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

mathematics of kalman-bucy filtering (springer series in information sciences)

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

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Book Description
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.

Mathematics of Kalman-Bucy Filtering (Springer Series in Information Sciences),P. A. Ruymgaart,T. T. Soong,Springer,0387187812,Calculus,Functional Analysis,Hilbert space,Information Theory,Kalman filtering,Mathematical Statistics,Mathematics,Physics,Probabilities,Probability & Statistics - General,Science/Mathematics

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