Fundamentals of Statistical Signal Processing,Volume II: Detection Theory

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这本书比Van Trees的书成书要晚，所以内容比较新。作者的作风很严谨，书中的推导极其严密。不失为一位严谨的学者的作风！虽说推导严密，但是本书 也不只是单纯讲数学的，与工程应用也很贴近。这就是本书的特点。这两册书是统计信号之集大成者。有志于这个领域的，此书必备。
Fundamentals of Statistical Signal Processing Volume ii Detection Theory Steven M. Kay University of Rhode Island Prentice hall PTR Upper Saddle River, New Jersey 07458 http://www.phptr.com 途 Contents 1 Introduction 1 Dctection Theory in Signal Processing 1.2 Thc Detection Problem 1.3 The Mathematical Detection Problem 1.4 Hierarchy of Detection Problems 5 Role of Asymptotics 4 1.6 Some Notes to the reader 2 Summary of Important PDFs 20 2.1 Introduct 20 2.2 Fundamental Probability Density Functions and Properties 2.2. 1 Gaussian(Normal) 20 2.2.2 Chi-Squared( Central) 24 2.2.3 Chi-Squared(Noncentral) 26 2.2.4 F(Central) 2.2.5 F(Noncentral 29 2.2.6 Rayleigh ..30 2.2.7 Rician 2.3 Quadratic Forms of Gaussian Random Variables∴·· 31 2.4 Asymptotic Gaussian PDF 2.5 Monte Carlo Performance Evaluation 2A Number of Required Monte Carlo Trials 2B Normal Probability Paper 47 2c MATLAB Program to Compute Gaussian Right-Tail Probability and 50 2D MATLAB Program to Compute Central and Noncentral x2 Right Tail Probability 52 2E MATLAB Program for Monte Carlo Computer Simulation CONTENTS 3 Statistical Decision Theory I 3.1 Introduction 60 3.2 Summary 3. 3 Neyrnall-Pearson Theorem 61 3.4 Receiver Operating Characteristics 74 3. 5 Irrelevant data 3.6 Minimum Probability of error 3.7 Bayes risk 80 3.8 Multiple hypothesis Testing 3A Neyman-Pearson Theorem 89 3B Minimum Bayes Risk Detector- Binary Hypothesis 90 3C Minimum Bayes Risk Dctcctor-Multiple Hypotheses 92 4 Deterministic signals 94 4.1直 ntroduction 94 4.2 Summary 94 4.3M d filt 4.3.1 Development of Detector 4.3.2 Performance of Matched Filter 4.4 Generalized Matched Filters 105 4.4.1 Performance of Generalized Matched Filter .108 4.5 tiple signals 112 4.5.1 Binary C 112 4.5.2 Performance for Binary Case 4.5.3 M-ary Case 119 4.6 Linear model 122 4.7 Signal Processing Examples 125 4A Reduced Form of the Linear model 139 5 Random Signals 141 5.1 Introduction 141 5.2 Summary 5.3 Estimator -Correlator 5.4 Linear model 154 5.5 Estimator- Correlator for Large Data records 5.6 General Gaussian Detection 5.7 Signal Processing Example 169 5.7.1 Tapped Delay Line Channel Model 169 5a Detection Performance of the Estinator-Correlator 183 慕就数影,表 CONTENTS 6 Statistical Decision Theory II 186 6.1 Introduction 186 6.2 Summary 186 6.2. 1 Summary of Composite Hypothesis Testing 187 6.3 Composite Hypothesis Testing ..191 6.4 Composite Hypothesis Testing Approaches 19了 6.4.1 Bayesian Approach 198 6.4.2 Generalized likelihood ratio test 200 6.5 Performance of GLRT for Large Data Records 205 6.6 Equivalent Large Data Records Tests 208 6.7 Locally Most Powerful Detectors 217 6.8 Mulliple Hypothesis Testing 22 1 6A Asymptotically Equivalent Tests-No Nuisance Parameters ..232 6B Asymptotically Equivalent Tests- Nuisance Parameters 6C Asymptotic pdF of glrt 239 6D Asymptotic Dctection Performance of LMP Test 241 6E Alternate Derivation of Locally Most Powerful Test 243 6F Derivation of Generalized mL rulc 7 Deterministic Signals with Unknown Parameters 248 7. 1 Introduction 248 7.2 Summar 248 7.3 Signal Modeling and Detection Pcrformance 249 7. 4 Unknown Amplitude 74.1GLRT,, 254 7.4.2 Bayesian Approach .257 7.5 Unknown Arrival Time 227.6 Sinusoidal Detection 261 7.6. 1 Amplitude Unknown 261 7.6.2 Amplitude and Phase Unknown 262 7.6.3 Amplitude, Phase, and Frequency Unknown 7.6.4 Amplitude, Phase, Frequency, and Arrival Time Unknown.. 269 87.7 Classical Linear model 7. 8 Signal Processing Examples 7A Asymptotic Performance of the Energy Detcctor 297 7b Derivation of GLRT for Classical Linear Model CONTENTS 8 Random Signals with Unknown Parameters 302 8.1 Introduction .302 8.2 Summary 8.3 Incompletely Known Signal Covariance 303 8.4 Large Data Record approximations 311 8.5 Weak Signal Detection 314 8.6 Signal Processing Example ...315 8a Derivation of pdf for Periodic gaussian random process 332 9 Unknown noise Parameters 336 9.1 Introduction 336 9.2 Summary 336 9.3 General Considerations...,....,. ..,,..337 9. 4 white gaussian noise 9. 4.1 Known Deterministic Signal ..341 9.4.2 Random Signal with Known PDF 343 9.4.3 Deterministic Signal with Unknown Parameters ..345 9.4.4 Random Signal with Unknown PDF Parameters ...... 349 9.5 Colored wSS Gaussian noise 350 9.5.1 Known Deterministic Signals 350 9.5.2 Deterministic Signals with Unknown Parameters 353 9.6 Signal Processing Example 358 9A Derivation of GLRT for Classical Linear Model for a2 Unknown 371 9b Rao Test for General Linear Model with Unknown Noise Parameters 375 9C Asymptotically Equivalent Rao Test for Signal Processing Example.377 10 Non Gaussian noise 381 10.1 Introduction 381 0.2 Summary ..381 10.3 NonGaussian noise Characteristics .,382 10.4 Known Deterministic Signals 385 10.5 Deterministic Signals with Unknown Parameters 10.6 Signal Processing Example 400 10A Asymptotic Performance of NP Detector for Weak Signals 410 10B Rao Test for Linear Model Signal with IID Non Gaussian Noise 413 CONTENTS 11 Summary of Detectors 416 11.1 Introduction 416 11.2 Detection Approaches 416 11.3 Linear model 427 11.4 Choosing a Detector 433 11.5 Other Approaches and other Texts 437 12 Model Change Detection 439 12.1 Introduction 439 12.2 Summarv 439 12.3 Description of Problem 440 12.4 Extensions to the Basic Problem 445 12.5 Multiple Change Times 449 12.6 Signal Processing Examples 455 12.6.1 Maneuver Detection 12.6.2 Time Varying PSD Detection 460 2A General Dynamic Programming Approach to Segmentation .... 469 12B MATLAB Program for Dynamic Programming 471 13 Complex/vector Extensions, and Array Processing 473 13.1 Introduction 473 13.2 Summary 473 13.3 Known pdfs 474 13.3.1 Matched Filter 474 13.3.2 Generalized Matched Filter 478 13.3.3 Estimator- Correlator 479 13.4 PDFs with Unknown Parameters 484 13.4. 1 Deterministic Signal 484 13.4.2 Random Signal 486 13.5 Vector Observations and PDFs .486 13.5.1 General Covariance matrix 490 13.5.2 Scaled Identity matrix ,,,491 13.5.3 Uncorrelated from Temporal Sample to Sample 491 13.5.4 Uncorrelated from Spatial Sample to Sample 492 13.6 Detectors for Vector Observations 492 136. 1 Known Deterministic Signal in CWGN ,492 13.6.2 Known Deterministic Signal and General Noise Covariance 495 CONTENTS 13.6.3 Known Deterministic Signal in Temporally Uncorrelated Noise 495 13.6. 4 Known Deterministic Signal in Spatially Uncorrelated Noise. 496 13.6.5 Random Signal in CWGN 13.6.6 Deterministic Signal with Unknown Parameters in CWGN.. 499 13.7 Estimator-Correlator for Large Data Records .501 13.8 Signal Processing Examples .508 13.8.1 Active Sonar/Radar 510 13.8.2 Broadband passive sonar 515 13A PDF of GLRT for Complex Linear Model ......,,,526 Al Review of Important Concepts 529 Al.1 Linear and Matrix algebra 529 Al. 1.1 Definitions 529 A1.1.2 Special Matrices ..531 Al. 1. 3 Matrix Manipulation and Formulas A1.1.4 Theorems 535 Al.1.5 Eigendecompostion of Matrices 536 Al. 1.6 Inequalities 537 Al.2 Random Processes and Time Series Modeling ...537 A1. 2.1 Random Process Characterization 538 A1.2.2 Gaussian Random Process 540 A1. 2.3 Time Series models 541 A2 Glossary of Symbols and Abbreviations (Vols. I Il 545 Preface This text is the second volume of a series of books addressing statistical signal processing. The first volume, Fundamentals of Statistical Signal Processing: Este mation Theory, was published in 1993 by Prentice-Hall, Inc. Henceforth, it will be referred to as [Kay-I 1993]. This second volume, entitled Fundamentals of Statisti- cal Signal Processing: Detection Theorg, is the application of statistical hypothesis testing to the detection of signals in noise. The series has been written to provide the reader with a broad introduction to the theory and application of statistical signal processing Hypothesis testing is a subject that is standard fare in the many books available dealing with statistics. These books range from the highly theoretical expositions written by statisticians to the more practical treatments contributed by the many users of applied statistics. This text is an attempt to strike a balance between these two extremes. The particular audience we have in mind is the community involved in the design and implementation of signal processing algorithms. As such, the primary focus is on obtaining optimal detection algorithms that may be implemented on a digital computer. The data sets are therefore assumed to be aSmples of a continuous-time waveform or a sequence of data points. Thc choice of topics reflects what we believe to be the important approaches to obtaining an optimal detector and analyzing its performance. As a consequence, some of the deeper theoretical issues have been omitted with references given instead It is the author's opinion that the best way to assimilate the material on det tion theory is by exposure to and working with good examples. Consequently, there are numerous examples that illustrate the theory and others that apply the theory to actual detection problems of current interest. We have made extensive use the matlab scientific programming language( Version 4.2b for all computer generated results. In some cases, actual MATLAB programs have been listed where a program was deemed to be of suficient utility to the reader. Additionally, an abundance of homework problems has been included. They range from simple ap- p lications of the theory to extensions of the basic concepts. a solutions manual is available from the author. To aid the reader, summary sections have been provided at the beginning of each chapter. Also, an overview of all the principal detection approaches and the rationale for choosing a particular method can be found in IMATLAB is a registered trademark of The Math Works, Inc 【实例截图】
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