Fundamentals of Kalman Filtering (Progress in Aeronautics and Astronautics)
In 2008 the National Academy of Engineering awarded Rudolf Kalman the Charles Stark Draper Prize--the engineering equivalent of the Nobel Prize -- for the development and dissemination of the optimal digital technique (known as the Kalman Filter) that is pervasively used to control a vast array of consumer, health, commercial, and defense products. Fundamentals of Kalman Filtering, Fourth Edition is a practical guide to building Kalman filters that shows how the filtering equations can be applied to real-life problems. Numerous examples are presented in detail, showing the many ways in which Kalman filters can be designed. For this edition, source code listings appearing in the text have been converted from FORTRAN to MATLAB(R). In addition, both FORTRAN and MATLAB* source code are available electronically for all of the examples so that the interested reader can verify concepts and explore issues beyond the scope of the text. In certain instances, the authors intentionally introduce mistakes to the initial filter designs to show the reader what happens when the filter is not working properly. The text carefully sets up a problem before the Kalman filter is actually formulated, to give the reader an intuitive feel for the problem being addressed. Because real problems are seldom presented as differential equations, and usually do not have unique solutions, the authors illustrate several different filtering approaches. Readers will gain experience in software and performance tradeoffs for determining the best filtering approach. The fourth edition features four new chapters presenting the following techniques: the State Dependent Ricatti Equation Filter (SDRE), the Unscented Kalman Filter (UKF), the Interactive Multiple Model (IMM) Filter Bank, and the Cramer-Rao lower bound (CRLB), for finding the best that a filter can perform.
Why Read This Book
You will get a hands‑on, practical road map for building, tuning, and debugging Kalman filters for real engineering problems — from navigation and radar tracking to communications and sensor fusion. The book couples clear derivations with numerous worked examples and MATLAB/FORTRAN code so you can move quickly from theory to implementation.
Who Will Benefit
Practicing engineers and graduate students in aerospace, radar, navigation, control, and signal processing who need to implement state estimation and sensor fusion in real systems.
Level: Intermediate — Prerequisites: Familiarity with linear algebra (matrices, eigenvalues), basic probability/statistics, linear systems/state‑space models, and some programming experience (MATLAB recommended).
Key Takeaways
- Derive and implement discrete and continuous Kalman filters for linear state‑space systems.
- Design and tune practical filters for navigation, radar tracking, and communications using real measurement models and noise covariance selection.
- Apply and implement the Extended Kalman Filter (EKF) for weakly nonlinear systems and understand linearization pitfalls.
- Evaluate filter performance through covariance propagation, innovations analysis, smoothing, and consistency checks.
- Translate algorithm descriptions into working MATLAB or FORTRAN code and diagnose numerical/implementation issues (stability, ill‑conditioning, discretization).
Topics Covered
- 1. Introduction and historical perspective on Kalman filtering
- 2. Review of linear algebra, probability, and state‑space models
- 3. Derivation of the discrete‑time Kalman filter
- 4. Continuous‑time Kalman‑Bucy filter and discrete approximations
- 5. Steady‑state filters and algebraic Riccati equations
- 6. Implementation issues: numerical stability, discretization, and covariance handling
- 7. Measurement models, process and measurement noise modeling, and tuning
- 8. Extended Kalman filter and nonlinear filtering techniques
- 9. Smoothing, batch processing, and fixed‑interval/lag estimators
- 10. Practical examples: navigation, radar tracking, and communications applications
- 11. Troubleshooting, innovations testing, and consistency checks
- 12. Source code appendices: MATLAB and FORTRAN listings
Languages, Platforms & Tools
How It Compares
Complementary to Grewal & Andrews' 'Kalman Filtering: Theory and Practice Using MATLAB' (more textbook‑style and extensive coverage), and Dan Simon's 'Optimal State Estimation' (more modern MATLAB examples and probabilistic perspective); Zarchan is particularly strong on practical engineering examples and legacy FORTRAN/MATLAB implementations.
