弱信号检测问题中匹配滤波器误检概率的正确估计。III（峰值分布法与Gumbel分布法）
Correct estimate of the probability of false detection of the matched filter in weak-signal detection problems. III (Peak distribution method versus the Gumbel distribution method)
摘要：
匹配滤波器（MF）代表了从嵌入在噪声中的已知源检测信号的主要工具之一。在高斯情况下，噪声被假定为高斯随机场（GRF）的实现。MF的最重要的属性，最大化的检测概率受到一个恒定的错误检测或错误报警（PFA）的概率，使它成为最流行的技术之一。然而，MF技术依赖于GRF中搜索信号的数量和位置的先验知识，这通常是不可用的。一种典型的解决方法是假设信号的位置与匹配滤波数据中的一个峰值重合。当给定峰值仅归因于噪声（即PFA）的概率小于预定阈值时，主张检测。在这种情况下，必须使用振幅的概率密度函数（PDF）来计算PFA，这与高斯函数不同。此外，检测为错误的概率取决于滤波的GRF中存在的峰值的数量，GRF中的峰值的数量越大，由于噪声而导致的峰值超过检测阈值的概率越高。如果不考虑，PFA可能会被严重低估。针对这个问题提出的许多解决方案都是非参数的，因此无法利用所有可用的信息。这一限制已经克服了两个有效的参数方法，一个基于PDF的峰值振幅的平滑和各向同性GRF，而另一个使用Gumbel分布（渐近PDF的相应的极端）。仿真和ALMA图表明，虽然这两种方法产生几乎相同的结果，第一个是更灵活，并允许我们检查的检测过程的可靠性。
英文摘要：
The matched filter (MF) represents one of the main tools to detect signals from known sources embedded in the noise. In the Gaussian case the noise is assumed to be the realization of a Gaussian random field (GRF). The most important property of the MF, the maximization of the probability of detection subject to a constant probability of false detection or false alarm (PFA), makes it one of the most popular techniques. However, the MF technique relies upon the a priori knowledge of the number and the position of the searched signals in the GRF which usually are not available. A typical way out is to assume that the position of a signal coincides with one of the peaks in the matched filtered data. A detection is claimed when the probability that a given peak is due only to the noise (i.e. the PFA) is smaller than a prefixed threshold. In this case the probability density function (PDF) of the amplitudes has to be used for the computation of the PFA, which is different from the Gaussian. Moreover, the probability that a detection is false depends on the number of peaks present in the filtered GRF, the greater the number of peaks in a GRF, the higher the probability of peaks due to the noise that exceed the detection threshold. If not taken into account, the PFA can be severely underestimated. Many solutions proposed to this problem are non-parametric hence not able to exploit all the available information. This limitation has been overcome by means of two efficient parametric approaches, one based on the PDF of the peak amplitudes of a smooth and isotropic GRF whereas the other uses the Gumbel distribution (the asymptotic PDF of the corresponding extreme). Simulations and ALMA maps show that, although the two methods produce almost identical results, the first is more flexible and allows us to check the reliability of the detection procedure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
