Instrumentation & Measurement Magazine 23-2 - 53

Enhancing the Frequency Stability
of National Time Scale Using EMD
Aly I. Mostafa, Gihan G. Hamza, and Abdelhalim Zekry

A

lmost all time keeping laboratories maintain the
5071A Cesium (Cs) frequency standard for generating their national time scales. The frequency
stability of this standard is limited by different types of noise,
especially the White Frequency Modulation noise. These noise
types affect the stability of the resultant average Time Scale
(TS). Kalman Filter (KF) is still applied until now within the
time scale algorithm for de-noising and predicting improved
resultant TS frequency stability. But, this method is very complicated and is based on difficult estimation techniques. In
2013, the Empirical Mode Decomposition (EMD) technique
was applied for the first time on Cs atomic clock signal de-noising and frequency prediction. In this paper, the EMD technique
is embedded in the TS generation algorithm for studying its effect on the stability of the resultant TS. Results show that the
frequency stability of the resultant TS is improved for averaging times up to nearly 40 days due to EMD. These results are
verified by comparing the effect of the EMD to that of the KF
on the resultant TS frequency stability. Results show that the
frequency stability of the resultant average TS is improved due
to using EMD or KF for Cs clock signal de-noising for averaging times up to nearly 40 days. In addition, EMD is found to be
more effective and simpler than the complicated KF.

De-Noising Atomic Clocks
The commercial Cesium (Cs) atomic clock 5071A is one of the
most important frequency standards at time and frequency
laboratories (Labs) around the world. It is used for accurate
time keeping because of its very good long-term frequency
stability. Also, it is less sensitive to temperature variations than
other familiar frequency standards used at time Labs, such as
Hydrogen maser (HM). Moreover, 5071A Cs clocks do not suffer from linear frequency drift due to aging, so they maintain a
small relative frequency offset [1], [2].
Unfortunately, there are various noise sources such as
White Frequency Modulation (WFM) noise that affect frequency stability and accuracy of the output signal of Cs atomic
clocks [3]. Since 5071A clocks are used in the realization of the
Coordinated Universal Time (UTC) at national time keeping
April 2020	

Labs in the form of UTC(K) time scales (TS), where K is the
Lab abbreviation, then the reduction of frequency stability
of Cs clocks due to noise reduces the frequency stability of
UTC(K) as well [4]. So, there must be a method for de-noising the atomic clock signal to enhance the frequency stability
of UTC(K). Also, high-performance 5071A Cs clocks are used
as master clocks in steering algorithms for the realization of
UTC(K) scales at some time keeping Labs. In that case, the
steering algorithm is based on the accurate prediction of the
output frequency of the master clock using a suitable technique [5].
Some famous signal processing techniques such as Fourier transform and wavelet transform can be used widely for
signal de-noising and distinguishing useful signal from noise
for accurate frequency prediction. Fourier transform converts
the signal from time domain to frequency domain to separate
and distinguish stationary signal from noise, but it visualizes
the signal only in frequency domain and is not valid for nonstationary and non-linear signals. Wavelet transform, on the
other hand, can visualize the signal in both time and frequency
domains and is valid for non-stationary signals, but it is limited by the difficulty of the base selection and assumes the
signal is stationary in the wavelet window [6].
Kalman filter (KF) is widely used at time keeping Labs in
TS and steering algorithms for signal de-noising and accurate
frequency prediction of atomic clock signals. It allows accurate
modelling of different noise sources that affect atomic clock
signals, so it can be considered as a powerful tool for noise reduction and frequency prediction. But, it is very complicated
in its implementation, modelling and programming, because
it depends on difficult matrices and estimation techniques [7].
Hilbert-Huang transform (HHT) is a new and adaptive
recent method that can be used for signal de-noising and prediction of non-stationary and non-linear signals in many
applications [6]. It is an empirical technique not a theoretical tool as compared to Fourier and wavelet transforms. The
HHT algorithm consists of two major steps. These are the Empirical mode Decomposition (EMD) and the Hilbert Spectral
Analysis (HSA), and HHT can visualize the non-stationary

IEEE Instrumentation & Measurement Magazine	53
1094-6969/20/$25.00©2020IEEE



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