Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. A solutions manual is available for instructors. With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries. A solutions manual is available upon request from the Wiley editorial board.
Why Read This Book
You will learn how to design, analyze, and implement optimal state estimators—from classic Kalman filters to robust H-infinity and modern nonlinear methods—using a clear bottom-up presentation that builds from fundamentals to advanced topics. The book balances rigorous theory with practical guidance and application examples (radar, communications, audio/speech, and general DSP), so you can apply estimators confidently in real systems.
Who Will Benefit
Graduate students and practicing engineers in signal processing, radar, communications, control, and audio/speech who need to design and implement state estimators and robust filters.
Level: Intermediate — Prerequisites: Linear algebra (matrix operations, eigenvalues), probability and random processes, basic signals/systems or control theory, and familiarity with numerical computation (MATLAB or similar recommended).
Key Takeaways
- Implement and tune optimal linear estimators including discrete- and continuous-time Kalman filters and their steady-state forms
- Design robust H-infinity estimators and understand trade-offs between robustness and optimality
- Apply nonlinear estimation techniques such as the extended Kalman filter, sigma-point/unscented methods, and particle filters for real-world non-Gaussian, nonlinear problems
- Perform smoothing (e.g., RTS smoother) and fixed-lag/finite-window estimation to improve off-line or delayed estimates
- Analyze estimator performance, stability, observability, and numerical issues (information form, square-root filters, covariance management)
Topics Covered
- 1. Introduction and Motivation for State Estimation
- 2. Mathematical and Statistical Preliminaries
- 3. Linear State-Space Models and Problem Formulation
- 4. The Discrete Kalman Filter (Derivation and Properties)
- 5. Continuous-Time Kalman Filtering and Steady-State Solutions
- 6. Numerical Implementations: Information & Square-Root Filters
- 7. Performance, Stability, and Observability
- 8. H-infinity and Robust Filtering
- 9. The Extended Kalman Filter and Nonlinear Linearization
- 10. Sigma-Point and Unscented Filtering Methods
- 11. Particle Filters and Sequential Monte Carlo Techniques
- 12. Smoothing Algorithms and Fixed-Lag Estimation
- 13. Parameter Estimation and Adaptive Filtering
- 14. Practical Considerations and Applications (radar, communications, audio/speech, sensor fusion)
- 15. References and Further Reading
Languages, Platforms & Tools
How It Compares
Covers similar practical and modern material to Grewal & Andrews' Kalman Filtering but places more emphasis on nonlinear approaches and H-infinity methods; Gelb's Applied Optimal Estimation is a classic reference but is more historical and less focused on recent nonlinear/robust techniques.
