Bureau International des Poids et Mesures
Laboratories clock data and UTC(k):
how do they enter in UTC
G. Panfilo
BIPM, Sèvres, 11 September 2012
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Outline
UTC, UTCr and UTC(k)
Clock data format
The use of the clock and time and transfer data
Steps in clock data
Weight of the clocks
Rates of the clocks with respect to TAI
Problems with clock data in UTC and UTCr calculation
Conclusions and discussion
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UTC, UTCr and UTC(k)
UTC is calculated by the BIPM in three steps:
1) EAL is computed as a weighted average of about
400 atomic clocks spread world-wide
2) The frequency of EAL is steered to maintain
agreement with the definition of the SI second, and
the resulting time scale is TAI
3) UTC is obtained with the addiction of leap seconds
to maintain agreement with the time derived from
the rotation of the Earth
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UTC, UTCr and UTC(k)
UTCr is calculated by the BIPM in two steps:
1) A free time scale is computed as a weighted average
of about 200 atomic clocks spread world-wide (a
similar UTC algorithm is used)
2) A steering algorithm is used to maintain UTC close
to UTCr
UTCr is a pilot project and the algorithm is under
study.
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UTC, UTCr and UTC(k)
UTC(k) – national realization of UTC.
UTC(k) can be generated in different way:
1) Single clock
2) Single clock corrected by the Micro Phase Stepper
(MPS)
3) An ensemble of atomic clocks (time scales)
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Clock data Format fo UTC
For UTC generation, monthly files are requested reporting
clock data at 5 days interval. The time and frequency steps
are reported in the same table.
MJD
Lab. Code
TA Code
Clock Code
UTC(Lab)-Clock
Time and frequency steps
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Clock data format for UTCr
For UTCr generation, daily files are requested
reporting clock data at 1 day interval. The time and
frequency steps are reported in the same file.
The file format is the same of the clock participating to
UTC.
MJD
Lab. Code
Clock Code
UTC(Lab)-Clock
Time and frequency steps
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Data exchange
Clock data
UTCr (weekly)
Circular T (monthly)
BIPM
Internet (FTP)
Time and frequency
laboratories and
Observatories
Clock weights
Clock rates
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Time transfer data
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Clock data in UTC generation
To generate UTC the clock data and the time link data are
used.
k (2 clocks clk1,clk2)
Ex: 3 labs named
p (2 clocks clk3,clk4) - PIVOT
m (1 clock clk5)
p
m
k
clk3 clk4
clk1 clk2
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clk5
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EX: data incoming and outcoming
Clock data:
UTC(k)-clk1
UTC(k)-clk2
UTC(p)-clk3
UTC(p)-clk4
UTC(m)-clk5
Time link data:
UTC(k)-UTC(p)
UTC(m)-UTC(p)
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Circular T:
UTC-UTC(k)
UTC-UTC(p)
UTC-UTC(m)
Main Product
Clock weights
Clock rates
Supplementary
information
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Algorithms
First step: EAL
5
𝐸𝐴𝐿 − 𝑐𝑙𝑘1 =
𝑤𝑖
𝑐𝑙𝑘1 ′ − (𝑐𝑙𝑘1 − 𝑐𝑙𝑘𝑖 )
𝑖=1
Weights
Clock differences
Prediction
TAI and UTC
𝑇𝐴𝐼 − 𝑐𝑙𝑘1 = 𝐸𝐴𝐿 − 𝑐𝑙𝑘1 + 𝐹
𝑈𝑇𝐶 − 𝑐𝑙𝑘1 = 𝑇𝐴𝐼 − 𝑐𝑙𝑘1 + 𝑙𝑒𝑎𝑝 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝑈𝑇𝐶 𝑘 are considered as clocks with zero weigth.
𝐸𝐴𝐿 − 𝑈𝑇𝐶 𝑘 , 𝑇𝐴𝐼 − 𝑈𝑇𝐶 𝑘 and finally 𝑈𝑇𝐶 − 𝑈𝑇𝐶(𝑘)
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Clock differences
To
obtain EAL-clk1,EAL-clk2 etc...
difference between the clocks.
p
we
need
the
m
k
clk3 clk4
clk1 clk2
clk5
Same laboratory:
clk1-clk2 =(UTC(k)-clk2)- (UTC(k)-clk1)
Different laboratories:
clk1-clk3 =(UTC(p)-clk3)- (UTC(k)-clk1)+(UTC(k)-UTC(p))
clk1-clk5 =(UTC(m)-clk5)- (UTC(k)-clk1)+(UTC(k)-UTC(p))-(UTC(m)-UTC(p))
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UTC-UTC(k), UTC-UTC(p) and UTC-UTC(m)
The published results in Circular T are obtained by:
UTC-UTC(k) =w1*( 𝑐𝑙𝑘1 ′-(UTC(k)-clk1))+w2*( 𝑐𝑙𝑘2 ′ -(UTC(k)-clk2))+.....
UTC-UTC(p) =w1*( 𝑐𝑙𝑘1 ′-(UTC(p)-clk1))+w2*( 𝑐𝑙𝑘2 ′ -(UTC(p)-clk2))+.....
UTC-UTC(m) =w1*( 𝑐𝑙𝑘1 ′ -(UTC(m)-clk1))+w2*( 𝑐𝑙𝑘2 ′ -(UTC(m)-clk2))+.....
The differences in the equations are found with the
combination of the clock and time link data.
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Time and Frequency Steps
An important role in UTC calculation is the time and
frequency steps affecting UTC(k) or the clocks.
The time and frequency steps affecting the clocks can
affect UTC.
Possible scenarios are possible:
1) Time or frequency steps in UTC(k)
2) Time and frequency steps in a single atomic clock
3) Time and frequency steps in all the clocks
The BIPM requires that time and frequency steps
are reported at the end of data clock file
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Effect of clock steps in UTC
UTC is affected by the time and frequency steps of the
atomic clocks and not declared by the laboratories.
8
Atomic clocks with
time step
Nanoseconds
6
4
Resulting time scale
with time step
2
0
Atomic clocks
-2
-4
0
200
400
600
800
1000
Time
If the laboratory declares steps in the clocks the BIPM:
1) Correct the past frequency data for the weigths
2) Correct the past clock data to have continous data
without steps
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1) Example of time step in UTC(k)
UTC(INPL) is generated
caesium clock 1352480
Time Link
UTC(INPL)-UTC(PTB)
by
the
500
Clock data
Nanoseconds
400
300
Time step
200
100
The declared time step
0
55999.46 1352480
-100
55980 55985
55990 55995
56000
MJD
56005 56010
56015
Bureau International des Poids et Mesures
-500.0
0.000 INPL 10061
56020
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2) Example of a time step in all the clocks
Time Link
UTC(IPQ) is generated
caesium clock +MPS
UTC(IPQ)-UTC(PTB)
400
the
Clock data
350
Nanoseconds
by
300
250
The declared time step
200
150
55615
55620
55625
55630
55635
MJD
55640
55645
55650
Bureau International des Poids et Mesures
55655
55645.53
55645.53
55645.53
1352169
1351797
1352012
-200.0
-200.0
-200.0
0.000
0.000
0.000
IPQ 10070
IPQ 10070
IPQ 10070
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3) Example of time steps in a single clock
Time Link
UTC(HKO) is generated
caesium clock 1351893
UTC(HKO)-UTC(PTB)
-200
by
the
Clock data
-210
Nanoseconds
-220
-230
-240
-250
The declared time step
-260
-270
-280
56040
56045
56050
56055
56060
MJD
56065
56070
56075
56080
UTC(HKO) is not affected by time steps
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Weight of the clocks
At each clock is assigned a weight to contribute to UTC.
The weight attributed to a clock reflects its long-term
stability. The clocks with deterministic signatures
like frequency drift or aging are de-weighted and
considered “bad” clocks.
In the time scale algorithms clock weights are generally
chosen as the reciprocals of a statistical quantity
which characterizes their frequency stability, such as
a frequency variance (classical variance, Allan
variance....)
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Check of the data clock
The weight attributed to clock Hi is the reciprocal of the individual
classical variance σi2
1
i 
 i2
N

i 1
1

Upper Limit  MAX 
2
i
A
N
A=2.5 empirical constant
Two particular situations are checked:
1. Clock Hi shows abnormal behaviour
2. The weight is bigger then the upper limit fixed to avoid that a
clock has a predominant role.
The weight attributed to clock Hi is computed from the frequencies
of the clock, relative to EAL, estimated over the corrent 30-day
interval and over the past 11 consecutive 30-day period. The
weight determination thus uses clock measurement covering one
year.
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Weights of the clocks
Each month the weights of the
clocks participating to UTC
calculation are published on
the ftp.
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Rates of the clocks
Each month the clock rates are
calculated with respect to TAI
for eac clock participating to
UTC calculation.
This information ca be used
by the laboratories to steer
their clocks to approach
UTC.
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Problems with clock data
Data clock problems:
1) Use of commas instead of points
2) Use of tabulations instead of space
3) The data format longer than requested
4) Wrong TA and clock codes
5) The sign of the time or frequency steps
6) The time or frequency steps are not reported at the
end of the clock data file
7) The format of the time and frequency steps should
be respected
8) .........
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The time step sign
Sometimes the sign reported for the steps is not correct.
The BIPM requires to evaluate the sign of a step:
NEW(clockvalue) - OLD(clockvalue)
Clock data
The declared time step
NEW(UTC(k)-clock))-OLD(UTC(k)-clock)) = -200.3-855.7 -1050 ns
The time step has the opposite sign = 1050 ns
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Problems with data clocks in UTCr
The laboratories report data clocks for UTCr and UTC.
Sometimes the data (of the same clock) reported for
UTCr are different from the data reported for UTC.
After UTC calculation UTC-clock data are used in UTCr
calculation to maintain UTCr close to UTC.
The clock values used for UTC and UTCr should be
consistent.
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Discussion and conclusions - 1
The calculation of UTC and UTCr rely on the clock data
comparison.
More then 400 atomic clocks are used for UTC and
more then 200 for UTCr.
The data clocks are checked and verified before
entering in the calculation.
The atomic clocks are weighted with respect to their
long term stability.
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Discussion and conclusions - 2
Time and frequency steps are particularly important
due to their impact on UTC quality.
Each time and frequency steps is checked and verified.
The BIPM published each month:
• Circular T
• The weights of the atomic clock
• The rates of the atomic clocks with respect to TAI.
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