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＜電子ブック＞
Estimation, Control, and the Discrete Kalman Filter / by Donald E. Catlin
(Applied Mathematical Sciences. ISSN:2196968X ; 71)

版	1st ed. 1989.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1989
本文言語	英語
大きさ	XIV, 276 p : online resource
著者標目	*Catlin, Donald E author SpringerLink (Online service)
件　名	LCSH:Control engineering LCSH:Robotics LCSH:Automation LCSH:Statistics  LCSH:System theory LCSH:Control theory LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Control, Robotics, Automation FREE:Statistics FREE:Systems Theory, Control FREE:Calculus of Variations and Optimization FREE:Mathematical and Computational Engineering Applications
一般注記	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 -- 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 -- 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 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, Kalman filters are used in such diverse areas as navigation, guid­ ance, oil drilling, water and air quality, and geodetic surveys. In addition, Kalman's work led to a multitude of books and papers on minimum vari­ ance estimation in dynamical systems, including one by Kalman and Bucy on continuous time systems [15]. Most of this work was done outside of the mathematics and statistics communities and, in the spirit of true academic parochialism, was, with a few notable exceptions, ignored by them. This text is my effort toward closing that chasm. For mathematics students, the Kalman filtering theorem is a beautiful illustration of functional analysis in action; Hilbert spaces being used to solve an extremely important problem in applied mathematics. For statistics students, the Kalman filter is a vivid example of Bayesian statistics in action. The present text grew out of a series of graduate courses given by me in the past decade. Most of these courses were given at the University of Mas­ sachusetts at Amherst HTTP:URL=https://doi.org/10.1007/978-1-4612-4528-5

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