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System Parameter Identification

Book Description

Recently, criterion functions based on information theoretic measures (entropy, mutual information, information divergence) have attracted attention and become an emerging area of study in signal processing and system identification domain. This book presents a systematic framework for system identification and information processing, investigating system identification from an information theory point of view. The book is divided into six chapters, which cover the information needed to understand the theory and application of system parameter identification. The authors’ research provides a base for the book, but it incorporates the results from the latest international research publications.

  • Named a 2013 Notable Computer Book for Information Systems by Computing Reviews
  • One of the first books to present system parameter identification with information theoretic criteria so readers can track the latest developments
  • Contains numerous illustrative examples to help the reader grasp basic methods

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. About the Authors
  6. Preface
  7. Symbols and Abbreviations
  8. 1. Introduction
    1. 1.1 Elements of System Identification
    2. 1.2 Traditional Identification Criteria
    3. 1.3 Information Theoretic Criteria
    4. 1.4 Organization of This Book
    5. Appendix A Unifying Framework of ITL
  9. 2. Information Measures
    1. 2.1 Entropy
    2. 2.2 Mutual Information
    3. 2.3 Information Divergence
    4. 2.4 Fisher Information
    5. 2.5 Information Rate
    6. Appendix B -Stable Distribution
    7. Appendix C Proof of (2.17)
    8. Appendix D Proof of Cramer–Rao Inequality
  10. 3. Information Theoretic Parameter Estimation
    1. 3.1 Traditional Methods for Parameter Estimation
    2. 3.2 Information Theoretic Approaches to Classical Estimation
    3. 3.3 Information Theoretic Approaches to Bayes Estimation
    4. 3.4 Information Criteria for Model Selection
    5. Appendix E: EM Algorithm
    6. Appendix F: Minimum MSE Estimation
    7. Appendix G: Derivation of AIC Criterion
  11. 4. System Identification Under Minimum Error Entropy Criteria
    1. 4.1 Brief Sketch of System Parameter Identification
    2. 4.2 MEE Identification Criterion
    3. 4.3 Identification Algorithms Under MEE Criterion
    4. 4.4 Convergence Analysis
    5. 4.5 Optimization of -Entropy Criterion
    6. 4.6 Survival Information Potential Criterion
    7. 4.7 Δ-Entropy Criterion
    8. 4.8 System Identification with MCC
    9. Appendix H Vector Gradient and Matrix Gradient
  12. 5. System Identification Under Information Divergence Criteria
    1. 5.1 Parameter Identifiability Under KLID Criterion
    2. 5.2 Minimum Information Divergence Identification with Reference PDF
  13. 6. System Identification Based on Mutual Information Criteria
    1. 6.1 System Identification Under the MinMI Criterion
    2. 6.2 System Identification Under the MaxMI Criterion
    3. Appendix I MinMI Rate Criterion
  14. References