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Titlebook: Lectures on Discrete Time Filtering; R. S. Bucy Textbook 1994 Springer-Verlag New York, Inc. 1994 Signal.electrical engineering.geophysics

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書目名稱Lectures on Discrete Time Filtering
編輯R. S. Bucy
視頻videohttp://file.papertrans.cn/584/583499/583499.mp4
叢書名稱Signal Processing and Digital Filtering
圖書封面Titlebook: Lectures on Discrete Time Filtering;  R. S. Bucy Textbook 1994 Springer-Verlag New York, Inc. 1994 Signal.electrical engineering.geophysics
描述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 d
出版日期Textbook 1994
關(guān)鍵詞Signal; electrical engineering; geophysics; numerical analysis; physics
版次1
doihttps://doi.org/10.1007/978-1-4613-8392-5
isbn_softcover978-1-4613-8394-9
isbn_ebook978-1-4613-8392-5Series ISSN 1431-7893
issn_series 1431-7893
copyrightSpringer-Verlag New York, Inc. 1994
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A Priori Bounds,sents the filter error covariance, the error covariance matrix of the signal process . at time . given data to time .. We have and will assume the matrix Φ. is invertible for all n. When the processes arise from sampling of continuous time diffusion processes this assumption is fulfilled. Define the mapping τ. as
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Signal Processing and Digital Filteringhttp://image.papertrans.cn/l/image/583499.jpg
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https://doi.org/10.1007/978-1-4613-8392-5Signal; electrical engineering; geophysics; numerical analysis; physics
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Review,Consider a space made up of points Ω = {ω.} where each ω. is an elementary event. The event . . Ω is a collection of ω.s. Ω is called the sure event, or certain event, and ? is the empty set.
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Random Noise Generation,If . is a covariance then . is positive semi definite and . with . orthogonal and . ≥ 0. The .-dimensional Gaussian integral is defined and the normalization satisfies
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Historical Background,For statistics references, we recommend [7], [8], and [9]. It is significant that in his book Muirhead [8] is able to find the distribution of the eigenvalues and eigenvectors for real systems of Gaussian random vectors:
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