论文标题
跨光谱测量统计
Cross-Spectrum Measurement Statistics
论文作者
论文摘要
跨光谱方法包括与两种独立仪器同时测量信号$ c（t）$。这些仪器中的每一个都通过其Intrinsec（白色）噪声导致了全球噪声，而我们想要表征的信号$ c（t）$可能是（红色）噪声。我们首先将跨光谱的实际部分定义为相关的估计器。然后，我们将此估计值的概率密度函数（PDF）描述为知道噪声水平（直接问题）作为方差 - 脉冲（v $γ$）分布。接下来，由于贝叶斯定理，我们解决了“逆问题”，以获得噪声水平的上限，了解估计值。经过大规模的蒙特卡洛模拟检查，V $γ$证明对任何数量的自由度（DOF）非常可靠。最后，我们将此方法与使用Karhunen-LoèveTransfrom（KLT）的其他方法进行了比较。由于KLT更好地考虑了可用的信息，因此我们发现信号级别的上限略有不同。
The cross-spectrum method consists in measuring a signal $c(t)$ simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsec (white) noise, whereas the signal $c(t)$ that we want to characterize could be a (red) noise. We first define the real part of the cross-spectrum as a relevant estimator. Then, we characterize the probability density function (PDF) of this estimator knowing the noise level (direct problem) as a Variance-Gamma (V$Γ$) distribution. Next, we solve the "inverse problem" thanks to Bayes' theorem to obtain an upper limit of the noise level knowing the estimate. Checked by massive Monte Carlo simulations, V$Γ$ proves to be perfectly reliable to any number of degrees of freedom (dof). Finally we compare this method with an other method using the Karhunen-Loève transfrom (KLT). We find an upper limit of the signal level slightly different as the one of V$Γ$ since KLT better takes into account the available informations.
