The Kalman Filter algorithm is a powerful tool for estimating and predicting system states in the presence of uncertainty and is widely used as a fundamental component in applications such as target tracking, navigation, and control.

Although the Kalman Filter is a straightforward concept, many resources on the subject require extensive mathematical background and fail to provide practical examples and illustrations, making it more complicated than necessary.

Back in 2017, I created an online tutorial based on numerical examples and intuitive explanations to make the topic more accessible and understandable. The online tutorial provides introductory material covering the univariate (one-dimensional) and multivariate (multidimensional) Kalman Filters.

Over time, I have received many requests to include more advanced topics, such as non-linear Kalman Filters (Extended Kalman Filter and Unscented Kalman Filter), sensors fusion, and practical implementation guidelines.

Based on the material covered in the online tutorial, I authored a book.

The original online tutorial is available for free access. The e-book and the source code (Python and MATLAB) for the numerical examples are available for purchase at a special introductory price.

The book takes the reader from the basics to the advanced topics, covering both theoretical concepts and practical applications. The writing style is intuitive, prioritizing clarity of ideas over mathematical rigor, and it approaches the topic from a philosophical perspective before delving into quantification.

The book contains many illustrative examples, including 14 fully solved numerical examples with performance plots and tables. Examples progress in a paced, logical manner and build upon each other.

The book also includes the necessary mathematical background, providing a solid foundation to expand your knowledge and help to overcome your math fears.

Upon finishing this book, you will be able to design, simulate, and evaluate the performance of the Kalman Filter.

The book includes four parts:

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  Part 1 serves as an introduction to the Kalman Filter, using eight numerical examples, and doesn’t require any prior mathematical knowledge. You can call it “The Kalman Filter for Dummies,” as it aims to provide an intuitive understanding and develop “Kalman Filter intuition.” Upon completing Part 1, readers will thoroughly understand the Kalman Filter’s concept and be able to design a univariate (one-dimensional) Kalman Filter.

  Most of this part is available for free access!

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  Part 2 presents the Kalman Filter in matrix notation, covering the multivariate (multidimensional) Kalman Filter. It includes a mathematical derivation of Kalman Filter equations, dynamic systems modeling, and two numerical examples. This section is more advanced and requires basic knowledge of Linear Alg