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| Titel |
Finding a detection threshold for Fisher Detector applied to beamforming |
| VerfasserIn |
Adrien Nouvellet, Francois Roueff, Maurice Charbit, Alexis Le Pichon |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250092334
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| Publikation (Nr.) |
 EGU/EGU2014-6669.pdf |
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| Zusammenfassung |
| The so called F-stat function of test (FoT) is a commonly used detector of signal of interest
(SOI) received by sensors with additive white Gaussian noise [1], [3]. This FoT is related to the
generalized likelihood ratio test based on the Gaussian assumption and on the parametrization of the
planar propagation of the wave carrying the SOI by a slowness vector. The detection test is obtained
by comparing the FoT to some threshold or by providing the p-value which is directly compared to
the targeted type-I error. In both cases, we need to compute the distribution of the FoT under the
null hypothesis i.e. in the absence of the SOI.
Unfortunately when the FoT is maximized over a set of various possible slowness vectors for
the SOI propagation, the distribution under the null hypothesis is no longer the expected Fisher
distribution [4]. In this study we present a new approach to approximate the null distribution when
this maximization is performed over a finite set of slowness parameters, which corresponds to the
most encountered practical setting. To this end, we derive the asymptotic (Gaussian) behavior of the
finite dimensional distributions of the FoT seen as a process indexed by the set of delays that appear
in its computation. This approach, although asymptotic, provides a practical way to tune the type-I
error of the detection test in a consistent and efficient way, which performs quite well on simulations. |
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