Detection Estimation and Modulation Theory, Part I

Originally published in 1968, Harry Van Trees’s Detection, Estimation, and Modulation Theory, Part I is one of the great time-tested classics in the field of signal processing. Highly readable and practically organized, it is as imperative today for professionals, researchers, and students in optimum signal processing as it was over thirty years ago. The second edition is a thorough revision and expansion almost doubling the size of the first edition and accounting for the new developments thus making it again the most comprehensive and up-to-date treatment of the subject.

With a wide range of applications such as radar, sonar, communications, seismology, biomedical engineering, and radar astronomy, among others, the important field of detection and estimation has rarely been given such expert treatment as it is here. Each chapter includes section summaries, realistic examples, and a large number of challenging problems that provide excellent study material. This volume which is Part I of a set of four volumes is the most important and widely used textbook and professional reference in the field.

Preface xv

Preface to the First Edition xix

1 Introduction 1

1.1 Introduction 1

1.2 Topical Outline 1

1.3 Possible Approaches 11

1.4 Organization 14

2 Classical Detection Theory 17

2.1 Introduction 17

2.2 Simple Binary Hypothesis Tests 20

2.3 m Hypotheses 51

2.4 Performance Bounds and Approximations 63

2.5 Monte Carlo Simulation 80

2.6 Summary 109

2.7 Problems 110

3 General Gaussian Detection 125

3.1 Detection of Gaussian Random Vectors 126

3.2 Equal Covariance Matrices 138

3.3 Equal Mean Vectors 174

3.4 General Gaussian 197

3.5 m Hypotheses 209

3.6 Summary 213

3.7 Problems 215

4 Classical Parameter Estimation 230

4.1 Introduction 230

4.2 Scalar Parameter Estimation 232

4.3 Multiple Parameter Estimation 293

4.4 Global Bayesian Bounds 332

4.5 Composite Hypotheses 348

4.6 Summary 375

4.7 Problems 377

5 General Gaussian Estimation 400

5.1 Introduction 400

5.2 Nonrandom Parameters 401

5.3 Random Parameters 483

5.4 Sequential Estimation 495

5.5 Summary 507

5.6 Problems 510

6 Representation of Random Processes 519

6.1 Introduction 519

6.2 Orthonormal Expansions: Deterministic Signals 520

6.3 Random Process Characterization 528

6.4 Homogeous Integral Equations and Eigenfunctions 540

6.5 Vector Random Processes 564

6.6 Summary 568

6.7 Problems 569

7 Detection of Signals–Estimation of Signal Parameters 584

7.1 Introduction 584

7.2 Detection and Estimation in White Gaussian Noise 591

7.3 Detection and Estimation in Nonwhite Gaussian Noise 629

7.4 Signals with Unwanted Parameters: The Composite Hypothesis Problem 675

7.5 Multiple Channels 712

7.6 Multiple Parameter Estimation 716

7.7 Summary 721

7.8 Problems 722

8 Estimation of Continuous-Time Random Processes 771

8.1 Optimum Linear Processors 771

8.2 Realizable Linear Filters: Stationary Processes, Infinite Past: Wiener Filters 787

8.3 Gaussian–Markov Processes: Kalman Filter 807

8.4 Bayesian Estimation of Non-Gaussian Models 842

8.5 Summary 852

8.6 Problems 855

9 Estimation of Discrete–Time Random Processes 880

9.1 Introduction 880

9.2 Discrete-Time Wiener Filtering 882

9.3 Discrete-Time Kalman Filter 919

9.4 Summary 1016

9.5 Problems 1016

10 Detection of Gaussian Signals 1030

10.1 Introduction 1030

10.2 Detection of Continuous-Time Gaussian Processes 1030

10.3 Detection of Discrete-Time Gaussian Processes 1067

10.4 Summary 1076

10.5 Problems 1077

11 Epilogue 1084

11.1 Classical Detection and Estimation Theory 1084

11.2 Representation of Random Processes 1093

11.3 Detection of Signals and Estimation of Signal Parameters 1095

11.4 Linear Estimation of Random Processes 1098

11.5 Observations 1105

11.6 Conclusion 1106

Appendix A: Probability Distributions and Mathematical Functions 1107

Appendix B: Example Index 1119

References 1125

Index 1145

HARRY L. VAN TREES, ScD., received his BSc. from the United States Military Academy and his ScD. from Massachusetts Institute of Technology. During his fourteen years as a Professor of Electrical Engineering at MIT, he wrote Parts I, II, and III of the DEMT series. On loan from MIT, he served in four senior DoD positions including Chief Scientist of the U.S. Air Force and Principal Deputy Assistant Secretary of Defense (C3I). Returning to academia as an endowed professor at George Mason University, he founded the C3I Center and published Part IV of the DEMT series, Optimum Array Processing. He is currently a University Professor Emeritus.

KRISTINE L. BELL, PhD, is a Senior Scientist at Metron, Inc., and an affiliate faculty member in the Statistics Department at George Mason University. She coedited with Dr. Van Trees the Wiley-IEEE book Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking.

ZHI TIAN, PhD, is a Professor of Electrical and Computer Engineering at Michigan Technological University. She is a Fellow of the IEEE.

"Since 1968 and after 30 printings of the first edition, Part I of DEMT has been the textbook for the two generations of students and researchers that have designed the signal processing in many of our operational systems. The Second Edition includes subsequent advances, retains clarity of explanation, and promises to be the text and reference for future generations."
— Dr. Arthur B. Baggeroer, Ford Professor Emeritus, MIT

The First Edition of Detection, Estimation, and Modulation Theory, Part I, enjoyed a long useful life. However, in the forty-four years since its publication, there have been a large number of changes:

• 1. The basic detection and estimation theory has remained the same but numerous new results and algorithms have been obtained.
• 2. The exponential growth in computational capability has enabled us to implement algorithms that were only of theoretical interest in 1968.
• 3. The theoretical results from DEMT have been widely applied in operational systems.
• 4. Simulation became more widely used in system design and analysis, research, and teaching.

The Second Edition is a significant expansion of the first edition with 450 pages of new material. Chapter 2 in the First Edition, Classical Detection and Estimation Theory, is expanded into four chapters. Many more examples are developed in detail to enhance readability, and more non-Gaussian models are included. A large number of significant developments that are appropriate for an introductory text—including global Bayesian bounds, efficient computational algorithms, equivalent estimation algorithms, sequential estimation, and importance sampling—are added. The Fisher and Bayesian linear Gaussian models are studied in more detail. The First Edition emphasized continuous-time random processes. The Second Edition includes a comprehensive development of linear estimation of discrete-time random processes leading to discrete-time Wiener and Kalman filters. A brief introduction to Bayesian estimation of non-Gaussian processes is included. An expanded version of material from Part III develops optimum detectors for continuous-time and discrete-time random processes that can be implemented using Wiener or Kalman filters.

As imperative today as it has been since its original publication in 1968, this work is sure to remain the leading reference for engineers who need to apply detection and estimation theory in diverse systems.