Books on Kalman Filter

Here is small note about the Kalman and Particle filters. The list and comment reflect only my humble point of view: I'm an engineer who does not particularly like terse theoretical-orientated volumes.

Optimal State Estimate by Dan Simon
A very comprehensive book and, which is more important, it uses a bottom-up approach that enables readers to master the material rather quickly. Dan Simon's book is the best and the most suitable for self-study. Explanations are concise and straightforward. This book relates control theory elegantly. The author uses well laid out algorithmic approaches, suitable for programming, and examples to explain the details and show the complexities in action.
You will find all estimation topics in one book: Kalman filter, Unscented Kalman (UKF), Extended Kalman (EKF) and a very good explanation of Particle filtering (PF).

Moreover, the author has a website with a lot of MATLAB code for the examples used in book. This is a great help in terms of understanding of the subject, as most of examples are very insightful.


Introduction to Random Signals and Applied Kalman Filtering by Brown and Hwang
The book is easy to read and easy to follow: it starts from the very detailed explanation of the background needed for the Kalman filter. Obviously, the authors had an extensive teaching experience. The explanation of the Discrete Kalman Filter is one of the best I ever found. The extended KF and some implementation issues (UDU filter, sequential estimation) are not covered as well as other topics.

One should admit, however, that starting from the Chapter 6, the authors evidently exhausted and the text started to be more and more terse. The chapter about Kalman smoothing I could hardly translate to human language - better to use Dan Simon book.



Advanced Kalman Filtering, Least Squares and Modelling: A practical Handbook by Bruce Gibbs
The book is very terse in terms of explanations, and one should read it only as a reference, with a good background in Kalman filtering. Advanced topics, such as Particle Filter and Unscented Kalman, are covered in a very short manner and not very insightful. This is a handbook after all and not the book for the self-study. However, the book provides a lot of in-depth information and insight into various areas not found elsewhere.
This will be most useful for somebody with a strong mathematical background, particularly in linear algebra, who is looking for a comprehensive understanding and the best solution for a particular application.
Overall: a good reference, but not very helpful in terms of explanation.