Fundamentals of Kalman Filtering: A Practical Approach (Progress in Astronautics and Aeronautics, 232)
This 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. Computer code written in FORTRAN, MATLAB[registered], and True BASIC accompanies 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 material that has been added to this edition is in response to questions and feedback from readers. The third edition has three new chapters on unusual topics related to Kalman filtering and other filtering techniques based on the method of least squares. Chapter 17 presents a type of filter known as the fixed or finite memory filter, which only remembers a finite number of measurements from the past. Chapter 18 shows how the chain rule from calculus can be used for filter initialization or to avoid filtering altogether. A realistic three-dimensional GPS example is used to illustrate the chain-rule method for filter initialization. Finally, Chapter 19 shows how a bank of linear sine-wave Kalman filters, each one tuned to a different sine-wave frequency, can be used to estimate the actual frequency of noisy sinusoidal measurements and obtain estimates of the states of the sine wave when the measurement noise is low.
Why Read This Book
You will learn how to take Kalman filtering theory off the page and make working estimators for real systems — from navigation and tracking to sensor fusion — using clear, example-driven instruction. The book’s many worked examples, accompanied by FORTRAN, MATLAB, and True BASIC code (and even intentionally flawed designs), give you the diagnostics and practical tuning experience needed to get filters to behave in the field.
Who Will Benefit
Engineers and applied researchers in navigation, radar, communications, and signal processing who need to design, implement, tune, and troubleshoot Kalman filters for real systems.
Level: Intermediate — Prerequisites: Familiarity with linear algebra (matrices, eigenvalues), probability and stochastic processes, basic control/state-space models, and comfort reading or writing code (MATLAB or another procedural language).
Key Takeaways
- Formulate state-space models and cast practical estimation problems into Kalman filter form.
- Implement discrete- and continuous-time Kalman filters and extended variants from provided pseudocode and examples.
- Tune process and measurement noise covariances and use diagnostics to detect and remedy filter divergence.
- Diagnose implementation pitfalls using intentionally flawed examples and learn robust numerical practices.
- Apply Kalman filtering to aerospace examples (tracking, navigation, sensor fusion) and similar engineering problems.
- Use provided FORTRAN, MATLAB, and True BASIC code as starting points for your own filter development and validation.
Topics Covered
- Introduction and Motivation — Practical Estimation Problems
- Review of Linear Systems and Stochastic Models
- Derivation of the Kalman Filter — Continuous and Discrete Forms
- Implementation Details and Numerical Stability
- Filter Tuning, Covariance Analysis, and Diagnostics
- Extended Kalman Filter and Nonlinear Extensions
- Smoothing and Batch Estimation Techniques
- Tracking, Navigation, and Sensor Fusion Examples
- Troubleshooting: Common Mistakes and Their Effects
- Worked Examples with FORTRAN, MATLAB, and True BASIC Code
- Advanced Topics: Discrete vs. Continuous Considerations, Initialization
- Appendices: Reference Material, Linear Algebra, and Code Listings
Languages, Platforms & Tools
How It Compares
More example- and implementation-focused than theory-first texts like Grewal & Andrews' Kalman Filtering, and more application-oriented than Dan Simon's Optimal State Estimation, making Zarchan especially useful if you want hands-on filter design and debugging guidance.
