonar Equation
87(8)
2.3.7.1 Signal Excess (SE)
88(2)
2.3.7.2 Figure of Merit (FOM)
90(1)
References
91(4)
3 Underwater Acoustics
95(108)
3.1 Introduction
95(1)
3.2 Acoustic Wave Propagation in the Ocean
95(63)
3.2.1 Acoustical Field and Power Quantities
97(4)
3.2.1.1 Acoustic Pressure and Pressure Levels
98(1)
3.2.1.2 Particle Velocity
99(1)
3.2.1.3 Acoustic Intensity
100(1)
3.2.1.4 Acoustic Power
100(1)
3.2.1.5 Acoustic Energy Flux Density
101(1)
3.2.2 Propagation and Spreading
101(10)
3.2.2.1 The Wave Equation, Spherical Waves, and Spherical Spreading
102(2)
3.2.2.2 Periodic Signals, Wavelength, and Wavenumber
104(2)
3.2.2.3 Cylindrical Spreading
106(1)
3.2.2.4 Plane Waves
107(2)
3.2.2.5 Near-Field and Far-Field Propagation
109(2)
3.2.3 Sound Projection and Propagation
111(9)
3.2.3.1 Inhomogeneous Wave Equation and the Channel Impulse Response
111(3)
3.2.3.2 Helmholtz Equation and Channel Frequency Response
114(1)
3.2.3.3 Doppler Effect via the Inhomogeneous Wave Equation
115(3)
3.2.3.4 Source Factor and Source Level (SL)
118(2)
3.2.4 Propagation Loss (PL)
120(4)
3.2.4.1 Propagation Loss for Different Spreading Models
121(1)
3.2.4.2 Propagation Loss and the Channel Frequency Response
122(1)
3.2.4.3 Coherent and Incoherent Propagation Loss
123(1)
3.2.5 Absorption and Dispersion
124(1)
3.2.5.1 Absorption
124(1)
3.2.5.2 Dispersion
124(1)
3.2.6 Sound-Speed, Snell&apso;s Law, and Refraction
125(6)
3.2.6.1 Sound Speed Profiles and Ray Tracing
128(3)
3.2.7 Boundaries and Reflection Loss
131(17)
3.2.7.1 Boundary Conditions Between Layers
132(1)
3.2.7.2 Constant-Density Layers
133(1)
3.2.7.3 Reflection at the Ocean Surface
134(2)
3.2.7.4 Reflection at the Ocean Bottom
136(2)
3.2.7.5 Total Internal Reflection and Phase Change
138(4)
3.2.7.6 Rough Surface Reflection
142(6)
3.2.8 Rays and Modes in Shallow Water
148(8)
3.2.8.1 Ray-Based Solution and Multipath
149(1)
3.2.8.2 Mode-Based Solution
150(4)
3.2.8.3 Dispersion in a Waveguide
154(2)
3.2.9 Reciprocity
156(2)
3.3 Ambient Noise
158(6)
3.3.1 Overview and Ambient Noise Spectrum Curves
158(2)
3.3.1.1 Converting Spectrum Rates of Change from per Octave to per Decade
160(1)
3.3.2 Very Low Frequency
160(1)
3.3.3 Low Frequency: Distant Shipping Noise
161(1)
3.3.4 Low to High Frequency: Wind-Related Surface Noise
162(1)
3.3.5 Very High Frequency: Thermal Noise
163(1)
3.3.6 Spatio-Temporal and Statistical Properties of Ambient Noise
164(1)
3.4 Scattering from Objects: Target Echoes and Target Strength
164(16)
3.4.1 Target Strength (TS)
165(4)
3.4.1.1 Relationship to Radar Cross Section
168(1)
3.4.2 Target Impulse Response
169(3)
3.4.2.1 Impulse Response of a Rigid Sphere
170(2)
3.4.3 Scattering from Objects: The ka Dependence
172(8)
3.4.3.1 Rayleigh Scattering Regime (ka 1)
173(1)
3.4.3.2 Geometric Scattering Regime (ka 1)
174(3)
3.4.3.3 Exact Modal Solutions
177(3)
3.5 Reverberation
180(16)
3.5.1 Sources of Reverberation
182(1)
3.5.2 Volume Reverberation
182(4)
3.5.3 Boundary Reverberation
186(3)
3.5.4 Signal to Reverberation Ratio
189(1)
3.5.5 Statistical Characterization of Reverberation
190(1)
3.5.6 Spectral Properties of Reverberation
191(2)
3.5.7 Reverberation from a Moving Source
193(3)
References
196(7)
Part II Systems, Signal Processing and Mathematical Statistics Background
4 Linear Systems and Signal Processing
203(48)
4.1 Introduction
203(1)
4.2 Linear-Time-Invariant (LTI) Systems and Convolution
203(5)
4.2.1 Impulse Response of an LTI System
204(3)
4.2.2 Frequency Response of an LTI System
207(1)
4.3 Fourier Transforms
208(7)
4.3.1 Inverse Fourier Transform
209(2)
4.3.2 Properties of the Fourier Transform
211(4)
4.4 Hilbert Transform
215(1)
4.5 Signal Time-Bandwidth Product
216(3)
4.6 Converting Analog Signals to Digital Signals
219(6)
4.6.1 Sampling and Aliasing
219(4)
4.6.2 Quantization
223(2)
4.7 Discrete-Time Signals and Systems
225(3)
4.7.1 Fourier Transform of a Discrete-Time Signal
226(1)
4.7.2 Properties of the Fourier Transform of Discrete-Time Signals
227(1)
4.8 Discrete and Fast Fourier Transforms (DFT and 1F1)
228(3)
4.9 Discrete-Time Filtering (LPF, HPF, and BPF)
231(8)
4.9.1 FIR and IIR Filters
232(2)
4.9.2 FIR Filter Design
234(2)
4.9.3 Bandpass and High-Pass Filters
236(1)
4.9.4 FIR Filter Implementation
237(2)
4.10 Windowing and Window Functions
239(7)
4.10.1 Rectangular, Uniform, or Boxcar Window
242(1)
4.10.2 Tukey Window
243(1)
4.10.3 Hamming Window
243(1)
4.10.4 Taylor Window
244(1)
4.10.5 Kaiser Window
245(1)
4.10.6 Hann Window
245(1)
4.10.7 Blackman Window
246(1)
4.11 Decimation and Interpolation
246(3)
References
249(2)
5 Mathematical Statistics
251(56)
5.1 Introduction
251(1)
5.2 Probability
251(2)
5.3 Random Variables
253(20)
5.3.1 Random Variables, Distributions, and Densities
253(4)
5.3.2 Moments and Expectations
257(2)
5.3.3 Functions of Random Variables
259(3)
5.3.4 Simulating Random Variables
262(1)
5.3.5 Histogram Estimates of the PDF and CDF
263(2)
5.3.6 Multiple Random Variables, Joint Densities, and Independence
265(3)
5.3.7 Central Limit Theorem (CLT)
268(1)
5.3.8 Conditional Distributions and Bayes&apso; Theorem
269(2)
5.3.9 Transform-Domain Functions
271(2)
5.3.9.1 Moment Generating Function
271(1)
5.3.9.2 Characteristic Function
272(1)
5.3.9.3 Cumulant Generating Function
272(1)
5.4 Random Processes
273(8)
5.4.1 Stationarity and Ergodicity
275(3)
5.4.2 Power Spectral Density
278(3)
5.5 Complex Random Variables and Random Processes
281(3)
5.6 Common Statistical Distributions
284(19)
5.6.1 Bernoulli Distribution
285(1)
5.6.2 Binomial Distribution
286(1)
5.6.3 Poisson Distribution
286(1)
5.6.4 Uniform Distribution
287(1)
5.6.5 Beta Distribution
288(1)
5.6.6 Gaussian or Normal Distribution
289(1)
5.6.7 Complex Gaussian Distribution
290(1)
5.6.8 Multivariate Gaussian Distribution
291(1)
5.6.9 Complex Multivariate Gaussian Distribution
291(1)
5.6.10 Exponential Distribution
292(1)
5.6.11 Gamma Distribution
293(1)
5.6.12 Rayleigh Distribution
294(1)
5.6.13 Rician Distribution
295(1)
5.6.14 Chi-Squared Distribution
296(1)
5.6.15 Non-central Chi-Squared Distribution
297(1)
5.6.16 F Distribution
298(1)
5.6.17 Non-central F Distribution
299(1)
5.6.18 Weibull Distribution
300(1)
5.6.19 K Distribution
301(1)
5.6.20 Generalized Pareto Distribution
302(1)
5.6.21 Log Normal Distribution
303(1)
References
303(4)
6 Statistical Signal Processing
307(42)
6.1 Introduction
307(1)
6.2 Signal Detection Theory
307(18)
6.2.1 Hypothesis Testing in Underwater Acoustics
308(1)
6.2.2 Performance Measures, Implementation, and Analysis of Detectors
309(7)
6.2.2.1 Receiver Operating Characteristic (ROC) Curves
312(2)
6.2.2.2 Estimating Pd and Pf
314(1)
6.2.2.3 Importance Sampling
315(1)
6.2.2.4 Equal-Error Point and Area Under the Curve
315(1)
6.2.3 Design of Detectors: Neyman-Pearson Optimal
316(2)
6.2.4 Composite Hypothesis Testing: Detecting When There Are Unknown Parameters
318(1)
6.2.5 Design of Detectors: Uniformly Most Powerful Tests and Invariance
319(1)
6.2.6 Design of Detectors: Small-Signal Situations
320(1)
6.2.7 Design of Detectors: Generalized Likelihood Ratio (GLR)
321(4)
6.2.7.1 Asymptotic Distribution of the GLR Detector Decision Statistic
324(1)
6.2.8 Design of Detectors: Bayesian Approaches
325(1)
6.3 Estimation Theory
325(20)
6.3.1 Point Estimation in Underwater Acoustics
326(1)
6.3.2 Performance Measures and Analysis of Estimators
327(2)
6.3.3 Cramer-Rao Lower Bound (CRLB)
329(6)
6.3.3.1 CRLB for Multiple Parameters
331(1)
6.3.3.2 CRLB for Transformations
332(2)
6.3.3.3 CRLB for a Multivariate Gaussian Model
334(1)
6.3.3.4 CRLB for a Complex Multivariate Gaussian Model
334(1)
6.3.4 Estimation Techniques: Maximum Likelihood
335(2)
6.3.4.1 Properties of the MLE
336(1)
6.3.5 Estimation Techniques: Method of Moments
337(3)
6.3.6 Estimation Techniques: Bayesian Inference
340(1)
6.3.7 Estimation Techniques: Expectation-Maximization (EM) Algorithm
341(3)
6.3.7.1 Example: Exponential Mixture
342(2)
6.3.8 Confidence Intervals and Bayesian Credible Sets
344(1)
References
345(4)
Part III Detection in Underwater Acoustics
7 Underwater Acoustic Signal and Noise Modeling
349(108)
7.1 Introduction
349(2)
7.2 Characterizing Underwater Acoustic Signals
351(16)
7.2.1 Signal Consistency and Knowledge
353(3)
7.2.2 Time-Frequency Characterization of the Signal
356(6)
7.2.2.1 Finite-Duration Signal Measurement as a Stationary Random Processes
358(1)
7.2.2.2 Narrowband, Broadband, and Bandpass Signals
359(3)
7.2.3 Effect of Propagation on Source-Signal Characterization
362(5)
7.2.3.1 Unknown and Random Phases
363(1)
7.2.3.2 Unknown and Random Amplitudes
364(3)
7.3 Bandpass and Baseband Representations of Signal and Noise
367(21)
7.3.1 Analytic Signals
368(3)
7.3.2 Basebanding and the Complex Envelope
371(6)
7.3.2.1 Signal Envelope and Instantaneous Intensity
373(1)
7.3.2.2 Different Ways to Baseband a Signal
374(1)
7.3.2.3 Basebanding a Signal Subject to Delay and Doppler
375(2)
7.3.3 Bandpass Signals and Linear Time-Invariant Systems
377(1)
7.3.4 Complex Envelope of Bandpass Noise
378(4)
7.3.5 Modeling the Complex Envelope After Sampling in Time
382(3)
7.3.5.1 Deterministic Signal Energy
382(1)
7.3.5.2 Noise Covariance Matrix
383(2)
7.3.6 Statistics of the Complex Envelope, Envelope, and Instantaneous Intensity
385(3)
7.3.6.1 Uniformly Random Phase
386(2)
7.4 Noise and Interference Models
388(41)
7.4.1 Ambient Noise
389(3)
7.4.2 Reverberation
392(11)
7.4.2.1 Reverberation as a Random Process
392(1)
7.4.2.2 Reverberation Autocorrelation Function
393(1)
7.4.2.3 Reverberation Power Spectral Density
394(2)
7.4.2.4 Doppler Spreading of Reverberation
396(7)
7.4.3 Heavy-Tailed Noise and Reverberation
403(26)
7.4.3.1 Effect of Beamforming and Matched Filtering on Reverberation Statistics
404(2)
7.4.3.2 Statistical Models for Heavy-Tailed Data
406(2)
7.4.3.3 K Distribution
408(5)
7.4.3.4 Poisson-Rayleigh Distribution
413(2)
7.4.3.5 Other Common Models
415(5)
7.4.3.6 Performance Bounds on Parameter Estimation
420(3)
7.4.3.7 Mixture Distributions
423(6)
7.5 Signal and Signal-Plus-Noise Statistical Models
429(23)
7.5.1 Deterministic Signal
430(5)
7.5.1.1 Probability of Detection
434(1)
7.5.1.2 Sum of Instantaneous-Intensity Samples
434(1)
7.5.2 Gaussian-Fluctuating Signal
435(2)
7.5.2.1 Probability of Detection
436(1)
7.5.2.2 Sum of Instantaneous-Intensity Samples
436(1)
7.5.3 Rician Signal
437(3)
7.5.3.1 Probability of Detection
438(1)
7.5.3.2 Sum of Instantaneous-Intensity Samples
439(1)
7.5.4 Gamma-Fluctuating-Intensity (GFI) Signal
440(2)
7.5.4.1 Probability of Detection
441(1)
7.5.4.2 Sum of Instantaneous-Intensity Samples
442(1)
7.5.5 Hankel Transform for Signal-Plus-Noise PDFs and CDFs
442(3)
7.5.6 Approximations to the CDF of Signals in Heavy-Tailed Noise
445(12)
7.5.6.1 Signal in Gaussian Noise
446(1)
7.5.6.2 Three-Moment Shifted-Gamma (TMSG) Approximation
446(2)
7.5.6.3 Three-Moment Non-central-gamma (TMNCG) Approximation
448(3)
7.5.6.4 Sums of Instantaneous-Intensity Samples
451(1)
7.5.6.5 Signal and Noise Model Instantaneous-Intensity Moments
452(1)
References
452(5)
8 Detecting Signals with Known Form: Matched Filters
457(164)
8.1 Introduction
457(7)
8.1.1 Introductory Examples
459(5)
8.2 Matched-Filter Detectors
464(34)
8.2.1 SNR Gain of the Matched Filter
469(2)
8.2.2 Detector for Signals with Known Form, Known Amplitude, and Known Phase
471(4)
8.2.3 Detector for Signals with Known Form and Unknown Phase
475(2)
8.2.4 Detector for Signals with Known Form and Uniformly Random Phase
477(2)
8.2.5 Detector for Signals with Known Form and Gaussian Amplitude Fluctuations
479(2)
8.2.6 Detector for Signals with Known Form and an Arbitrary Amplitude Distribution
481(1)
8.2.7 Detector for Signals with Known Form and a Rician Distributed Amplitude
482(3)
8.2.8 Detectors When Parameters Other Than Phase and Amplitude Are Unknown
485(4)
8.2.8.1 Detectors for Unknown Noise Parameters
485(3)
8.2.8.2 Detectors for Unknown Signal Parameters
488(1)
8.2.9 Noise-Normalized and Adaptive Matched Filters
489(2)
8.2.10 Effect of Oversampling on a Matched-Filter Detector
491(3)
8.2.11 False-Alarm Rate (FAR)
494(4)
8.2.11.1 FAR Under Oversampling
497(1)
8.3 Waveform Autocorrelation and Ambiguity Functions
498(29)
8.3.1 SNR Loss from Waveform Mismatch
500(7)
8.3.1.1 Coherent Matched Filter
500(1)
8.3.1.2 Quadrature Matched Filter
501(1)
8.3.1.3 The Complex Ambiguity Function and SNR Loss
502(5)
8.3.2 Ambiguity Functions
507(3)
8.3.2.1 Narrowband Signals
508(1)
8.3.2.2 Cross-Ambiguity
509(1)
8.3.3 Autocorrelation Functions
510(1)
8.3.4 CW Pulses
511(4)
8.3.4.1 Autocorrelation Function for a CW Pulse
511(2)
8.3.4.2 Ambiguity Function for a CW Pulse
513(2)
8.3.5 LFM Pulses
515(5)
8.3.5.1 Autocorrelation Function for an LFM Pulse
516(1)
8.3.5.2 Narrowband Ambiguity Function for an LFM Pulse
517(2)
8.3.5.3 Wideband Ambiguity Function for an LFM Pulse
519(1)
8.3.6 HFM Pulses
520(7)
8.3.6.1 Autocorrelation Function for an HFM Pulse
522(2)
8.3.6.2 Ambiguity Function for an HFM Pulse
524(3)
8.4 Beamforming as a Detection Process
527(8)
8.4.1 Plane Waves and Line Arrays
527(1)
8.4.2 Narrowband Beamformer
528(3)
8.4.2.1 Array Signal and Noise Models
529(2)
8.4.3 Array Beam Response and Beampattern
531(2)
8.4.4 Array Gain and Directivity
533(2)
8.5 Signal-Parameter Estimation Performance
535(27)
8.5.1 Waveform Resolution vs. Estimation Accuracy
537(4)
8.5.1.1 Resolution of the Standard Sonar Pulses
537(3)
8.5.1.2 Accuracy vs. Resolution
540(1)
8.5.2 Performance Bounds for Estimating Signal Strength and Phase
541(4)
8.5.3 Performance Bounds for Estimating Arrival Time
545(8)
8.5.3.1 Frequency-Modulated Pulses
550(2)
8.5.3.2 Continuous-Wave Pulses
552(1)
8.5.4 Performance Bounds for Estimating Doppler Scale
553(5)
8.5.4.1 Shaded CW-Pulse Example
556(2)
8.5.5 Performance Bounds for Joint Estimation of Arrival Time and Doppler Scale
558(4)
8.5.5.1 LFM-Pulse Example
560(2)
8.6 Normalization: Background Power Estimation
562(22)
8.6.1 Cell-Averaging CFAR Normalizer
566(8)
8.6.1.1 Decision-Threshold Analysis
567(2)
8.6.1.2 Equivalent Number of Independent Samples
569(3)
8.6.1.3 Performance Analysis and CFAR Loss
572(2)
8.6.2 Target Masking and False-Alarm-Rate Inflation
574(1)
8.6.3 Order-Statistic CFAR Normalizer
575(9)
8.6.3.1 Decision-Threshold Analysis
577(1)
8.6.3.2 Performance Analysis
578(4)
8.6.3.3 Which Order Statistic to Use?
582(2)
8.7 Doppler Processing
584(19)
8.7.1 Doppler Filter Bank
586(8)
8.7.1.1 Probability of False Alarm in a Filter Bank
587(1)
8.7.1.2 Probability of Detection in a Filter Bank
588(2)
8.7.1.3 Doppler Filter Bank Example
590(2)
8.7.1.4 FFT Implementation of a CW-Pulse Doppler Filter Bank
592(2)
8.7.2 Reverberation in a Doppler Filter Bank
594(5)
8.7.2.1 Detection in Reverberation and Noise
596(1)
8.7.2.2 Reverberation Temporal-Support Function for CW and FM Pulses
597(2)
8.7.3 Normalization for CW Pulses
599(4)
8.8 Temporal Spreading and Incoherent Integration
603(13)
8.8.1 Energy Spreading Loss (ESL)
604(6)
8.8.2 Incoherent Integration
610(15)
8.8.2.1 Decision-Threshold Analysis
612(2)
8.8.2.2 Performance Analysis
614(2)
Appendix 8.A: Example MATLAB® Code for a Doppler Filter Bank
616(1)
References
617(4)
9 Detecting Signals with Unknown Form: Energy Detectors
621(122)
9.1 Introduction
621(4)
9.2 Energy Detectors
625(57)
9.2.1 Statistical Characterization of the Signal and Noise
628(2)
9.2.2 SNR After the Coherent Portion of Detection Processing
630(2)
9.2.3 Detector for Random Signals and Noise Having Constant Spectra in a Known Frequency Band
632(6)
9.2.3.1 The Basic Energy Detector and Its Performance Analysis
634(4)
9.2.4 Frequency-Domain Processing for Shaped Signal and Noise Spectra
638(4)
9.2.4.1 Decorrelation of DFT Bin Data
640(2)
9.2.5 Detectors for Random Signals with Known Spectra in a Known Frequency Band
642(4)
9.2.5.1 Optimal Detector for a Signal with a Known Spectrum
642(1)
9.2.5.2 Locally Optimal Detector for a Signal with a Known Spectral Shape
643(1)
9.2.5.3 Eckart Filter for Maximum Detection Index
644(2)
9.2.6 Detectors for Random Signals with Unknown Spectra in a Known Frequency Band
646(2)
9.2.6.1 Large and. Small Signal-to-Noise Spectral-Density Ratios
646(1)
9.2.6.2 Generalized Likelihood Ratio Energy Detector for an Unknown Signal Spectrum
647(1)
9.2.7 Performance of a Weighted-Sum Energy Detector for Gaussian Random Signals and Noise
648(9)
9.2.7.1 Exact Solution via the Characteristic Function
651(1)
9.2.7.2 Numerical Evaluation of the CDF from the Characteristic Function
652(3)
9.2.7.3 Gaussian Approximation
655(1)
9.2.7.4 Gamma Approximation
656(1)
9.2.7.5 Shifted Gamma Approximation
656(1)
9.2.8 Detectors for Random Signals with Unknown Spectra in an Unknown Frequency Band
657(6)
9.2.8.1 Modified Generalized Likelihood Ratio Energy Detector
658(1)
9.2.8.2 Power-Law Energy Detector
659(4)
9.2.9 Detectors for Deterministic Signals with Unknown or Partially Known Form
663(6)
9.2.9.1 Deterministic Signals with Unknown Structure in a Known Frequency Band
664(2)
9.2.9.2 Deterministic Signals with Partially Known Form
666(2)
9.2.9.3 Completely Unknown Deterministic Signals
668(1)
9.2.10 Time-Domain Energy Detector: Coherent and Incoherent Averaging
669(7)
9.2.10.1 Choosing the Coherent-Processing- Window Size and Spacing
674(1)
9.2.10.2 Choosing the Analysis Window Extent
675(1)
9.2.11 Detection Threshold for the Noise-Normalized Energy Detector
676(6)
9.2.11.1 Deterministic Signals
677(2)
9.2.11.2 Gaussian-Based Approximation for Gaussian Random Signals
679(2)
9.2.11.3 Gamma-Based Approximation for Gaussian Random Signals
681(1)
9.3 Normalization: Background Power Estimation
682(16)
9.3.1 Auxiliary Data for Narrowband and Broadband Processing
683(2)
9.3.2 Cell-Averaging Normalizer
685(3)
9.3.3 Exponential-Average Normalizers
688(4)
9.3.4 Weighted-Average Normalizers
692(6)
9.3.4.1 Characteristic Function of a Weighted-Average Background Estimate
693(1)
9.3.4.2 Single-Sample Normalizer Distribution, Characteristic Function and Moments
693(5)
9.4 Time-Delay Estimation
698(23)
9.4.1 Cross-Correlation Processing
701(12)
9.4.1.1 Inter-Sensor-Delay Estimation
706(4)
9.4.1.2 Cramer-Rao Lower Bound for Inter-Sensor Delay
710(3)
9.4.2 Autocorrelation Processing
713(8)
9.4.2.1 Estimating Parameters of a PSD
714(1)
9.4.2.2 Multipath-Delay Estimation
715(5)
9.4.2.3 Cramer-Rao Lower Bound for Multipath Delay
720(1)
9.5 Narrowband-Signal Parameter Estimation
721(12)
9.5.1 Sinusoidal Signals
722(6)
9.5.1.1 Estimation of the Frequency, Phase, and Amplitude of a Sinusoid
723(2)
9.5.1.2 Phase Estimator Distribution
725(2)
9.5.1.3 Cramer-Rao Lower Bounds
727(1)
9.5.2 Narrowband Gaussian Random Signals
728(24)
9.5.2.1 Cramer-Rao Lower Bounds
729(3)
9.5.2.2 Estimation of the Center Frequency and Bandwidth
732(1)
Appendix 9.A: Numerical Evaluation of the CDF of a Sum of Exponential Random Variables
733(2)
Appendix 9.B: Moments of the Modified GLR Energy Detector Decision Statistic
735(1)
Appendix 9.C: Algorithm for Estimating the Bandwidth and Center-Frequency of a Narrowband Random Signal in Noise
736(3)
References
739(4)
10 Detecting Signals with Unknown Duration and/or Starting Time: Sequential Detectors
743(76)
10.1 Introduction
743(4)
10.2 Performance Measures for Sequential Signal Detectors
747(5)
10.3 Detectors for Signals with Known Duration and Known Starting Time
752(6)
10.3.1 M-of-N Detector: Binary Integration
753(5)
10.3.1.1 M-of-N Detector Design: Choosing Thresholds
755(3)
10.4 Detectors for Signals with Known Duration and Unknown Starting Time
758(8)
10.4.1 Sliding Incoherent Sum Detector
760(3)
10.4.2 Sliding M-of-N Detector
763(3)
10.5 Detectors for Long-Duration Signals
766(27)
10.5.1 Known Starting Time: Sequential Probability Ratio Test (SPRT)
767(9)
10.5.1.1 Decision Thresholds and Error Probabilities
769(1)
10.5.1.2 Average Sample Numbers for the SPRT
770(4)
10.5.1.3 Overshoot Corrections to the SPRT Average Sample Numbers
774(2)
10.5.2 Unknown Starting Time: Page&apso;s Test
776(17)
10.5.2.1 Average Sample Numbers for Page&apso;s Test
780(4)
10.5.2.2 Unity Roots of the Moment Generating Function
784(2)
10.5.2.3 ROC Curves and Asymptotic Performance of Page&apso;s Test
786(3)
10.5.2.4 Biasing a General Input to Page&apso;s Test
789(2)
10.5.2.5 Page&apso;s Test with Nuisance Parameter Estimation
791(1)
10.5.2.6 Overshoot Corrections to Page&apso;s Test Average Sample Numbers
792(1)
10.6 Detectors for Signals with Unknown, Intermediate Duration
793(24)
10.6.1 Known Starting Time: Sequential Probability Ratio Test (SPRT)
795(9)
10.6.1.1 SPRT Analysis by Quantization
797(5)
10.6.1.2 Truncated SPRT
802(2)
10.6.2 Unknown Starting Time: Page&apso;s Test
804(13)
10.6.2.1 Alternating Hypothesis Page&apso;s Test
804(3)
10.6.2.2 Page&apso;s Test Analysis by Quantization
807(3)
10.6.2.3 Design Example
810(7)
References
817(2)
Index 819
Douglas A. Abraham received B.S., M.S., and Ph.D. degrees in electrical engineering and an M.S. degree in statistics from the University of Connecticut, Storrs.  He has performed basic and applied research in underwater acoustic signal processing at the Naval Undersea Warfare Center (New London, CT), the NATO SACLANT Undersea Research Centre (La Spezia, Italy), and the Applied Research Laboratory at Pennsylvania State University. He presently continues his professional and technical activities as a consultant.  Dr. Abraham has also taught at the University of Connecticut as visiting faculty, and managed basic and applied research programs at the Office of Naval Research through an intergovernmental personnel assignment.
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