Instrumentation & Measurement Magazine 23-5 - 39
Fig. 4. Time scale of traditional exponential filtering.
accurately. Therefore, this paper also studies the dynamic estimation method of the frequency drift of the hydrogen maser.
Exponential Filtering Time Scale Based on
Minimum Error Theory
A method based on minimum error theory is used to estimate
the frequency drift parameters of hydrogen masers. Firstly,
the method is used to estimate the frequency drift and average
time of hydrogen masers, and then the exponential filtering
time scale algorithm is used to calculate the time scale of the
hydrogen maser ensemble. Meanwhile, the classical weighted
average ALGOS algorithm is used to generate the time scale of
hydrogen masers.
Similarly, the time scale of the three hydrogen masers is
calculated by using the atomic clock difference data in three
months. The basic measurement interval τ is 1 h, and the average time τ1 is 20 h. Then, the exponential filtering time scale
based on minimum error theory is computed. The results are
shown in Fig. 5. Comparing the time scales calculated by the
three methods, the Allan deviation data are shown in Table 2.
From Fig. 5, it can be seen that the method based on minimum error theory can estimate the frequency drift parameters
of hydrogen masers accurately. The absolute value of the maximum deviation between the time scale of minimum error
theory exponential filtering method and TA(NTSC) in one
month is less than 5 ns, which is equivalent to the time scale
produced by ALGOS algorithm, but is obviously better than
the time scale calculated by traditional exponential filtering
method, and improves the accuracy of the time scale. From Table 2, it can be seen that the time scale stability of the hydrogen
maser ensemble based on minimum error theory is slightly
better than that of a traditional exponential filtering time scale.
The stability of the time scale which uses the minimum error
theory exponential filtering method is 7.56e-15 in 1h and 3e15 in 5 days. Its stability
is always better than that
generated by the ALGOS
algorithm. That is to say,
the method based on minimum error theory greatly
improves the accuracy
of the time scale without
affecting the stability of
the time scale of hydrogen masers. This method
reduces the influence of
frequency drift term of hydrogen clocks on time scale
effectively.
Fig. 5. Time scale results of the three methods.
Table 2 - The stability of time scales of three methods
ADEV
Averaging time (h)
Traditional exponential
filtering
Minimum error theory
exponential filtering
ALGOS
1
7.56e-15
8.59e-15
8.61e-15
2
5.06e-15
5.53e-15
5.82e-15
4
5.78e-15
5.98e-15
6.21e-15
8
6.95e-15
7.03e-15
6.97e-15
16
5.32e-15
5.80e-15
6.64e-15
32
4.70e-15
4.72e-15
4.82e-15
64
4.05e-15
4.44e-15
4.45e-15
128
2.75e-15
3.24e-15
3.23e-15
256
1.62e-15
2.76e-15
2.64e-15
August 2020
IEEE Instrumentation & Measurement Magazine 39
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