Optimal Filtering: Volume I: Filtering of Stochastic Processes (Mathematics and Its Applications (457))

Fomin, V.N.

ISBN 10: 0792352866 / ISBN 13: 9780792352860

Edité par Springer, 1998

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Titre : Optimal Filtering: Volume I: Filtering of ...

Éditeur : Springer

Date d'édition : 1998

Reliure : Hardcover

Etat : Like New

Type de livre : book

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Synopsis :

This book is devoted to an investigation of some important problems of mod- ern filtering theory concerned with systems of 'any nature being able to per- ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter- ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor- tant contributions to estimation theory, an understanding and moderniza- tion of some of its results and methods, with the intention of applying them to recursive filtering problems.

Présentation de l'éditeur:

This book considers methods of optimal signal processing. The generalised 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 unique 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 analysing linear filtering problems. Many novel results on filtering theory are also introduced.
Audience: This volume will be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, and mathematical physics.