| Description |
1 online resource |
| Contents |
Intro -- Preface -- Contents -- About the Author -- Acronyms -- List of Figures -- List of Tables -- 1 Review of Probability Theory -- 1.1 Interpretations of Probability -- 1.2 Axiomatic Definition of Probability -- 1.3 Marginal Probability -- 1.4 Conditional Probability -- 1.5 Independence -- 1.6 Bayes' Theorem -- Bibliography -- 2 Random Variables -- 2.1 Mathematical Characterization of a Random Variable -- 2.2 Expectation of a Random Variable -- 2.3 Moments -- 2.3.1 Moment Generating Function and Characteristic Function -- 2.4 Normal or Gaussian Density -- 2.4.1 Right Tail Probability |
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2.5 Multiple Random Variables -- 2.5.1 Marginal Distributions -- 2.5.2 Conditional Probability Density -- 2.6 Correlation RX and Covariance CX -- 2.7 Multivariate Normal Distribution -- 2.7.1 Properties of Multivariate Normal -- 2.8 Transformation of Random Variables -- 2.8.1 Linear Transformation -- 2.8.2 Diagonalizing Transformation -- 2.8.3 Nonlinear Transformation -- 2.9 Pseudorandom Number Generators -- 2.9.1 True Random Number Generators -- 2.10 The Method of Moments -- Bibliography -- 3 Random Signals -- 3.1 Random Processes -- 3.1.1 Joint Densities -- 3.1.2 Gaussian Random Process |
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3.2 Autocorrelation -- 3.3 Stationary Random Process -- 3.4 Ergodic Random Processes -- 3.5 Properties of Autocorrelation -- 3.6 Cross-Correlation Function -- 3.6.1 Time Delay Estimation -- 3.7 Power Spectral Density Function (PSD) -- 3.7.1 Properties of the Power Spectral Density (PSD) -- 3.7.2 Cross-Spectral Density Function -- 3.8 Spectral Factorization -- 3.8.1 Continuous-Time Processes -- 3.8.2 Discrete-Time Processes -- 3.9 Examples of Stochastic Processes -- 3.9.1 Markov Processes -- Appendix 3.1 Brief Review of the Two-Sided Z-Transform -- Bibliography |
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4 Linear System Response to Random Inputs -- 4.1 Calculus for Random Signals -- 4.1.1 Continuity -- 4.2 Response to Random Input -- 4.3 Continuous-Time (CT) Random Signals -- 4.3.1 Mean Response -- 4.3.2 Stationary Steady-State Analysis for Continuous-Time Systems -- 4.3.3 Shaping (Innovations) Filter -- 4.4 Nonstationary Analysis for Continuous-Time Systems -- 4.4.1 Zero-Input Response -- 4.4.2 Forced (Zero-State) Response MIMO Time-Varying Case -- 4.4.3 Covariance Computation -- 4.5 Discrete-Time (DT) Random Signals -- 4.5.1 Mean Response |
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4.5.2 Stationary Steady-State Analysis for Discrete-Time Systems -- 4.5.3 Nonstationary Analysis for Discrete-Time Systems -- Bibliography -- 5 Estimation and Estimator Properties -- 5.1 Small Sample Properties -- 5.1.1 Unbiased Estimators -- 5.1.2 Efficiency -- 5.2 Large Sample Properties -- 5.2.1 Consistent Estimators -- 5.2.2 Asymptotic Efficiency -- 5.2.3 Asymptotic Normality -- 5.3 Random Sample -- 5.3.1 Sufficient Statistics -- 5.4 Estimation for the Autocorrelation and the Power Spectral Density -- 5.4.1 Autocorrelation Standard Estimate (ACS) -- 5.4.2 Periodogram -- References |
| Summary |
This book provides first-year graduate engineering students and practicing engineers with a solid introduction to random signals and estimation. It includes a statistical background that is often omitted in other textbooks but is essential for a clear understanding of estimators and their properties. The book emphasizes applicability rather than mathematical theory. It includes many examples and exercises to demonstrate and learn the theory that makes extensive use of MATLAB and its toolboxes. Although there are several excellent books on random signals and Kalman filtering, this book fulfills the need for a book that is suitable for a single-semester course that covers both random signals and Kalman filters and is used for a two-semester course for students that need remedial background. For students interested in more advanced studies in the area, the book provides a bridge between typical undergraduate engineering education and more advanced graduate-level courses |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed April 17, 2024) |
| Subject |
Stochastic processes.
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Estimation theory.
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Kalman filtering.
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| ISBN |
9789819980635 |
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9819980631 |
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