Model Identification and Data Analysis

Model Identification and Data Analysis

by Sergio Bittanti
Released April 2019
Publisher(s): Wiley
ISBN: 9781119546368

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Book description

This book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control.

Written for graduate students, this textbook offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University.

The book:

  • Contains accessible methods explained step-by-step in simple terms
  • Offers an essential tool useful in a variety of fields, especially engineering, statistics, and mathematics
  • Includes an overview on random variables and stationary processes, as well as an introduction to discrete time models and matrix analysis
  • Incorporates historical commentaries to put into perspective the developments that have brought the discipline to its current state
  • Provides many examples and solved problems to complement the presentation and facilitate comprehension of the techniques presented

Table of contents

  1. Cover
  2. Introduction
  3. Acknowledgments
  4. 1 Stationary Processes and Time Series
    1. 1.1 Introduction
    2. 1.2 The Prediction Problem
    3. 1.3 Random Variable
    4. 1.4 Random Vector
    5. 1.5 Stationary Process
    6. 1.6 White Process
    7. 1.7 MA Process
    8. 1.8 AR Process
    9. 1.9 Yule–Walker Equations
    10. 1.10 ARMA Process
    11. 1.11 Spectrum of a Stationary Process
    12. 1.12 ARMA Model: Stability Test and Variance Computation
    13. 1.13 Fundamental Theorem of Spectral Analysis
    14. 1.14 Spectrum Drawing
    15. 1.15 Proof of the Fundamental Theorem of Spectral Analysis
    16. 1.16 Representations of a Stationary Process
  5. 2 Estimation of Process Characteristics
    1. 2.1 Introduction
    2. 2.2 General Properties of the Covariance Function
    3. 2.3 Covariance Function of ARMA Processes
    4. 2.4 Estimation of the Mean
    5. 2.5 Estimation of the Covariance Function
    6. 2.6 Estimation of the Spectrum
    7. 2.7 Whiteness Test
  6. 3 Prediction
    1. 3.1 Introduction
    2. 3.2 Fake Predictor
    3. 3.3 Spectral Factorization
    4. 3.4 Whitening Filter
    5. 3.5 Optimal Predictor from Data
    6. 3.6 Prediction of an ARMA Process
    7. 3.7 ARMAX Process
    8. 3.8 Prediction of an ARMAX Process
  7. 4 Model Identification
    1. 4.1 Introduction
    2. 4.2 Setting the Identification Problem
    3. 4.3 Static Modeling
    4. 4.4 Dynamic Modeling
    5. 4.5 External Representation Models
    6. 4.6 Internal Representation Models
    7. 4.7 The Model Identification Process
    8. 4.8 The Predictive Approach
    9. 4.9 Models in Predictive Form
  8. 5 Identification of Input–Output Models
    1. 5.1 Introduction
    2. 5.2 Estimating AR and ARX Models: The Least Squares Method
    3. 5.3 Identifiability
    4. 5.4 Estimating ARMA and ARMAX Models
    5. 5.5 Asymptotic Analysis
    6. 5.6 Recursive Identification
    7. 5.7 Robustness of Identification Methods
    8. 5.8 Parameter Tracking
  9. 6 Model Complexity Selection
    1. 6.1 Introduction
    2. 6.2 Cross‐validation
    3. 6.3 FPE Criterion
    4. 6.4 AIC Criterion
    5. 6.5 MDL Criterion
    6. 6.6 Durbin–Levinson Algorithm
  10. 7 Identification of State Space Models
    1. 7.1 Introduction
    2. 7.2 Hankel Matrix
    3. 7.3 Order Determination
    4. 7.4 Determination of Matrices and
    5. 7.5 Determination of Matrix
    6. 7.6 Mid Summary: An Ideal Procedure
    7. 7.7 Order Determination with SVD
    8. 7.8 Reliable Identification of a State Space Model
  11. 8 Predictive Control
    1. 8.1 Introduction
    2. 8.2 Minimum Variance Control
    3. 8.3 Generalized Minimum Variance Control
    4. 8.4 Model‐Based Predictive Control
    5. 8.5 Data‐Driven Control Synthesis
  12. 9 Kalman Filtering and Prediction
    1. 9.1 Introduction
    2. 9.2 Kalman Approach to Prediction and Filtering Problems
    3. 9.3 The Bayes Estimation Problem
    4. 9.4 One‐step‐ahead Kalman Predictor
    5. 9.5 Multistep Optimal Predictor
    6. 9.6 Optimal Filter
    7. 9.7 Steady‐State Predictor
    8. 9.8 Innovation Representation
    9. 9.9 Innovation Representation Versus Canonical Representation
    10. 9.10 K‐Theory Versus K–W Theory
    11. 9.11 Extended Kalman Filter – EKF
    12. 9.12 The Robust Approach to Filtering
  13. 10 Parameter Identification in a Given Model
    1. 10.1 Introduction
    2. 10.2 Kalman Filter‐Based Approaches
    3. 10.3 Two‐Stage Method
  14. 11 Case Studies
    1. 11.1 Introduction
    2. 11.2 Kobe Earthquake Data Analysis
    3. 11.3 Estimation of a Sinusoid in Noise
  15. Appendix A: Linear Dynamical Systems
    1. A.1 State Space and Input–Output Models
    2. A.2 Lagrange Formula
    3. A.3 Stability
    4. A.4 Impulse Response
    5. A.5 Frequency Response
    6. A.6 Multiplicity of State Space Models
    7. A.7 Reachability and Observability
    8. A.8 System Decomposition
    9. A.9 Stabilizability and Detectability
  16. Appendix B: Matrices
    1. B.1 Basics
    2. B.2 Eigenvalues
    3. B.3 Determinant and Inverse
    4. B.4 Rank
    5. B.5 Annihilating Polynomial
    6. B.6 Algebraic and Geometric Multiplicity
    7. B.7 Range and Null Space
    8. B.8 Quadratic Forms
    9. B.9 Derivative of a Scalar Function with Respect to a Vector
    10. B.10 Matrix Diagonalization via Similarity
    11. B.11 Matrix Diagonalization via Singular Value Decomposition
    12. B.12 Matrix Norm and Condition Number
  17. Appendix C: Problems and Solutions
  18. Bibliography
    1. Further reading
  19. Index
  20. End User License Agreement

Product information

  • Title: Model Identification and Data Analysis
  • Author(s): Sergio Bittanti
  • Release date: April 2019
  • Publisher(s): Wiley
  • ISBN: 9781119546368