Linear Algebra for Localization

Algorithms, Use Cases, and C++ Implementations

Ahmed Al-Muraeb

• Publisher: Chapman and Hall/CRC
• Year: 2026
• eBook ISBN: 9781040685815
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This book emphasises the vital role of linear algebraic models in solving localization problems, as well as many other problems in algorithms, data science, and Artificial Intelligence. Localization has multi-industrial applications, which this book attempts to address through linear algebraic approaches while using the dominant C++ programming language in those industries.

Features

• Provides clear, illustrative descriptions of the main linear algebra topics and advanced algorithms in localization problems.

• C++ implementations available via associated GitHub repository, including detailed explanations, flowcharts, UML diagrams and text, and code runs output.

• Case study by the author for an advanced topics in automotive application.

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Contents
• Preface
• Acronyms and Abbreviations
• Introduction
• 1 Basic Matrix Operations
• 2 Special Matrices
• 3 Orthogonal Transformations
• 4 Matrix Factorization
• 5 Orthogonal Projections and Psudoinverse
• 6 Covariance
• 7 Singular Value Decomposition
• 8 Jacobian, Hessian, and Gradient
• 9 Fisher Information Matrix and the Cramér–Rao Lower Bound
• 10 Matrix Block Operations and Matrix Kernel
• Appendix A C++ Resources, Code Build, Code Run, and Code Debug
• Appendix B Case Study: Effect of Reference Points Locations on Cramér–Rao Lower Bound for Arbitrary Position Estimators
• Index