An Introduction to Signal Detection and EstimationThe purpose of this book is to introduce the reader to the basic theory of signal detection and estimation. It is assumed that the reader has a working knowledge of applied probability and random processes such as that taught in a typical first-semester graduate engineering course on these subjects. This material is covered, for example, in the book by Wong (1983) in this series. More advanced concepts in these areas are introduced where needed, primarily in Chapters VI and VII, where continuous-time problems are treated. This book is adapted from a one-semester, second-tier graduate course taught at the University of Illinois and at Princeton University. However, this material can also be used for a shorter or first-tier course by restricting coverage to Chapters I through V, which for the most part can be read with a background of only the basics of applied probability, including random vectors and conditional expectations. Sufficient background for the latter option is given for example in the book by Thomas (1986), also in this series. This treatment is also suitable for use as a text in other modes. For example, two smaller courses, one in signal detection (Chapters II, III, and VI) and one in estimation (Chapters IV, V, and VII), can be taught from the materials as organized here. Similarly, an introductory-level course (Chapters I through IV) followed by a more advanced course (Chapters V through VII) is another possibility. |
Contents
II | 1 |
III | 5 |
IV | 13 |
V | 22 |
VI | 29 |
VII | 39 |
VIII | 45 |
IX | 82 |
XXXI | 233 |
XXXII | 234 |
XXXIII | 239 |
XXXIV | 258 |
XXXV | 263 |
XXXVI | 264 |
XXXVIII | 272 |
XXXIX | 278 |
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Common terms and phrases
a-level applications approximate assume assumption asymptotic autocovariance Bayes estimate Bayes risk bound causal Chapter Chernoff bound compute consider continuous-time converges covariance Cramér-Rao lower bound decision rule defined denote derived detection problem discrete-time discussed distribution equivalent error probabilities estimation problems example finite function Gaussian noise Gaussian random given H₁ hypothesis pair hypothesis testing implies independent integral Kalman Kalman-Bucy filter likelihood equation likelihood ratio likelihood ratio test linear estimator log pe(y MAP estimate matrix mean-square measure minimax MMSE MMSE estimate MVUE Neyman-Pearson nonlinear Note observation optimum detector orthogonal P₁ parameter particular Po(y prior Proposition quantity random process random variables recursion result Section sequence signal detection solution SPRT stochastic straightforward sufficient statistic Suppose term theorem threshold tion variance versus H₁ white noise Wiener process Wiener-Hopf equation Wiener-Kolmogorov Y₁ zero zero-mean