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OverviewThis work considers methods of optimal signal processing. The generalized filtering theory presented includes both highly developed, now classical branches like the Wiener-Kolmogorov and Kalman-Bucy theories, as well as relatively new branches such as semidegenerate processes and minimax filtering. The two-level approach to filtering problems is applied depending on their complexity. Starting with the conventional notions of filtering theory, in terms of difference-differential models, the research proceeds to notions and constructions of functional analysis convenient for analyzing linear filtering problems. Many novel results on filtering theory are also introduced. This volume should be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, and mathematical physics. Full Product DetailsAuthor: V.N. FominPublisher: Springer Imprint: Springer Edition: 1999 ed. Volume: 457 Dimensions: Width: 17.00cm , Height: 2.20cm , Length: 24.40cm Weight: 1.610kg ISBN: 9780792352860ISBN 10: 0792352866 Pages: 378 Publication Date: 30 November 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1 Introduction to estimation and filtering theory.- 1.1 Basic notions of probability theory.- 1.2 Introduction to estimation theory.- 1.3 Examples of estimation problems.- 1.4 Estimation and filtering: similarity and distinction.- 1.5 Basic notions of filtering theory.- 1.6 Appendix: Proofs of Lemmas and Theorems.- 2 Optimal filtering of stochastic processes in the context of the Wiener-Kolmogorov theory.- 2.1 Linear filtering of stochastic processes.- 2.2 Filtering of stationary processes.- 2.3 Recursive filtering.- 2.4 Linear filters maximizing a signal to noise ratio.- 2.5 Appendix: Proofs of Lemmas and Theorems.- 2.6 Bibliographical comments.- 3 Abstract optimal filtering theory.- 3.1 Random elements.- 3.2 Linear stable estimation.- 3.3 Resolution space and relative finitary transformations.- 3.4 Extended resolution space and linear transformations in it.- 3.5 Abstract version of the Wiener-Kolmogorov filtering theory.- 3.6 Optimal estimation in discrete resolution space.- 3.7 Spectral factorization.- 3.8 Optimal filter structure for discrete time case.- 3.9 Abstract Wiener problem.- 3.10 Appendix: Proofs of Lemmas and Theorems.- 3.11 Bibliographical comments.- 4 Nonlinear filtering of time series.- 4.1 Statement of nonlinear optimal filtering problem.- 4.2 Optimal filtering of conditionally Gaussian time series.- 4.3 Connection of linear and nonlinear filtering problems.- 4.4 Minimax filtering.- 4.5 Proofs of Lemmas and Theorems.- 4.6 Bibliographical comments.- References.- Notation.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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