Ruymgaart / Soong Mathematics of Kalman-Bucy Filtering

2. Auflage 1988
ISBN: 978-3-642-73341-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 14, 170 Seiten, eBook

Reihe: Springer Series in Information Sciences

The second edition has not deviated significantly from the first. The printing of this edition, however, has allowed us to make a number of corrections which escaped our scrutiny at the time of the first printing, and to generally improve and tighten our presentation of the material. Many of these changes were suggested to us by colleagues and readers and their kindness in doing so is greatly appreciated. Delft, The Netherlands and P. A. Ruymgaart Buffalo, New York, December, 1987 T. T. Soong Preface to the First Edition Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but as all also in the social sciences, biological sciences, medical sciences, as well other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters.

Zielgruppe

Graduate

Autoren/Hrsg.

Ruymgaart, Peter A.

Soong, Tsu T.

Inhaltsverzeichnis

1. Elements of Probability Theory.- 1.1 Probability and Probability Spaces.- 1.2 Random Variables and “Almost Sure” Properties.- 1.3 Random Vectors.- 1.4 Stochastic Processes.- 2. Calculus in Mean Square.- 2.1 Convergence in Mean Square.- 2.2 Continuity in Mean Square.- 2.3 Differentiability in Mean Square.- 2.4 Integration in Mean Square.- 2.5 Mean-Square Calculus of Random N Vectors.- 2.6 The Wiener-Lévy Process.- 2.7 Mean-Square Calculus and Gaussian Distributions.- 2.8 Mean-Square Calculus and Sample Calculus.- 3. The Stochastic Dynamic System.- 3.1 System Description.- 3.2 Uniqueness and Existence of m.s. Solution to (3.3).- 3.3 A Discussion of System Representation.- 4. The Kalman-Bucy Filter.- 4.1 Some Preliminaries.- 4.2 Some Aspects of L2 ([a, b]).- 4.3 Mean-Square Integrals Continued.- 4.4 Least-Squares Approximation in Euclidean Space.- 4.5 A Representation of Elements of H (Z, t).- 4.6 The Wiener-Hopf Equation.- 4.7 Kalman-Bucy Filter and the Riccati Equation.- 5. A Theorem by Liptser and Shiryayev.- 5.1 Discussion on Observation Noise.- 5.2 A Theorem of Liptser and Shiryayev.- Appendix: Solutions to Selected Exercises.- References.