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Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering. To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are interrelated. Written as a collection of lessons, this book introduces readers o the general field of estimation theory and includes abundant supplementary material.
1. Introduction, Coverage, Philosophy, and Computation.
2. The Linear Model.
3. Least-Squares Estimation: Batch Processing.
4. Least-Squares Estimation: Singular-Value Decomposition.
5. Least-Squares Estimation: Recursive Processing.
6. Small Sample Properties of Estimators.
7. Large Sample Properties of Estimators.
8. Properties of Least-Squares Estimators.
9. Best Linear Unbiased Estimation.
11. Maximum-Likelihood Estimation.
12. Multivariate Gaussian Random Variables.
13. Mean-Squared Estimation of Random Parameters.
14. Maximum A Posteriori Estimation of Random Parameters.
15. Elements of Discrete-Time Gauss-Markov Random Sequences.
16. State Estimation: Prediction.
17. State Estimation: Filtering (The Kalman Filter).
18. State Estimation: Filtering Examples.
19. State Estimation: Steady-State Kalman Filter and Its Relationships to a Digital Wiener Filter.
20. State Estimation: Smoothing.
21. State Estimation: Smoothing (General Results).
22. State Estimation for the Not-So-Basic State-Variable Model.
23. Linearization and Discretization of Nonlinear Systems.
24. Iterated Least Squares and Extended Kalman Filtering.
25. Maximum-Likelihood State and Parameter Estimation.
26. Kalman-Bucy Filtering.
A. Sufficient Statistics and Statistical Estimation of Parameters.
B. Introduction to Higher-Order Statistics.
C. Estimation and Applications of Higher-Order Statistics.
D. Introduction to State-Variable Models and Methods.
Appendix A: Glossary of Major Results.
Appendix B: Estimation of Algorithm M-Files.