Bayesian Filtering and Smoothing

Author: Lennart Svensson and Simo Särkkä Series: Institute of Mathematical Statistics Textbooks

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

The second edition of this accessible introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. The book introduces all the main concepts and ideas, and contains numerous examples and exercises to let you put the theory into practice.

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Summary

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

Description

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.

Critic Reviews

'The book represents an excellent treatise of non-linear filtering from a Bayesian perspective. It has a nice balance between details and breadth, and it provides a nice journey from the basics of Bayesian inference to sophisticated filtering methods.' Petar M. Djurić, Stony Brook
'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

About the Author

Simo Särkkä is Associate Professor in the Department of Electrical Engineering and Automation at Aalto University, Finland. His research interests center on state estimation and stochastic modeling, and he has authored two books (2013 and 2019) on these topics. He is Fellow of ELLIS, Senior Member of IEEE, a recipient of multiple paper awards, and he has been Chair of MLSP and FUSION conferences. Lennart Svensson is Professor in the Department of Electrical Engineering at Chalmers University of Technology, Gothenberg. His research focuses on nonlinear ﬁltering, deep learning, and tracking in particular. He has organized a massive open online course on multiple object tracking, and received paper awards at the International Conference on Information Fusion in 2009, 2010, 2017, 2019, and 2021.