振荡器稳定度时域-频域参数转换的新方法

A New Approach to Converting the Parameters of Oscillator Instabilities from Time-Domain to Frequency-Domain

依据相位起伏谱密度至阿伦方差的转换公式,提出了一种由阿伦方差至相位起伏谱密度转换基本数学模型,考虑到转换结果的不唯一性,采用相位起伏谱密度的通用幂律模型,给出了转换方法的约束最大似然解,并结合正则化方法消除模型求解过程中的病态特性.计算表明,由该方法转换所得的相位起伏谱密度与真实谱密度数据能很好地吻合;此外,还分析了正则化因子的选择与输入阿伦方差参数的选择对反演性能的影响.

A new mathematical model is proposed to convert the oscillator instability parameters from Allan Variance to Spectrum Density （SD） of random phase fluctuations, which is the inversion of the classic transformation formula from SD to Allan Variance. The power-law model of the SD of oscillator phase fluctuations is introduced to the converting algorithm due to the fact that Allan Variance does not always determine a unique SD, which gives a constrained maximum likelihood solution of the inversion. Considering that the inversion problem is ill-posed, a regularization method is brought forward in the solving process. Simulation results show that the converted SD of phase fluctuations from Allan Variance parameters agrees well with the real SD function. Furthermore, the effects of the selected regularization factors and the input Allan variances are analyzed in detail.