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
- About the Cover
- Title page
- Copyright page
- CHAPTER 1 INTRODUCTION
- CHAPTER 2 SYSTEM DYNAMICS AND MODELS
- CHAPTER 3 MODELING EXAMPLES
- CHAPTER 4 LINEAR LEAST-SQUARES ESTIMATION: FUNDAMENTALS
CHAPTER 5 LINEAR LEAST-SQUARES ESTIMATION: SOLUTION TECHNIQUES
- 5.1 MATRIX NORMS, CONDITION NUMBER, OBSERVABILITY, AND THE PSEUDO-INVERSE
- 5.2 NORMAL EQUATION FORMATION AND SOLUTION
- 5.3 ORTHOGONAL TRANSFORMATIONS AND THE QR METHOD
- 5.4 LEAST-SQUARES SOLUTION USING THE SVD
- 5.5 ITERATIVE TECHNIQUES
- 5.6 COMPARISON OF METHODS
- 5.7 SOLUTION UNIQUENESS, OBSERVABILITY, AND CONDITION NUMBER
- 5.8 PSEUDO-INVERSES AND THE SINGULAR VALUE TRANSFORMATION (SVD)
- 5.9 SUMMARY
- CHAPTER 6 LEAST-SQUARES ESTIMATION: MODEL ERRORS AND MODEL ORDER
- CHAPTER 7 LEAST-SQUARES ESTIMATION: CONSTRAINTS, NONLINEAR MODELS, AND ROBUST TECHNIQUES
- CHAPTER 8 KALMAN FILTERING
- CHAPTER 9 FILTERING FOR NONLINEAR SYSTEMS, SMOOTHING, ERROR ANALYSIS/MODEL DESIGN, AND MEASUREMENT PREPROCESSING
- CHAPTER 10 FACTORED (SQUARE-ROOT) FILTERING
CHAPTER 11 ADVANCED FILTERING TOPICS
- 11.1 MAXIMUM LIKELIHOOD PARAMETER ESTIMATION
- 11.2 ADAPTIVE FILTERING
- 11.3 JUMP DETECTION AND ESTIMATION
- 11.4 ADAPTIVE TARGET TRACKING USING MULTIPLE MODEL HYPOTHESES
- 11.5 CONSTRAINED ESTIMATION
- 11.6 ROBUST ESTIMATION: H-INFINITY FILTERS
- 11.7 UNSCENTED KALMAN FILTER (UKF)
- 11.8 PARTICLE FILTERS
- 11.9 SUMMARY
- CHAPTER 12 EMPIRICAL MODELING
- APPENDIX A SUMMARY OF VECTOR/MATRIX OPERATIONS
- APPENDIX B PROBABILITY AND RANDOM VARIABLES
- Title: Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook
- Release date: March 2011
- Publisher(s): Wiley
- ISBN: 9780470529706