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by Bruce P. Gibbs
Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook
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DEDICATION
PREFACE
CHAPTER 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
CHAPTER 2 SYSTEM DYNAMICS AND MODELS
2.1 DISCRETE-TIME MODELS
2.2 CONTINUOUS-TIME 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
CHAPTER 3 MODELING EXAMPLES
3.1 ANGLE-ONLY 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 FOSSIL-FUELED POWER PLANT
3.6 SUMMARY
CHAPTER 4 LINEAR LEAST-SQUARES ESTIMATION: FUNDAMENTALS
4.1 LEAST-SQUARES 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
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
6.1 ASSESSING THE VALIDITY OF THE SOLUTION
6.2 SOLUTION ERROR ANALYSIS
6.3 REGRESSION ANALYSIS FOR WEIGHTED LEAST SQUARES
6.4 SUMMARY
CHAPTER 7 LEAST-SQUARES ESTIMATION: CONSTRAINTS, NONLINEAR MODELS, AND ROBUST TECHNIQUES
7.1 CONSTRAINED ESTIMATES
7.2 RECURSIVE LEAST SQUARES
7.3 NONLINEAR LEAST SQUARES
7.4 ROBUST ESTIMATION
7.5 MEASUREMENT PREPROCESSING
7.6 SUMMARY
CHAPTER 8 KALMAN FILTERING
8.1 DISCRETE-TIME KALMAN FILTER
8.2 EXTENSIONS OF THE DISCRETE FILTER
8.3 CONTINOUS-TIME KALMAN-BUCY FILTER
8.4 MODIFICATIONS OF THE DISCRETE KALMAN FILTER
8.5 STEADY-STATE SOLUTION
8.6 WIENER FILTER
8.7 SUMMARY
CHAPTER 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 REDUCED-ORDER MODELING
9.4 MEASUREMENT PREPROCESSING
9.5 SUMMARY
CHAPTER 10 FACTORED (SQUARE-ROOT) FILTERING
10.1 FILTER NUMERICAL ACCURACY
10.2 U-D 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
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
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
A.1 DEFINITION
A.2 ELEMENTARY VECTOR/MATRIX OPERATIONS
A.3 MATRIX FUNCTIONS
A.4 MATRIX TRANSFORMATIONS AND FACTORIZATION
APPENDIX B PROBABILITY AND RANDOM VARIABLES
B.1 PROBABILITY
B.2 RANDOM VARIABLE
B.3 STOCHASTIC PROCESSES
BIBLIOGRAPHY
Index
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