Kalman Filtering

Mohinder S. Grewal, PhD, PE, is Professor of Electrical Engineering in the College of Engineering and Computer Science at California State University, Fullerton. He has more than forty years of experience in inertial navigation and control, and his mechanizations are currently used in commercial and military aircraft, surveillance satellites, missile and radar systems, freeway traffic control, and Global Navigation Satellite Systems.Angus P. Andrews, PhD, is an MIT graduate with a PhD in mathematics from UCLA.  His career in aerospace technology development spans more than 50 years, starting with navigation analysis for the Apollo moon missions, and including a dozen years in the analysis, design, development, and testing of inertial navigation systems.  His discoveries included the orbital navigation method called unknown landmark tracking, alternative solutions for square root filters, and a model for bearing torques of electrostatic gyroscopes.  Since retiring as a senior scientist from the Rockwell Science Center in 2000, he has continued consulting and instructing in sensor error modeling and analysis, and publishing articles and books on these subjects.

"The book "Kalman Filtering: Theory and practice with MATLAB" is a well-written text with modern ideas which are expressed in a rigorous and clear manner. It is also a professional reference on Kalman filtering: fully updated, revised, and expanded." (Zentralblatt MATH 2016)

• Preface to the Fourth Edition ixAcknowledgements xiiiList of Abbreviations xv1 Introduction 11.1 Chapter Focus 11.2 On Kalman Filtering 11.3 On Optimal Estimation Methods 61.4 Common Notation 281.5 Summary 30Problems 31References 342 Linear Dynamic Systems 372.1 Chapter Focus 372.2 Deterministic Dynamic System Models 422.3 Continuous Linear Systems and their Solutions 472.4 Discrete Linear Systems and their Solutions 592.5 Observability of Linear Dynamic System Models 612.6 Summary 66Problems 69References 713 Probability and Expectancy 733.1 Chapter Focus 733.2 Foundations of Probability Theory 743.3 Expectancy 793.4 Least-Mean-Square Estimate (LMSE) 873.5 Transformations of Variates 933.6 The Matrix Trace in Statistics 1023.7 Summary 106Problems 107References 1104 Random Processes 1114.1 Chapter Focus 1114.2 Random Variables Processes and Sequences 1124.3 Statistical Properties 1144.4 Linear Random Process Models 1244.5 Shaping Filters (SF) and State Augmentation 1314.6 Mean and Covariance Propagation 1354.7 Relationships Between Model Parameters 1454.8 Orthogonality Principle 1534.9 Summary 157Problems 159References 1675 Linear Optimal Filters and Predictors 1695.1 Chapter Focus 1695.2 Kalman Filter 1725.3 Kalman–Bucy Filter 1975.4 Optimal Linear Predictors 2005.5 Correlated Noise Sources 2005.6 Relationships Between Kalman and Wiener Filters 2015.7 Quadratic Loss Functions 2025.8 Matrix Riccati Differential Equation 2045.9 Matrix Riccati Equation in Discrete Time 2195.10 Model Equations for Transformed State Variables 2235.11 Sample Applications 2245.12 Summary 228Problems 232References 2356 Optimal Smoothers 2396.1 Chapter Focus 2396.2 Fixed-Interval Smoothing 2446.3 Fixed-Lag Smoothing 2566.4 Fixed-Point Smoothing 2686.5 Summary 275Problems 276References 2787 Implementation Methods 2817.1 Chapter Focus 2817.2 Computer Roundoff 2837.3 Effects of Roundoff Errors on Kalman Filters 2887.4 Factorization Methods for “Square-Root” Filtering 2947.5 “Square-Root” and UD Filters 3187.6 SigmaRho Filtering 3307.7 Other Implementation Methods 3467.8 Summary 358Problems 360References 3638 Nonlinear Approximations 3678.1 Chapter Focus 3678.2 The Affine Kalman Filter 3708.3 Linear Approximations of Nonlinear Models 3728.4 Sample-and-Propagate Methods 3988.5 Unscented Kalman Filters (UKF) 4048.6 Truly Nonlinear Estimation 4178.7 Summary 419Problems 420References 4239 Practical Considerations 4279.1 Chapter Focus 4279.2 Diagnostic Statistics and Heuristics 4289.3 Prefiltering and Data Rejection Methods 4579.4 Stability of Kalman Filters 4609.5 Suboptimal and Reduced-Order Filters 4619.6 Schmidt–Kalman Filtering 4719.7 Memory Throughput and Wordlength Requirements 4789.8 Ways to Reduce Computational Requirements 4869.9 Error Budgets and Sensitivity Analysis 4919.10 Optimizing Measurement Selection Policies 4959.11 Summary 501Problems 501References 50210 Applications to Navigation 50310.1 Chapter Focus 50310.2 Navigation Overview 50410.3 Global Navigation Satellite Systems (GNSS) 51010.4 Inertial Navigation Systems (INS) 54410.5 GNSS/INS Integration 57810.6 Summary 588Problems 590References 591Appendix A Software 593A.1 Appendix Focus 593A.2 Chapter 1 Software 594A.3 Chapter 2 Software 594A.4 Chapter 3 Software 595A.5 Chapter 4 Software 595A.6 Chapter 5 Software 596A.7 Chapter 6 Software 596A.8 Chapter 7 Software 597A.9 Chapter 8 Software 598A.10 Chapter 9 Software 599A.11 Chapter 10 Software 599A.12 Other Software Sources 601References 603Index 605