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 xvPreface to the First Edition xix1 Introduction 11.1 Introduction 11.2 Topical Outline 11.3 Possible Approaches 111.4 Organization 142 Classical Detection Theory 172.1 Introduction 172.2 Simple Binary Hypothesis Tests 202.3 M Hypotheses 512.4 Performance Bounds and Approximations 632.5 Monte Carlo Simulation 802.6 Summary 1092.7 Problems 1103 General Gaussian Detection 1253.1 Detection of Gaussian Random Vectors 1263.2 Equal Covariance Matrices 1383.3 Equal Mean Vectors 1743.4 General Gaussian 1973.5 M Hypotheses 2093.6 Summary 2133.7 Problems 2154 Classical Parameter Estimation 2304.1 Introduction 2304.2 Scalar Parameter Estimation 2324.3 Multiple Parameter Estimation 2934.4 Global Bayesian Bounds 3324.5 Composite Hypotheses 3484.6 Summary 3754.7 Problems 3775 General Gaussian Estimation 4005.1 Introduction 4005.2 Nonrandom Parameters 4015.3 Random Parameters 4835.4 Sequential Estimation 4955.5 Summary 5075.6 Problems 5106 Representation of Random Processes 5196.1 Introduction 5196.2 Orthonormal Expansions: Deterministic Signals 5206.3 Random Process Characterization 5286.4 Homogeous Integral Equations and Eigenfunctions 5406.5 Vector Random Processes 5646.6 Summary 5686.7 Problems 5697 Detection of Signals-Estimation of Signal Parameters 5847.1 Introduction 5847.2 Detection and Estimation in White Gaussian Noise 5917.3 Detection and Estimation in Nonwhite Gaussian Noise 6297.4 Signals with Unwanted Parameters: The Composite Hypothesis Problem 6757.5 Multiple Channels 7127.6 Multiple Parameter Estimation 7167.7 Summary 7217.8 Problems 7228 Estimation of Continuous-Time Random Processes 7718.1 Optimum Linear Processors 7718.2 Realizable Linear Filters: Stationary Processes, Infinite Past: Wiener Filters 7878.3 Gaussian-Markov Processes: Kalman Filter 8078.4 Bayesian Estimation of Non-Gaussian Models 8428.5 Summary 8528.6 Problems 8559 Estimation of Discrete-Time Random Processes 8809.1 Introduction 8809.2 Discrete-Time Wiener Filtering 8829.3 Discrete-Time Kalman Filter 9199.4 Summary 10169.5 Problems 101610 Detection of Gaussian Signals 103010.1 Introduction 103010.2 Detection of Continuous-Time Gaussian Processes 103010.3 Detection of Discrete-Time Gaussian Processes 106710.4 Summary 107610.5 Problems 107711 Epilogue 108411.1 Classical Detection and Estimation Theory 108411.2 Representation of Random Processes 109311.3 Detection of Signals and Estimation of Signal Parameters 109511.4 Linear Estimation of Random Processes 109811.5 Observations 110511.6 Conclusion 1106Appendix A: Probability Distributions and Mathematical Functions 1107Appendix B: Example Index 1119References 1125Index 1145