The framework of this paper is that of adaptive detection in Gaussian noise with unknown covariance matrix when the training samples do not share the same covariance matrix as the vector under test. We consider a class of constant false alarm rate detectors which depend on two statistics $(\beta,\ttilde)$ whose distribution is parameter-free in the case of no mismatch and we analyze the impact of covariance mismatched training samples. More precisely, we provide a statistical representation of these two variables for an arbitrary mismatch. We show that covariance mismatch induces significant variations of the probability of false alarm and we investigate a way to mitigate this effect.

翻译：本文的框架是高山噪音的适应性检测和未知的共变矩阵,当培训样本与正在测试的矢量不具有相同的共变矩阵时。 我们考虑的是一种常态假警报率检测器,它取决于两个统计数据$(\beta,\ttilde),如果不存在不匹配,其分布没有参数,我们分析共变不匹配培训样本的影响。更确切地说,我们为任意错配提供了这两个变量的统计说明。我们表明,共变错配导致假警报概率的显著变化,我们研究如何减轻这一影响。