Bayesian Filtering and Smoothing
Institute of Mathematical Statistics Textbooks Series

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 code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

Preface; Symbols and abbreviations; 1. What are Bayesian filtering and smoothing?; 2. Bayesian inference; 3. Batch and recursive Bayesian estimation; 4. Bayesian filtering equations and exact solutions; 5. Extended and unscented Kalman filtering; 6. General Gaussian filtering; 7. Particle filtering; 8. Bayesian smoothing equations and exact solutions; 9. Extended and unscented smoothing; 10. General Gaussian smoothing; 11. Particle smoothing; 12. Parameter estimation; 13. Epilogue; Appendix: additional material; References; Index.

Simo Särkkä worked, from 2000 to 2010, with Nokia Ltd, Indagon Ltd and Nalco Company in various industrial research projects related to telecommunications, positioning systems and industrial process control. Currently, he is a Senior Researcher with the Department of Biomedical Engineering and Computational Science at Aalto University, Finland, and Adjunct Professor with Tampere University of Technology and Lappeenranta University of Technology. In 2011 he was a visiting scholar with the Signal Processing and Communications Laboratory of the Department of Engineering at the University of Cambridge. His research interests are in state and parameter estimation in stochastic dynamic systems, and in particular, Bayesian methods in signal processing, machine learning, and inverse problems with applications to brain imaging, positioning systems, computer vision and audio signal processing. He is a Senior Member of IEEE.