Mathematics of Kalman-Bucy Filtering /
This book addresses the mathematics of Kalman-Bucy filtering and is designed for readers who are well versed in the practice of Kalman-Bucy filters but are interested in the mathematics on which they are based. The main topic in this book is the continuous-time Kalman-Bucy filter. Although the discr...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
1988.
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| Edition: | Second edition. |
| Series: | Springer series in information sciences ;
14. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book addresses the mathematics of Kalman-Bucy filtering and is designed for readers who are well versed in the practice of Kalman-Bucy filters but are interested in the mathematics on which they are based. The main topic in this book is the continuous-time Kalman-Bucy filter. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously; they are thus more appropriately modeled by differential equations than by difference equations. Confining attention to the Kalman-Bucy filter, the mathematics needed consists mainly of operations in Hilbert spaces. A relatively complete treatment of mean square calculus is given, leading to a discussion of the Wiener-Levy process. This is followed by a treatment of the stochastic differential equations central to the modeling of the Kalman-Bucy filtering process. The mathematical theory of the Kalman-Bucy filter is then introduced, and with the aid of a theorem of Liptser and Shiryayev, new light is shed on the dependence of the Kalman-Bucy estimator on observation noise. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xii, 170 pages 19 illustrations) |
| ISBN: | 9783642733413 (electronic bk.) 3642733417 (electronic bk.) |
| ISSN: | 0720-678X ; |