عنوان

Mathematics of Kalman-Bucy Filtering

3642733417

9783642733413

b573159

Mathematics of Kalman-Bucy Filtering

[Book]

by Peter A. Ruymgaart, Tsu T. Soong.

Second edition

Berlin, Heidelberg

Springer Berlin Heidelberg

1988

(xii, 170 pages 19 illustrations)

Springer series in information sciences, 14.

Elements of Probability Theory --; Calculus in Mean Square --; The Stochastic Dynamic System --; The Kalman-Bucy Filter --; A Theorem by Liptser and Shiryayev --; Appendix: Solutions to Selected Exercises --; References --; Subject Index.

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.

Coding theory.

Computer science.

Distribution (Probability theory)

by Peter A. Ruymgaart, Tsu T. Soong.

Peter A Ruymgaart

T T Soong

[Book]

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