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Estimation, Control, and the Discrete Kalman Filter

In 1960, R. E. Kalman published his celebrated paper on recursive min­ imum variance estimation in dynamical systems [14]. This paper, which introduced an algorithm that has since been known as the discrete Kalman filter, produced a virtual revolution in the field of systems engineering. Today, Kalm...

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Bibliographic Details
Main Author: Catlin, Donald E.
Format: eBook
Language:English
Published: New York, NY Springer New York 1989, 1989
Edition:1st ed. 1989
Series:Applied Mathematical Sciences
Subjects:
Control, Robotics, Automation
Engineering Mathematics
Statistics 
Calculus Of Variations And Optimization
Control Theory
Systems Theory, Control
System Theory
Control Engineering
Robotics
Engineering / Data Processing
Statistics
Mathematical Optimization
Automation
Mathematical And Computational Engineering Applications
Calculus Of Variations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Basic Probability
  • 1.1. Definitions
  • 1.2. Probability Distributions and Densities
  • 1.3. Expected Value, Covariance
  • 1.4. Independence
  • 1.5. The Radon—Nikodym Theorem
  • 1.6. Continuously Distributed Random Vectors
  • 1.7. The Matrix Inversion Lemma
  • 1.8. The Multivariate Normal Distribution
  • 1.9. Conditional Expectation
  • 1.10. Exercises
  • 2 Minimum Variance Estimation—How the Theory Fits
  • 2.1. Theory Versus Practice—Some General Observations
  • 2.2. The Genesis of Minimum Variance Estimation
  • 2.3. The Minimum Variance Estimation Problem
  • 2.4. Calculating the Minimum Variance Estimator
  • 2.5. Exercises
  • 3 The Maximum Entropy Principle
  • 3.1. Introduction
  • 3.2. The Notion of Entropy
  • 3.3. The Maximum Entropy Principle
  • 3.4. The Prior Covariance Problem
  • 3.5. Minimum Variance Estimation with Prior Covariance
  • 3.6. Some Criticisms and Conclusions
  • 3.7. Exercises
  • 4 Adjoints, Projections, Pseudoinverses
  • 4.1. Adjoints
  • 9.3. The Two-Filter Form of the Smoother
  • 9.4. Exercises
  • Appendix A Construction Measures
  • Appendix B Two Examples from Measure Theory
  • Appendix C Measurable Functions
  • Appendix D Integration
  • Appendix E Introduction to Hilbert Space
  • Appendix F The Uniform Boundedness Principle and Invertibility of Operators
  • 4.2. Projections
  • 4.3. Pseudoinverses
  • 4.4. Calculating the Pseudoinverse in Finite Dimensions
  • 4.5. The Grammian
  • 4.6. Exercises
  • 5 Linear Minimum Variance Estimation
  • 5.1. Reformulation
  • 5.2. Linear Minimum Variance Estimation
  • 5.3. Unbiased Estimators, Affine Estimators
  • 5.4. Exercises
  • 6 Recursive Linear Estimation (Bayesian Estimation)
  • 6.1. Introduction
  • 6.2. The Recursive Linear Estimator
  • 6.3. Exercises
  • 7 The Discrete Kalman Filter
  • 7.1. Discrete Linear Dynamical Systems
  • 7.2. The Kalman Filter
  • 7.3. Initialization, Fisher Estimation
  • 7.4. Fisher Estimation with Singular Measurement Noise
  • 7.5. Exercises
  • 8 The Linear Quadratic Tracking Problem
  • 8.1. Control of Deterministic Systems
  • 8.2. Stochastic Control with Perfect Observations
  • 8.3. Stochastic Control with Imperfect Measurement
  • 8.4. Exercises.-9 Fixed Interval Smoothing
  • 9.1. Introduction
  • 9.2. The Rauch, Tung, Streibel Smoother

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