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Full Description
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.
Contents
Preface Acronyms and Abbreviations Chapter 0 Introduction Chapter 1 Basic Matrix Operations Chapter 2 Special Matrices Chapter 3 Orthogonal Transformations Chapter 4 Matrix Factorization Chapter 5 Orthogonal Projections and Psudoinverse Chapter 6 Covariance Chapter 7 Singular Value Decomposition Chapter 8 Jacobian, Hessian, and Gradient Chapter 9 Fisher Information Matrix and the Cramér-Rao Lower Bound Chapter 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
