Ebook
Advanced Kalman Filtering, LeastSquares and Modeling: A Practical HandbookISBN: 9781118003169
640 pages
March 2011

Its primary goal is to discuss model development in sufficient detail so that the reader may design 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 realworld 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 highlevel
drivers that allow both easy analysis of alternative models and
access to extensions of the basic filtering.
Supplemental materials and uptodate errata are downloadable at http://booksupport.wiley.com.
1 INTRODUCTION.
1.1 The Forward and Inverse Modeling Problem.
1.2 A Brief History of Estimation.
1.3 Filtering, Smoothing, and Prediction.
1.4 Prerequisites.
1.5 Notation.
1.6 Summary.
2 SYSTEM DYNAMICS AND MODELS.
2.1 DiscreteTime Models.
2.2 ContinuousTime Dynamic Models.
2.3 Computation of State Transition and Process Noise Matrices.
2.4 Measurement Models.
2.5 Simulating Stochastic Systems.
2.6 Common Modeling Errors and System Biases.
2.7 Summary.
3 MODELING EXAMPLES.
3.1 AngleOnly Tracking of Linear Target Motion.
3.2 Maneuvering Vehicle Tracking.
3.3 Strapdown Inertial Navigation System (INS) Error Model.
3.4 Spacecraft Orbit Determination (OD).
3.5 FossilFueled Power Plant.
3.6 Summary.
4 LINEAR LEASTSQUARES ESTIMATION: FUNDAMENTALS.
4.1 LeastSquares Data Fitting.
4.2 Weighted Least Squares.
4.3 Bayesian Estimation.
4.4 Probabilistic Approaches—Maximum Likelihood and Maximum A Posteriori.
4.5 Summary of Linear Estimation Approaches.
5 LINEAR LEASTSQUARES ESTIMATION: SOLUTION TECHNIQUES.
5.1 Matrix Norms, Condition Number, Observability, and the PseudoInverse.
5.2 Normal Equation Formation and Solution.
5.3 Orthogonal Transformations and the QR Method.
5.4 LeastSquares Solution Using the SVD.
5.5 Iterative Techniques.
5.6 Comparison of Methods.
5.7 Solution Uniqueness, Observability, and Condition Number.
5.8 PseudoInverses and the Singular Value Transformation (SVD).
5.9 Summary.
6 LEASTSQUARES ESTIMATION: MODEL ERRORS AND MODEL ORDER.
6.1 Assessing the Validity of the Solution.
6.2 Solution Error Analysis.
6.3 Regression Analysis for Weighted Least Squares.
6.4 Summary.
7 LEASTSQUARES ESTIMATION: CONSTRAINTS, NONLINEAR MODELS, AND ROBUST TECHNIQUES.
7.1 Constrained Estimates.
7.1.1 LeastSquares with Linear Equality Constraints (Problem LSE).
7.1.2 LeastSquares with Linear Inequality Constraints (Problem LSI).
7.2 Recursive Least Squares.
7.3 Nonlinear Least Squares.
7.4 Robust Estimation.
7.5 Measurement Preprocessing.
7.6 Summary.
8 KALMAN FILTERING.
8.1 DiscreteTime Kalman Filter.
8.2 Extensions of the Discrete Filter.
8.3 ContinousTime KalmanBucy Filter.
8.4 Modifi cations of the Discrete Kalman Filter.
8.5 SteadyState Solution.
8.6 Wiener Filter.
8.7 Summary.
9 FILTERING FOR NONLINEAR SYSTEMS, SMOOTHING, ERROR ANALYSIS/MODEL DESIGN, AND MEASUREMENT PREPROCESSING.
9.1 Nonlinear Filtering.
9.2 Smoothing.
9.3 Filter Error Analysis and ReducedOrder Modeling.
9.4 Measurement Preprocessing.
9.5 Summary.
10 FACTORED (SQUAREROOT) FILTERING.
10.1 Filter Numerical Accuracy.
10.2 UD Filter.
10.3 Square Root Information Filter (SRIF).
10.4 Inertial Navigation System (INS) Example Using Factored Filters.
10.5 Large Sparse Systems and the SRIF.
10.6 Spatial Continuity Constraints and the SRIF Data Equation.
10.7 Summary.
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: HInfinity Filters.
11.7 Unscented Kalman Filter (UKF).
11.8 Particle Filters.
11.9 Summary.
12 EMPIRICAL MODELING .
12.1 Exploratory Time Series Analysis and System Identification.
12.2 Spectral Analysis Based on the Fourier Transform.
12.3 Autoregressive Modeling.
12.4 ARMA Modeling.
12.5 Canonical Variate Analysis.
12.6 Conversion from Discrete to Continuous Models.
12.7 Summary.
APPENDIX A SUMMARY OF VECTOR/MATRIX OPERATIONS.
APPENDIX B PROBABILITY AND RANDOM VARIABLES.
BIBLIOGRAPHY.
INDEX.

Discusses model development in sufficient detail so that the reader may design an estimator that meets all application requirements and is robust to modeling assumptions.

Presents methods for deciding on the "best" model

Presents little known extensions of least squares estimation or Kalman filtering that provide guidance on model structure and parameters

Discusses implementation issues that make the estimator more accurate or efficient, or that make it flexible so that model alternatives can be easily compared.

Provides a subroutine library that simplifies implementation, and flexible general purpose highlevel drivers that allow both easy analysis of alternative models and access to extensions of the basic filtering