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研究了在空间协方差未知的背景高斯噪声的情况下检测一列信号时的恒虚警率（CFAR）检验方案。考虑了不变量检验，就是说，这些检验的性能与像背景噪声协方差那样的多余参数无关。证明了这种检验具有合乎需要的CFAR特性。通过证明任何不变判定统计量都可以写成两个基本统计量的函数，表征了所有这种检验的类，这两个基本统计量实际上就是自适应匹配滤波（AMF）统计量和凯利广义似然比统计量。而且在低信号噪声比（SNR）范围内确定了最佳检验，即局部最大功效不变量（LMPI）检验。我们还得出任何不变量检测器在固定虚警率情况下的检测概率的边界，并把LMPI以及已公布的检测器（凯利和AMF）与MP不变量检测器作了比较。
The CFAR test scheme for detecting a series of signals under the background Gaussian noise with unknown spatial covariance was studied. The invariant tests are considered, that is, the performance of these tests is independent of the extra parameters like background noise covariance. This test proved the desirable CFAR characteristics. By demonstrating that any invariant decision statistic can be written as a function of two basic statistics, all classes of such tests are characterized, which are essentially the Adaptive Matched Filter (AMF) statistics and the Kelly-Generalized However, statistics. The best test, the LMPI test, was also determined in the low signal-to-noise ratio (SNR) range. We also obtained the bounds of detection probabilities for any invariant detector at a fixed false alarm rate and compared LMPI with published detectors (Kelly and AMF) with MP invariant detectors.