Kalman Filtering: with Real-Time Applications
This new edition presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering. Over 100 exercises and problems with solutions help deepen the knowledge. This new edition has a new chapter on filtering communication networks and data processing, together with new exercises and new real-time applications.
Why Read This Book
You will gain a clear, mathematically grounded understanding of Kalman filtering and its many practical variants, from basic discrete-time filters to wavelet and interval approaches for uncertain systems. The book mixes elementary but rigorous derivations with real-time radar-tracking examples so you can both follow the theory and see how algorithms behave in practice.
Who Will Benefit
Graduate students, signal-processing and controls engineers, and practitioners seeking a rigorous yet accessible treatment of Kalman filtering and its real-time applications (especially in radar and tracking).
Level: Advanced — Prerequisites: Linear algebra (matrix operations, eigenvalues), probability and stochastic processes (Gaussian processes, covariance), basic signals & systems/state-space modeling, differential equations, and some programming experience (MATLAB or Python helpful).
Key Takeaways
- Derive and implement the discrete-time Kalman filter using both direct step-by-step and innovation-projection methods
- Design and analyze Kalman filters for systems with correlated or colored noise and compute limiting gains for time-invariant systems
- Formulate and implement the extended Kalman filter for nonlinear state-space models and understand its approximation limits
- Apply interval Kalman filtering to handle model uncertainty and learn wavelet Kalman filtering for multiresolution analysis of random signals
- Evaluate numerical and real-time implementation issues through simplified radar-tracking examples and stability considerations
Topics Covered
- 1. Introduction and Historical Background
- 2. Mathematical Preliminaries: Matrices, Random Vectors, and State-Space Models
- 3. Derivation of the Discrete Kalman Filter — Direct Elementary Steps
- 4. Innovation-Projection Approach to Kalman Filtering
- 5. Kalman Filtering with Correlated and Colored Noise
- 6. Limiting Kalman Filter for Time-Invariant Systems and Steady-State Gains
- 7. Extended Kalman Filter and Nonlinear Estimation
- 8. Interval Kalman Filtering for Uncertain Systems
- 9. Wavelet Kalman Filtering and Multiresolution Analysis
- 10. Numerical Considerations, Real-Time Implementation, and Algorithmic Issues
- 11. Simplified Radar Tracking Examples and Case Studies
- 12. Appendices: Useful Identities, Proofs, and Implementation Notes
Languages, Platforms & Tools
How It Compares
Compared with Simon's Optimal State Estimation (practical code and implementation focus), Chui provides a more mathematical, derivation-driven presentation and, unlike Bar-Shalom et al.'s tracking-centric texts, gives broader coverage that includes interval and wavelet Kalman filtering.
