Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- 1 A First Example: Optimal Quadratic Control
- 2 Dynamical Systems
- 3 LTV (Quasi-separable) Systems
- 4 System Identification
- 5 State Equivalence, State Reduction
- 6 Elementary Operations
- 7 Inner Operators and External Factorizations
- 8 Inner−Outer Factorization
- 9 The Kalman Filter as an Application
- 10 Polynomial Representations
- 11 Quasi-separable Moore−Penrose Inversion
- Part II Further Contributions to Matrix Theory
- Appendix: Data Model and Implementations
- References
- Index
9 - The Kalman Filter as an Application
from Part I - Lectures on Basics with Examples
Published online by Cambridge University Press: 24 October 2024
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- 1 A First Example: Optimal Quadratic Control
- 2 Dynamical Systems
- 3 LTV (Quasi-separable) Systems
- 4 System Identification
- 5 State Equivalence, State Reduction
- 6 Elementary Operations
- 7 Inner Operators and External Factorizations
- 8 Inner−Outer Factorization
- 9 The Kalman Filter as an Application
- 10 Polynomial Representations
- 11 Quasi-separable Moore−Penrose Inversion
- Part II Further Contributions to Matrix Theory
- Appendix: Data Model and Implementations
- References
- Index
Summary
The set of basic topics then continues with a major application domain of our theory: linear least-squares estimation (llse) of the state of an evolving system (aka Kalman filtering), which turns out to be an immediate application of the outer–inner factorization theory developed in Chapter 8. To complete this discussion, we also show how the theory extends naturally to cover the smoothing case (which is often considered “difficult”).
- Type
- Chapter
- Information
- Time-Variant and Quasi-separable SystemsMatrix Theory, Recursions and Computations, pp. 136 - 153Publisher: Cambridge University PressPrint publication year: 2024