عنوان

Mathematics of Kalman-Bucy Filtering

(Number (ISBN

3642733417

(Number (ISBN

9783642733413

Number

b573159

Title Proper

Mathematics of Kalman-Bucy Filtering

General Material Designation

[Book]

First Statement of Responsibility

by Peter A. Ruymgaart, Tsu T. Soong.

Edition Statement

Second edition

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1988

Specific Material Designation and Extent of Item

(xii, 170 pages 19 illustrations)

Series Title

Springer series in information sciences, 14.

Text of Note

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.

Text of Note

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)

Class number

Book number

by Peter A. Ruymgaart, Tsu T. Soong.

Peter A Ruymgaart

T T Soong

Electronic name

[Book]

Y