Detection of Random Signals in Dependent Gaussian Noise
Springer International Publishing (Verlag)
978-3-319-79392-4 (ISBN)
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.
Prolog.- Part I: Reproducing Kernel Hilbert Spaces.- Part II: Cramér-Hida Representations.- Part III: Likelihoods.- Credits and Comments.- Notation and Terminology.- References.- Index.
"The book rigorously develops the mathematical foundations to assess the possible likelihoods for detection problems with Gaussian noise. ... The text would be very useful for graduate students and researchers alike in the fields of mathematics, engineering and statistics." (John Schmeelk, zbMATH 1364.60004, 2017)
| Erscheinungsdatum | 19.12.2018 |
|---|---|
| Zusatzinfo | XXXIV, 1176 p. 5 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1788 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Cramér-Hida representations • dependent signals with arbitrary laws • Girsanov's theory • Girsanov‘s theory • Goursat processes • Information and Communication, Circuits • prediction processes • Reproducing kernel Hilbert spaces • Signal Detection • uniqueness class of continuous local martingales |
| ISBN-10 | 3-319-79392-6 / 3319793926 |
| ISBN-13 | 978-3-319-79392-4 / 9783319793924 |
| Zustand | Neuware |
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