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Detection of Swerling III-IV rank-one signals in Gaussian noise with unknown statistics

机译:统计信息未知的高斯噪声中Swerling III-IV等级信号的检测

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We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix, based on multiple primary data and a set of secondary data containing noise only. The most celebrated approach to this problem is Kelly's generalized likelihood ratio test (GLRT), derived under the hypothesis of deterministic target amplitudes. However, for a Swerling I-II target (Gaussian amplitudes), it has been shown lately that the associated GLRT, which can outperform Kelly's GLRT for small sample sizes, is the product of Kelly's GLRT and a corrective, data dependent, term. We show that at high signal-to-noise ratio (SNR), the GLRT associated to a Swerling III-IV target is “almost surely”' equivalent to the newly-proposed GLRT for Swerling I-II target, and outperforms, as well, Kelly's GLRT for small sample sizes at intermediate-to-high SNR values.
机译:我们考虑了基于多个主数据和一组仅包含噪声的辅助数据来检测具有未知协方差矩阵的高斯噪声目标的经典雷达问题。解决此问题最著名的方法是凯利的广义似然比检验(GLRT),它是在确定性目标幅度假设下得出的。但是,对于Swerling I-II目标(高斯振幅)而言,最近已证明相关的GLRT是凯利GLRT和校正性的,与数据相关的术语的乘积,该GLRT对于小样本量而言可以胜过Kelly的GLRT。我们显示,在高信噪比(SNR)下,与Swerling III-IV目标相关的GLRT几乎可以肯定地等同于针对Swerling I-II目标的最新建议的GLRT,而且性能也优于,凯利(Kelly)的GLRT,适用于中小到高SNR值的小样本量。

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