Mathematics of Kalman-Bucy Filtering (Springer Series in Information Sciences) - Hardcover

P. A. Ruymgaart

Hardcover

ISBN 10: 0387187812 ISBN 13: 9780387187815

Publisher: Springer-Verlag, 1988

Synopsis

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.

Edition details

• Publisher: Springer-Verlag
• Publication date: 1988
• Language: English
• ISBN 10: 0387187812
• ISBN 13: 9780387187815
• Binding: Hardcover
• Number of pages: 170