Mathematics of Kalman-Bucy filtering
P. A. Ruymgaart, T. T. Soong.
Bok Engelsk 1985 · Electronic books.
| Medvirkende | Soong, T. T., (author.)
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|---|---|
| Omfang | 1 online resource (180 pages).
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| Utgave | 1st ed. 1985.
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| Opplysninger | Bibliographic Level Mode of Issuance: Monograph. - 1. Elements of Probability Theory -- 1.1 Probability and Probability Spaces -- 1.2 Random Variables and “Almost Sure” Properties -- 1.3 Random Vectors -- 1.4 Stochastic Processes -- 2. Calculus in Mean Square -- 2.1 Convergence in Mean Square -- 2.2 Continuity in Mean Square -- 2.3 Differentiability in Mean Square -- 2.4 Integration in Mean Square -- 2.5 Mean-Square Calculus of Random N Vectors -- 2.6 The Wiener-Lévy Process -- 2.7 Mean-Square Calculus and Gaussian Distributions -- 2.8 Mean-Square Calculus and Sample Calculus -- 3. The Stochastic Dynamic System -- 3.1 System Description -- 3.2 Uniqueness and Existence of m.s. Solution to (3.3) -- 3.3 A Discussion of System Representation -- 4. The Kalman-Bucy Filter -- 4.1 Some Preliminaries -- 4.2 Some Aspects of L2 ([a, b]) -- 4.3 Mean-Square Integrals Continued -- 4.4 Least-Squares Approximation in Euclidean Space -- 4.5 A Representation of Elements of H (Z, t) -- 4.6 The Wiener-Hopf Equation -- 4.7 Kalman-Bucy Filter and the Riccati Equation -- 5. A Theorem by Liptser and Shiryayev -- 5.1 Discussion on Observation Noise -- 5.2 A Theorem of Liptser and Shiryayev -- Appendix: Solutions to Selected Exercises -- References.. - Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but also in the social sciences, biological sciences, medical sciences, as well as all other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without them fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters. The material is meant to be a theoretical complement to courses dealing with applications and is designed for students who are well versed in the techniques of Kalman-Bucy filtering but who are also interested in the mathematics on which these may be based. The main topic addressed in this book is continuous-time Kalman-Bucy filtering. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously, which are hence more appropriately mod eled by differential equations than by difference equations. On the other hand, observations from the former can be obtained in a discrete fashion.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 3-642-96842-2
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