Becker A. Kalman Filter from the Ground Up

Alex Becker, 2023. — 436 p.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 explanations are presented in a straightforward and intuitive manner, accompanied by examples and illustrations. Additionally, each section provides the necessary mathematical background to reinforce your comprehension.This book is suitable for beginners and experts alike, focusing on practical applications and real-world scenarios. Whether you're a researcher, engineer, or student, you'll find valuable insights and actionable advice in this book.The book includes 14 fully solved numerical examples to enhance your understanding of the concepts. Additionally, you can purchase the source code for all examples in either Python or MatLAB. The source code is designed with a modular structure and can be used as a starting point for implementing Kalman Filters, Extended Kalman Filters, and Unscented Kalman Filters for other systems beyond those covered in the book.Introduction to Kalman Filter
The Necessity of Prediction
Essential background I
The α − β − γ filter
Kalman Filter in one dimension
Adding process noise
Multivariate Kalman Filter
Foreword
Essential background II
Kalman Filter Equations Derivation
Multivariate KF Examples
Non-linear Kalman Filters
Foreword
Essential background III
Non-linearity problem
Extended Kalman Filter (EKF)
Unscented Kalman Filter (UKF)
Non-linear filters comparison
Conclusion
Kalman Filter in practice
Sensors Fusion
Variable measurement error
Treating missing measurements
Treating outliers
Kalman Filter Initialization
KF Development Process
Appendices
The expectation of variance
Confidence Interval
Modeling linear dynamic systems
Derivative of matrix product trace
Pendulum motion simulation
Statistical Linear Regression
The product of univariate Gaussian PDFs
Product of multivariate Gaussian PDFs
Bibliography
Articles
Books
Index