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Generalized Likelihood Ratio Test for Detection of Gaussian Rank-One Signals in Gaussian Noise With Unknown Statistics

Besson, Olivier and Coluccia, Angelo and Chaumette, Eric and Ricci, Giuseppe and Vincent, François Generalized Likelihood Ratio Test for Detection of Gaussian Rank-One Signals in Gaussian Noise With Unknown Statistics. (2017) IEEE Transactions on Signal Processing, 65 (4). 1082-1092. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2016.2633241


We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix. In contrast to the usual assumption of deterministic target amplitudes, we assume here that the latter are drawn from a Gaussian distribution. The generalized likelihood ratio test (GLRT) is derived based on multiple primary data and a set of secondary data containing noise only. The new GLRT is shown to be the product of Kelly's GLRT and a corrective, data dependent term. We also investigate two-step approaches where the GLRT for a known disturbance covariance matrix is first derived. In order to come up with detectors that provide a good tradeoff between detection of matched signals and rejection of mismatched signals, we also investigate the two-step GLRT when a fictitious signal is included in the null hypothesis. The constant false alarm rate properties of the detectors are analyzed. Numerical simulations are presented, which show that for small sample sizes the newly-proposed GLRT can outperform Kelly's GLRT and, in addition, that detectors including a fictitious signal are very powerful, at least for low-to-intermediate clutter to noise ratio values.

Item Type:Article
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78 “© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01430750
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Università del Salento (ITALY)
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Deposited On:10 Jan 2017 10:15

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