Mathematics of Kalman-Bucy Filtering

Mathematics of Kalman-Bucy Filtering by P.A. Ruymgaart, Tsu T. Soong.

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 engineerin...

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Bibliographic Details
Main Authors: Ruymgaart, P.A (Author), Soong, Tsu T. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1985.
Edition:1st ed. 1985.
Series:Springer Series in Information Sciences, 14
Springer eBook Collection.
Subjects:
Coding theory.
Information theory.
Probabilities.
Statistics .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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