利用小波方差进行原子钟频率稳定度的估计

The Estimation of Atomic Clock's Frequency Stability by Wavelet Variance

离散小波变换可以在不同尺度上分解时间序列,而不同尺度的波动性可用小波方差来表征。从小波方差的定义入手,系统地归纳了基于极大重叠离散小波变换(MODWT)的小波方差估计方法,及其等效自由度(EDF)的实用计算方法。最后利用一个实测算例进行计算分析,并与相应的重叠阿伦方差、重叠哈达玛方差进行比较,通过实验分析可以看出小波方差可有效消除原子钟信号非线性和非平稳性的影响,通过选择适当的小波基函数,如D4、D6小波,其方差可以像哈达玛方差一样,减少调频闪变噪声和调频随机游走噪声的泄露,适用于原子钟频率稳定度的表征。

The discrete wavelet transform can be used to decompose a time series at different scales, the properties of which can then be summarized by the wavelet variance. First starts with the definition of Wavelet variance, then presents the the estimation formula of wavelet variance based on the MODWT, and the practical computing methods of EDF. By using a numercial example, the estimated values and equivalent degree of freedom of overlapping Allan variance and overlapping Hadamard variance are compared with those of wavelet variance in the end. From that can get some useful conclusions. Wavelet variance put a curb on the influence of atomic clock signal＇s nonlinear and non-stationary process. By choosing wavelet basis function rationally, D4 and D6 wavelet variance just as Hadamard variance can decrease both the leakage of FM flicker noise and random walk noise,and is suitable to present the frequency stability of atomic clock.