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The theory of linear discrete time filtering started with a paper by Kol mogorov in 1941. He addressed the problem for stationary random se quences and introduced the idea of the innovations process, which is a useful tool for the more general problems considered here. The reader may object and note that Gauss discovered least squares much earlier; however, I want to distinguish between the problem of parameter estimation, the Gauss problem, and that of Kolmogorov estimation of a process. This sep aration is of more than academic interest as the least squares problem leads to the normal equations, which are numerically ill conditioned, while the process estimation problem in the linear case with appropriate assumptions leads to uniformly asymptotically stable equations for the estimator and the gain. The conditions relate to controlability and observability and will be detailed in this volume. In the present volume, we present a series of lectures on linear and nonlinear sequential filtering theory. The theory is due to Kalman for the linear colored observation noise problem; in the case of white observation noise it is the analog of the continuous-time Kalman-Bucy theory. The discrete time filtering theory requires only modest mathematical tools in counterpoint to the continuous time theory and is aimed at a senior-level undergraduate course. The present book, organized by lectures, is actually based on a course that meets once a week for three hours, with each meeting constituting a lecture.
Reseña del editor
This book is based on a course given at the University of Southern California, at the University of Nice, and at Cheng Kung University in Taiwan. It discusses linear and nonlinear sequential filtering theory: that is, the problem of estimating the process underlying a stochastic signal. For the linear colored-noise problem, the theory is due to Kalman, and in the case of white noise it is the continuous Kalman-Bucy theory. The techniques considered have applications in fields as diverse as economics (e.g., prediction of the money supply), geophysics (e.g., processing of sonar signals), electrical engineering (e.g., detection of radar signals), and numerical analysis (e.g., in integration packages). The nonlinear theory is treated thoroughly, along with some novel synthesis methods for this computationally demanding problem. The author also discusses the Burg technique, and gives a detailed analysis of the matrix Riccati equation that is not available elsewhere.
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- VerlagSpringer New York
- Erscheinungsdatum1994
- ISBN 10 1461383943
- ISBN 13 9781461383949
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten176
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Lectures on Discrete Time Filtering (Signal Processing and Digital Filtering)
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The theory of linear discrete time filtering started with a paper by Kol mogorov in 1941. He addressed the problem for stationary random se quences and introduced the idea of the innovations process, which is a useful tool for the more general problems considered here. The reader may object and note that Gauss discovered least squares much earlier; however, I want to distinguish between the problem of parameter estimation, the Gauss problem, and that of Kolmogorov estimation of a process. This sep aration is of more than academic interest as the least squares problem leads to the normal equations, which are numerically ill conditioned, while the process estimation problem in the linear case with appropriate assumptions leads to uniformly asymptotically stable equations for the estimator and the gain. The conditions relate to controlability and observability and will be detailed in this volume. In the present volume, we present a series of lectures on linear and nonlinear sequential filtering theory. The theory is due to Kalman for the linear colored observation noise problem; in the case of white observation noise it is the analog of the continuous-time Kalman-Bucy theory. The discrete time filtering theory requires only modest mathematical tools in counterpoint to the continuous time theory and is aimed at a senior-level undergraduate course. The present book, organized by lectures, is actually based on a course that meets once a week for three hours, with each meeting constituting a lecture. Artikel-Nr. 9781461383949
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