原子钟时域频率稳定度分析中等效自由度的计算与分析

The Calculation and Analysis of the Confidence of the Time-domain Frequency Stability

该文基于标准化自协方差函数的组合算法计算了阿仑方差、哈达玛方差的重叠和非重叠形式以及改进阿仑方差、时间方差的等效自由度,并用经验公式计算了总方法估计的等效自由度,在此基础上对各种方差估计不同噪声情况下的等效自由度进行了比较分析,得出如下结论,总方法估计的等效自由度大于相应非总方法估计的等效自由度,重叠和非重叠阿仑方差估计的等效自由度大于相应哈达玛方差估计的等效自由度;对非重叠估计而言,噪声的频率越低,其等效自由度越大;而相应的重叠估计和总方法估计与之相反,噪声的频率越高,其等效自由度越大,这也说明重叠估计和相应的总方法估计对高频噪声等效自由度的提高优于低频噪声.

The equivalent number of X2 degrees of freedom （edf） for the overlapping arid nonoverlapping estimators of the Allan variance and the Hadamard variance, the modified Allan variance and the related time variance is calculated from a combined algorithm based on its generalized autocovariance function. The edf for the total estimators is calculated from the empirical formulas in this paper. By comparison and analysis of the edf for all variances and all noises, some useful conclusions are drawn： 1） The edf for the total estimators is larger than the edf for the corresponding non-total estimators. And the edf for the overlapping and nonoverlapping estimator of the Allan variance is also larger than the edf for the corresponding Hadamard estimator. 2） The lower the Fourier frequency of the noise is, the larger the corresponding edf for the nonoverlapping estimators. However, the higher the Fourier frequency of the noise is, the larger the correspond- ing edf for the overlapping estimators and the total estimators. The improvement on the edf for the higher frequency noise is better than that for the lower frequency noise in the overlapping estimators and the total estimators.