Analyze and process atomic clock difference data with Hilbert-Huang Transform

Atomic clock difference (errors) contains various kinds of noise and it can be characterized to as non-stationary. Hilbert-Huang Transform (HHT), a new adaptive method based on empirical mode decomposition (EMD) and Hilbert spectral analysis, was used to analyze and process atomic clock difference. Taking real data for discussion, the results show that HHT method is practical and versatile to handle noisy data and characterize the clock behavior.

[1]  Patrick Flandrin,et al.  Trend filtering via empirical mode decompositions , 2013, Comput. Stat. Data Anal..

[2]  Patrick Flandrin,et al.  Trend Filtering: Empirical Mode Decompositions versus ℓ1 and Hodrick-Prescott , 2011, Adv. Data Sci. Adapt. Anal..

[3]  P Tavella,et al.  Atomic clock prediction based on stochastic differential equations , 2008 .

[4]  D. B. Percival,et al.  A wavelet-based multiscale ensemble time-scale algorithm , 2012, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  Norden E. Huang,et al.  On Hilbert Spectral Representation: a True Time-Frequency Representation for nonlinear and nonstationary Data , 2011, Adv. Data Sci. Adapt. Anal..

[6]  Jean-Michel Poggi,et al.  Trend Extraction for seasonal Time Series Using Ensemble Empirical Mode Decomposition , 2011, Adv. Data Sci. Adapt. Anal..

[7]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Yuriy S Shmaliy Linear unbiased prediction of clock errors , 2009, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  J. Rutman Characterization of phase and frequency instabilities in precision frequency sources: Fifteen years of progress , 1978, Proceedings of the IEEE.

[10]  D. W. Allan,et al.  Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators , 1987, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[11]  Gabriel Rilling,et al.  Empirical mode decomposition as a filter bank , 2004, IEEE Signal Processing Letters.

[12]  Wu Haitao,et al.  Dynamic grey-autoregressive model of an atomic clock , 2008 .

[13]  Norden E. Huang,et al.  A review on Hilbert‐Huang transform: Method and its applications to geophysical studies , 2008 .

[14]  P. Tavella,et al.  Time and the Kalman Filter , 2010, IEEE Control Systems.

[15]  N. Huang,et al.  A study of the characteristics of white noise using the empirical mode decomposition method , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.