Instrumentation & Measurement Magazine 23-2 - 59

Fig. 10. Frequency stability of TA3, TA4 and TA5 using UTCr as a reference.

From Fig. 10 it is noticed that the frequency stability of TA4
and TA5 was improved for averaging times from 1 day up to
nearly 40 days (3456000 s), as compared to TA3 (without denoising), due to de-noising the WFM noise of atomic clock
signal using EMD and KF, respectively. For longer averaging
times, the frequency stability of TA3, TA4, and TA5 is nearly
the same because other noise sources dominate atomic clock
signals. Also, the EMD method is as effective as the KF for denoising the WFM noise of Cs clocks for most of the averaging
times, at short and medium averaging times up to 40 days,
as shown in Fig. 10. So, the simple EMD method can be used
together with the average TS algorithm for enhancing the frequency stability of TA(K) and UTC(K) TS for averaging times
up to nearly 40 days, as compared to the more complicated
KF method. The detailed processing steps of the KF are mentioned in [3], [7] and that of the EMD are summarized above in
section 2. By comparing both of them, it is found that the EMD
is a simple averaging method that requires a lower processing effort than the complicated KF which depends on difficult
modelling, estimation and matrices operations. The estimated
MATLAB programs processing times of EMD and KF are approximately 3.4 s and 4.9 s, respectively, on a computer with
processor corei3-2100 CPU, cash memory of 3.10 GHz and
RAM of 2.00 GB.

Acknowledgment
The authors would like to thank Dr. Yuko Hanado from the
National Institute of Information and Communication Technology (NICT) for the very useful discussions on the basic
algorithm used in building the TS. The authors gratefully acknowledge the great effort exerted by the team of the OP lab
for maintaining a time scale (UTC(OP)) with excellent stability and accuracy. Also there is a great effort exerted by the team
of the time department at the BIPM in calculating and disseminating UTC and UTCr, preserving the results of the clock
comparisons of the different labs from all over the world on the
time server, and ensuring the availability of these data to the
outside community is really a very appreciated job.

References
[1]	 F. Riehle, Frequency Standards Basics and Applications. Hoboken,
NJ, USA: WILEY-VCH, 2004.
[2]	 D. B. Sullivan, D. A. Howe, F. L. Walls, and D. W. Allan,
"Characterization of clocks and oscillators," NIST Tech. Note, vol.
1337, 1990.
[3]	 L. Galleani, L. Sacerdote, P. Tavella, and C. Zucca, "A
mathematical model for the atomic clock error," Metrologia, vol.

Conclusion

40, pp. S257-S264, 2003.

In this paper, a detailed overview of the EMD method and
its use for decomposing non-stationary and non-linear signals into a finite number of IMFs using sifting process was
presented. Then, a MATLAB program was designed for using the EMD method for de-noising Cs1, Cs2, Cs3, and Cs4 of
OP. Obtained results showed that the frequency stability of
these clocks was greatly improved due to using EMD for signal de-noising for averaging times up to almost 40 days. An
average TS (TA1) was built first using the four real Cs clocks
of OP before de-noising using the simple average TS algorithm. Then, the de-noised Cs clocks were used instead of
the original ones for building TA2 TS. Results showed that
the frequency stability of TA2 was improved as compared to
TA1 for most of the averaging times up to almost 40 days due
to using EMD method for Cs clock signal de-noising. Finally,
April 2020	

the performance of EMD was compared to that of the KF for
de-noising the WFM noise of CS clocks and enhancing the frequency stability of TA(K) and UTC(K) TS. Obtained results
show that using both EMD and KF enhance the frequency
stability of TA4 and TA5 TS as compared to the simple average TS (TA3) for averaging times from 1 day up to nearly 40
days. Also, the EMD is as effective as the complicated KF for
enhancing TA(K) frequency stability for most of the averaging times up to 40 days. But, the EMD method is simpler than
the KF in its programming and implementation. So, a time
keeping Lab can build an average TS scale algorithm together
with the EMD method for atomic clock signal de-noising to
obtain a highly stable reference TA(K) that can be used for
UTC(K) steering for averaging times up to almost 40 days to
enhance its frequency stability. In the future, all possible uses
of the EMD method in TS and steering algorithms will be further studied.

[4]	 S.-Y. Lin and H. M. Peng, "A paper clock model for the Cesium
clock ensemble of TL," in Proc. 35th Precise Time Time Interval
Meet., pp. 297-307, 2003.
[5]	 S.-Y. Lin, "A paper clock prediction model for UTC(TL)," in Proc.
IEEE 2016 European Frequency and Time Forum (EFTF), pp. 152-155,
2016.
[6]	 N. E. Huang et al., "The empirical mode decomposition and the
Hilbert spectrum for nonlinear and non-stationary time series
analysis," R. Soc. London Proc. Ser. A, vol. 454, no. 1, pp. 903-995,
1998.
[7]	 L. Galleani and P. Tavella, "On the use of the Kalman filter in
timescales," Metrologia, vol. 40, pp. S326-S334, 2003.
[8]	 Q. Lili and L. Bian, "Analysis and application of atomic clock
signal based on EMD," in Proc. 2013 IEEE 11th Int. Conf. Electron.
Meas. Instruments, Harbin, China, pp. 84-87, Aug. 2013.

IEEE Instrumentation & Measurement Magazine	59



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