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Two detectors based on the GLRT (generalized maximum likelihood ratio test) are presented to detect a chirplet in coloured Gaussian noise for known and unknown covariance structures, respectively. They are applied to detect multiple chirplets by atomic decomposition, which is modified to account for the operating conditions of both detectors. Both detectors are CFAR with respect to the noise power. The second one is CFAR with respect to the covariance structure as well.