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.
Contents: 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.
Series: Springer Series in Information Sciences
Number Of Pages: 170
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.27
Edition Number: 2
Edition Type: Revised