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Titlebook: Detection of Random Signals in Dependent Gaussian Noise; Antonio F. Gualtierotti Book 2015 Springer International Publishing Switzerland 2

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发表于 2025-3-21 17:45:17 | 显示全部楼层 |阅读模式
书目名称Detection of Random Signals in Dependent Gaussian Noise
编辑Antonio F. Gualtierotti
视频video
概述Derives a new likelihood function for solving basic problems in the theory of signal detection.Completes the Cramér-Hida representation theory.Investigates the scope of the signal-plus-noise model.Inc
图书封面Titlebook: Detection of Random Signals in Dependent Gaussian Noise;  Antonio F. Gualtierotti Book 2015 Springer International Publishing Switzerland 2
描述.The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with Gaussian noise. To facilitate comprehension the text is divided into three broad areas – reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context..One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis..The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics..
出版日期Book 2015
关键词Cramér-Hida representations; Girsanov‘s theory; Goursat processes; dependent signals with arbitrary law
版次1
doihttps://doi.org/10.1007/978-3-319-22315-5
isbn_softcover978-3-319-79392-4
isbn_ebook978-3-319-22315-5
copyrightSpringer International Publishing Switzerland 2015
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Scope of the Signal Plus “White Noise” Model (II)the Cramér-Hida framework, it becomes important to know that such a representation exists, as it is that representation which allows an explicit form for the likelihood. In the previous chapter, it was seen that the existence of the likelihood has the consequence that the observations are represente
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Relations Between Reproducing Kernel Hilbert Spacesd RKHS’s, and the entire topic may be seen as a partial answer to the following question: given an RKHS of signals, which noises does it accommodate? What follows covers thus relations between RKHS’s and, in particular inclusions and intersections.
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Cramér-Hida Representations from “First Principles”hich have a representation as integrals, with respect to an orthogonal vector measure, itself determined by a function with orthogonal increments. The decomposition is obtained under some “natural” assumptions [Assumption 6.4.1].
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Likelihoods for Signal Plus “White Noise” Versus “White Noise”ase, the road to the likelihood is based on a version of Girsanov’s theorem, and the likelihood itself follows when the “signal plus noise,” that is, the observation process, has a representation as the solution of a stochastic differential equation.
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