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Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook

Book Description

This book provides a complete explanation of estimation theory and application, modeling approaches, and model evaluation. Each topic starts with a clear explanation of the theory (often including historical context), followed by application issues that should be considered in the design. Different implementations designed to address specific problems are presented, and numerous examples of varying complexity are used to demonstrate the concepts.

This book is intended primarily as a handbook for engineers who must design practical systems. Its primary goal is to explain all important aspects of Kalman filtering and least-squares theory and application. Discussion of estimator design and model development is emphasized so that the reader may develop an estimator that meets all application requirements and is robust to modeling assumptions. Since it is sometimes difficult to a priori determine the best model structure, use of exploratory data analysis to define model structure is discussed. Methods for deciding on the "best" model are also presented.

A second goal is to present little known extensions of least squares estimation or Kalman filtering that provide guidance on model structure and parameters, or make the estimator more robust to changes in real-world behavior.

A third goal is discussion of implementation issues that make the estimator more accurate or efficient, or that make it flexible so that model alternatives can be easily compared.

The fourth goal is to provide the designer/analyst with guidance in evaluating estimator performance and in determining/correcting problems.

The final goal is to provide a subroutine library that simplifies implementation, and flexible general purpose high-level drivers that allow both easy analysis of alternative models and access to extensions of the basic filtering.

Table of Contents

  1. Cover
  2. About the Cover
  3. Title page
  4. Copyright page
  5. DEDICATION
  6. PREFACE
  7. CHAPTER 1 INTRODUCTION
    1. 1.1 THE FORWARD AND INVERSE MODELING PROBLEM
    2. 1.2 A BRIEF HISTORY OF ESTIMATION
    3. 1.3 FILTERING, SMOOTHING, AND PREDICTION
    4. 1.4 PREREQUISITES
    5. 1.5 NOTATION
    6. 1.6 SUMMARY
  8. CHAPTER 2 SYSTEM DYNAMICS AND MODELS
    1. 2.1 DISCRETE-TIME MODELS
    2. 2.2 CONTINUOUS-TIME DYNAMIC MODELS
    3. 2.3 COMPUTATION OF STATE TRANSITION AND PROCESS NOISE MATRICES
    4. 2.4 MEASUREMENT MODELS
    5. 2.5 SIMULATING STOCHASTIC SYSTEMS
    6. 2.6 COMMON MODELING ERRORS AND SYSTEM BIASES
    7. 2.7 SUMMARY
  9. CHAPTER 3 MODELING EXAMPLES
    1. 3.1 ANGLE-ONLY TRACKING OF LINEAR TARGET MOTION
    2. 3.2 MANEUVERING VEHICLE TRACKING
    3. 3.3 STRAPDOWN INERTIAL NAVIGATION SYSTEM (INS) ERROR MODEL
    4. 3.4 SPACECRAFT ORBIT DETERMINATION (OD)
    5. 3.5 FOSSIL-FUELED POWER PLANT
    6. 3.6 SUMMARY
  10. CHAPTER 4 LINEAR LEAST-SQUARES ESTIMATION: FUNDAMENTALS
    1. 4.1 LEAST-SQUARES DATA FITTING
    2. 4.2 WEIGHTED LEAST SQUARES
    3. 4.3 BAYESIAN ESTIMATION
    4. 4.4 PROBABILISTIC APPROACHES—MAXIMUM LIKELIHOOD AND MAXIMUM A POSTERIORI
    5. 4.5 SUMMARY OF LINEAR ESTIMATION APPROACHES
  11. CHAPTER 5 LINEAR LEAST-SQUARES ESTIMATION: SOLUTION TECHNIQUES
    1. 5.1 MATRIX NORMS, CONDITION NUMBER, OBSERVABILITY, AND THE PSEUDO-INVERSE
    2. 5.2 NORMAL EQUATION FORMATION AND SOLUTION
    3. 5.3 ORTHOGONAL TRANSFORMATIONS AND THE QR METHOD
    4. 5.4 LEAST-SQUARES SOLUTION USING THE SVD
    5. 5.5 ITERATIVE TECHNIQUES
    6. 5.6 COMPARISON OF METHODS
    7. 5.7 SOLUTION UNIQUENESS, OBSERVABILITY, AND CONDITION NUMBER
    8. 5.8 PSEUDO-INVERSES AND THE SINGULAR VALUE TRANSFORMATION (SVD)
    9. 5.9 SUMMARY
  12. CHAPTER 6 LEAST-SQUARES ESTIMATION: MODEL ERRORS AND MODEL ORDER
    1. 6.1 ASSESSING THE VALIDITY OF THE SOLUTION
    2. 6.2 SOLUTION ERROR ANALYSIS
    3. 6.3 REGRESSION ANALYSIS FOR WEIGHTED LEAST SQUARES
    4. 6.4 SUMMARY
  13. CHAPTER 7 LEAST-SQUARES ESTIMATION: CONSTRAINTS, NONLINEAR MODELS, AND ROBUST TECHNIQUES
    1. 7.1 CONSTRAINED ESTIMATES
    2. 7.2 RECURSIVE LEAST SQUARES
    3. 7.3 NONLINEAR LEAST SQUARES
    4. 7.4 ROBUST ESTIMATION
    5. 7.5 MEASUREMENT PREPROCESSING
    6. 7.6 SUMMARY
  14. CHAPTER 8 KALMAN FILTERING
    1. 8.1 DISCRETE-TIME KALMAN FILTER
    2. 8.2 EXTENSIONS OF THE DISCRETE FILTER
    3. 8.3 CONTINOUS-TIME KALMAN-BUCY FILTER
    4. 8.4 MODIFICATIONS OF THE DISCRETE KALMAN FILTER
    5. 8.5 STEADY-STATE SOLUTION
    6. 8.6 WIENER FILTER
    7. 8.7 SUMMARY
  15. CHAPTER 9 FILTERING FOR NONLINEAR SYSTEMS, SMOOTHING, ERROR ANALYSIS/MODEL DESIGN, AND MEASUREMENT PREPROCESSING
    1. 9.1 NONLINEAR FILTERING
    2. 9.2 SMOOTHING
    3. 9.3 FILTER ERROR ANALYSIS AND REDUCED-ORDER MODELING
    4. 9.4 MEASUREMENT PREPROCESSING
    5. 9.5 SUMMARY
  16. CHAPTER 10 FACTORED (SQUARE-ROOT) FILTERING
    1. 10.1 FILTER NUMERICAL ACCURACY
    2. 10.2 U-D FILTER
    3. 10.3 SQUARE ROOT INFORMATION FILTER (SRIF)
    4. 10.4 INERTIAL NAVIGATION SYSTEM (INS) EXAMPLE USING FACTORED FILTERS
    5. 10.5 LARGE SPARSE SYSTEMS AND THE SRIF
    6. 10.6 SPATIAL CONTINUITY CONSTRAINTS AND THE SRIF DATA EQUATION
    7. 10.7 SUMMARY
  17. CHAPTER 11 ADVANCED FILTERING TOPICS
    1. 11.1 MAXIMUM LIKELIHOOD PARAMETER ESTIMATION
    2. 11.2 ADAPTIVE FILTERING
    3. 11.3 JUMP DETECTION AND ESTIMATION
    4. 11.4 ADAPTIVE TARGET TRACKING USING MULTIPLE MODEL HYPOTHESES
    5. 11.5 CONSTRAINED ESTIMATION
    6. 11.6 ROBUST ESTIMATION: H-INFINITY FILTERS
    7. 11.7 UNSCENTED KALMAN FILTER (UKF)
    8. 11.8 PARTICLE FILTERS
    9. 11.9 SUMMARY
  18. CHAPTER 12 EMPIRICAL MODELING
    1. 12.1 EXPLORATORY TIME SERIES ANALYSIS AND SYSTEM IDENTIFICATION
    2. 12.2 SPECTRAL ANALYSIS BASED ON THE FOURIER TRANSFORM
    3. 12.3 AUTOREGRESSIVE MODELING
    4. 12.4 ARMA MODELING
    5. 12.5 CANONICAL VARIATE ANALYSIS
    6. 12.6 CONVERSION FROM DISCRETE TO CONTINUOUS MODELS
    7. 12.7 SUMMARY
  19. APPENDIX A SUMMARY OF VECTOR/MATRIX OPERATIONS
    1. A.1 DEFINITION
    2. A.2 ELEMENTARY VECTOR/MATRIX OPERATIONS
    3. A.3 MATRIX FUNCTIONS
    4. A.4 MATRIX TRANSFORMATIONS AND FACTORIZATION
  20. APPENDIX B PROBABILITY AND RANDOM VARIABLES
    1. B.1 PROBABILITY
    2. B.2 RANDOM VARIABLE
    3. B.3 STOCHASTIC PROCESSES
  21. BIBLIOGRAPHY
  22. Index