导航卫星原子钟频率稳定度估计的小波方差方法

The Wavelet variance estimation methods of frequency stability for atomic clocks of navigation satellites

国内外学者对小波方差理论在原子钟性能分析方面的应用做了一些研究,但相关文献对小波方差的定义及其表征稳定度的特性描述却并不完全一致,这给应用研究造成不便。为此,首先根据时域方差定义的原理,相应地提出了小波方差、重叠小波方差和小波总方差的概念,然后经综合归纳,针对性地选择给出了应用于原子钟频率稳定度估计的"尺度域"小波方差的定义计算公式及等效自由度的计算方法。最后,通过一个算例与时域方差进行比较分析,总结明确了两者的关系及小波方差的特点,从而说明小波系列方差可以有效地进行原子钟频率稳定度的估计。

As the development of the wavelet analysis methods, the experts at home and abroad have done much research on the application of the wavelet variance to the properties analysis of atomic clock. But the definition of wavelet variance and its properties description of representational stability didn＇ t agree well in some literatures, which led to confusion on applicative research. Conse- quently, according to the definition principle of the variance at time domain, this paper firstly put forward the concepts of wavelet variance, overlapping wavelet variance and wavelet total variance. Then, by synthesizing and concluding the existing references, the calcu- lation formulas and the calculation methods of its equivalent degrees of freedom were given. By comparing with the variances at time domain, the relations and different characteristics of the variances at time and scale domain were defined clearly, which showed that the wavelet variance could be available to estimate the frequency stability for atomic clocks.