Bayesian Filtering and Smoothing

A Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Simo Särkkä (Author), Lennart Svensson (Author)

9781108926645, Cambridge University Press

Paperback / softback, published 15 June 2023

430 pages
22.8 x 15.2 x 2.3 cm, 0.64 kg

'An excellent and pedagogical treatment of the complex world of nonlinear filtering.  It is very valuable for both researchers and practitioners.' Lennart Ljung, Linköping University

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Symbols and abbreviations
1. What are Bayesian filtering and smoothing?
2. Bayesian inference
3. Batch and recursive Bayesian estimation
4. Discretization of continuous-time dynamic models
5. Modeling with state space models
6. Bayesian filtering equations and exact solutions
7. Extended Kalman filtering
8. General Gaussian filtering
9. Gaussian filtering by enabling approximations
10. Posterior linearization filtering
11. Particle filtering
12. Bayesian smoothing equations and exact solutions
13. Extended Rauch-Tung-Striebel smoothing
14. General Gaussian smoothing
15. Particle smoothing
16. Parameter estimation
17. Epilogue
Appendix. Additional material
References
Index.

Subject Areas: Probability & statistics [PBT]