Bayesian Filtering and Smoothing (Institute of Mathematical Statistics Textbooks, Series Number 3)
Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.
Why Read This Book
You will get a compact, mathematically clear introduction to modern Bayesian state estimation that unifies Kalman-type filters, particle filters, and smoothing in one framework. The book emphasizes practical algorithms, trade-offs, and when to prefer analytic Gaussian approximations versus sampling-based sequential Monte Carlo methods, so you can apply the right filter to tracking, communications, or audio/speech problems.
Who Will Benefit
Graduate students, advanced undergraduates, and practicing engineers in signal processing, communications, or navigation who need a rigorous but practical treatment of Bayesian filtering and smoothing for time-series and state-space models.
Level: Advanced — Prerequisites: Probability and stochastic processes, linear algebra, multivariable calculus, and basic familiarity with state-space models or the Kalman filter; programming experience helpful for implementing algorithms.
Key Takeaways
- Implement the linear-Gaussian Kalman filter and Rauch–Tung–Striebel smoother and understand their Bayesian derivation
- Apply and compare nonlinear Kalman filters (EKF, UKF and sigma-point methods) for approximate Bayesian filtering
- Design and use particle filters and particle smoothers for highly nonlinear/non-Gaussian problems
- Combine state estimation with parameter learning using Bayesian parameter estimation, EM, and Monte Carlo methods
- Analyze algorithmic trade-offs (accuracy, computational cost, degeneracy) and choose appropriate filtering/smoothing strategies for practical problems
Topics Covered
- 1. Introduction to Bayesian State Estimation and Notation
- 2. Fundamentals of Bayesian Filtering and Smoothing
- 3. Linear Gaussian Models: Kalman Filter and RTS Smoother
- 4. Nonlinear Filtering: Extended Kalman Filter and Limitations
- 5. Sigma-Point and Unscented Filtering Methods
- 6. Particle Filtering: Sequential Monte Carlo Methods
- 7. Particle Smoothers and Advanced Sequential Techniques
- 8. Bayesian Parameter Estimation and EM for State-Space Models
- 9. Markov Chain Monte Carlo Methods in Smoothing and Parameter Learning
- 10. Practical Implementation Issues and Algorithmic Comparisons
- 11. Case Studies and Applications (tracking, navigation, communications, audio)
- Appendices: Mathematical Background and Computational Notes
Languages, Platforms & Tools
How It Compares
More focused and mathematically concise than Probabilistic Robotics (Thrun et al.), and narrower in scope but complementary to Sequential Monte Carlo Methods in Practice (Doucet et al.), with a stronger unified emphasis on smoothing and Kalman-type approximations.
