nach oben

1994 | Buch | 2. Auflage

Kapitel lesen Erstes Kapitel lesen

An Introduction to Signal Detection and Estimation

verfasst von: H. Vincent Poor

Verlag: Springer New York

Buchreihe : Springer Texts in Electrical Engineering

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten

Über dieses Buch

The 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.

Inhaltsverzeichnis

Frontmatter

I. Introduction

Abstract

Generally speaking, signal detection and estimation is the area of study that deals with the processing of information-bearing signals for the purpose of extracting information from them. Applications of the theory of signal detection and estimation are found in many areas, such as communications and automatic control. For example, in communications applications such as data transmission or radar, detection and estimation provides the theoretical and analytical basis for the design of effective communication receivers. Alternatively, in automatic control applications, detection and estimation theory leads to techniques for making accurate inferences concerning the conditions present in a process or system to be controlled.

H. Vincent Poor

II. Elements of Hypothesis Testing

Abstract

Most signal detection problems can be cast in the framework of M-ary hypothesis testing,in which we have an observation (possibly a vector or function) on the basis of which we wish to decide among M possible statistical situations describing the observations. For example, in an M-ary communications receiver we observe an electrical waveform that consists of one of M possible signals corrupted by random channel or receiver noise, and we wish to decide which of the M possible signals is present. Obviously, for any given decision problem, there are a number of possible decision strategies or rules that could be applied; however, we would like to choose a decision rule that is optimum in some sense. There are several useful definitions of optimality for such problems, and in this chapter we consider the three most common formulations—Bayes, minimax, and Neyman-Pearson—and derive the corresponding optimum solutions. In general, we consider the particular problem of binary (M = 2) hypothesis testing, although the extension of many of the results of this chapter to the general M-ary case is straightforward and will be developed in the exercises. The application of this theory to those models specific to signal detection is considered in detail in Chapters III and VI.

H. Vincent Poor

III. Signal Detection in Discrete Time

Abstract

In Chapter II we discussed several basic optimality criteria and design methods for binary hypothesis-testing problems. In this chapter we apply these and related methods to derive optimum procedures for detecting signals embedded in noise. To avoid analytical complications, we consider exclusively the case of discrete-time detection, leaving the continuous-time case for Chapter VI. The discrete-time case is of considerable practical interest due to the predominance of digital implementations for signal processing functions.

H. Vincent Poor

IV. Elements of Parameter Estimation

Abstract

In Chapters II and III we have considered the design of optimum procedures for deciding between two possible statistical situations on the basis of a random observation Y. In many situations arising in practice we are interested not in making a choice between two (or among several) discrete situations, but rather in making a choice among a continuum of possible states of nature. In particular, as in the composite hypothesis-testing problems discussed in Chapter II, we can think of a family of distributions on the observation space, indexed by a parameter or set of parameters. But unlike the case of composite hypothesis testing in which we wish to make a binary decision about the parameter, we wish here to determine as accurately as possible the actual value of the parameter from the observation.

H. Vincent Poor

V. Elements of Signal Estimation

Abstract

In Chapter IV we discussed methods for designing estimators for static parameters, that is, for parameters that are not changing with time. In many applications we are interested in the related problem of estimating dynamic or time-varying parameters. In the traditional terminology, a dynamic parameter is usually called a signal, so the latter problem is known as signal estimation or tracking.

H. Vincent Poor

VI. Signal Detection in Continuous Time

Abstract

In the preceding chapters we have presented the basic principles of signal detection and estimation, assuming throughout that our observation set is either a set of vectors or is a discrete set. Throughout this analysis a key role was played by a family of densities {_pθ; θ ∈ Λ} on the observation space, either through the likelihood ratio in hypothesis testing, through the computation of an a posteriori parameter distribution in Bayesian estimation, or through the study of MVUEs and MLEs in nonBayesian parameter estimation. This necessity of specifying a family of densities on the observation space is the primary reason for restricting our observation sets in the way that we have done. In particular, all the problems considered thus far have been treated using the ordinary probability calculus of probability density functions and probability mass functions.¹

H. Vincent Poor

VII. Signal Estimation in Continuous Time

Abstract

In Chapter VI we treated the problem of signal detection with continuous-time observations. In this chapter we consider the problem of signal estimation in continuous time. We treat three basic problems: parameter estimation for signals of known form (up to a set of unknown parameters) observed in additive Gaussian noise; linear/Gaussian estimation in which either we assume that the signals and noise of interest are Gaussian processes or we restrict attention to linear estimators; and nonlinear filtering, in which we derive estimators for non-Gaussian random signals generated by nonlinear differential equations when observed in additive Gaussian noise. In all cases, we consider primarily the case of white Gaussian noise, although as we have seen in Chapter VI, other Gaussian noise models can be transformed to this model, so that these results are more general.

H. Vincent Poor

Backmatter

Titel: An Introduction to Signal Detection and Estimation
verfasst von: H. Vincent Poor
Verlag: Springer New York
Electronic ISBN: 978-1-4757-2341-0
Print ISBN: 978-1-4419-2837-5
DOI: https://doi.org/10.1007/978-1-4757-2341-0

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

I. Introduction

II. Elements of Hypothesis Testing

III. Signal Detection in Discrete Time

IV. Elements of Parameter Estimation

V. Elements of Signal Estimation

VI. Signal Detection in Continuous Time

VII. Signal Estimation in Continuous Time

Backmatter