Bayesian Filtering and Smoothing

Institute of Mathematical Statistics Textbooks

by Simo Särkkä, Simo S Rkk

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.

Genres: Mathematics

252 pages, Paperback

First published August 31, 2013

Reviews

[Ali Frz · Rating 5 out of 5]

the best reference for kalman filtering and kalman smoothing

[Per Ljung · Rating 4 out of 5]

Very good introduction to the topic. I mainly focused on the filtering part, and more or less skimmed the smoothing sections, which regardless gave a general overview by referring to its analogy with previously established filtering methods. The structure of the book, and its balance between intuition, algorithm definitions, and theory makes for a readable text which one easily can use as a thorough source for practical use in the future.

[Emil Petersen · Rating 3 out of 5]

I read the first four chapters and chapter eight intensively, as I needed to implement the linear filter and smoother; the remaining chapters I have only skimmed. They are significantly harder to understand, if you ask me. There are plenty of examples, but sadly they are reused a lot with no real difference in understanding. Also, the book is relatively short (~250 pages), which at points make the content terse and unexplained. In relation to that, Wikipedia has an amazing article on the Kalman filter, which I referred to often when I was confused about the content of this book. I would say that you can find equally good content elsewhere on the linear filters, but once you get into the advanced filters, you are probably going to be thankful that you came to this one. The epilogue is also very neat and makes some needed considerations on when and where to apply the different filters.