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Bureau International des Poids et Mesures

IMPACT OF NEW FREQUENCY STANDARDS ON THE INTERNATIONAL TIME SCALES E. F. Arias, G. Panfilo

JD 6 ­ Commission 31 XXVII IAU General Assembly Rio de Janeiro (Brazil), 7 August 2009
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Elements of a time scale Minimum requisite: 1 clock

Reliable Stable and accurate in frequency Accessible Algorithm

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Atomic standards performances

· Secondary standards Stability Cs standard (st. tube) Cs standard (high perf.) H- maser (active) 5 x 10 1 x 10
-14

Accuracy 1 x 10 5 x 10
-12

@ 5 days

-14

-13

@ 5 days

< 2 x 10
@ 1 day

-16

· Primary standards

fe w 1 0

- 16

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Principles of calculation of UTC/TAI with the algorithm ALGOS

Time and frequency differences Clock data d a ta EAL + PFS data
·Optimized frequency stability ·Accurate in frequency Frequency corrections

Time transfer
·Optimized frequency stability ·No constrained to be accurate in frequency

TAI

+

(-n x s)

UTC

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H-maser
400

5071A

Other clocks

350

300

250

N

200

150

100

50

0

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Year
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EA L
Weighting algorithm Prediction algorithm

EAL(t ) =

w [h (t )
i =1 i i

N

+ hi(t

)]

· · · ·

N is the number of atomic clocks wi the relative weight of the clock Hi. hi(t) is the reading of clock Hi at time t hi'(t) is the prediction of the reading of clock Hi
N

The weights of the clocks obey the relation: wmax= 2.5/N


i =1

wi = 1

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Prediction Algorithm
t
i -1

t 30 days

t
i

i +1

30 days

In two different intervals the clock ensemble can change

EAL(ti-ti-1)

EAL(ti+1-ti)

The consequences:

EAL

t

i -1

t

i

t

EAL
t

i +1

i -1

t

t
i

i +1

Time step

Frequency step

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Prediction Algorithm on EAL
The prediction term hi'(t) for clock Hi is the sum of two terms:
Term to avoid time steps
'

Term to avoid frequency steps

hi (t ) = ai , I i + Bi
t
i -1

p,I

i

(t
Ii

-t
t

i

)

Ii

-1

t

i

i +1

EAL-Hi (ti-ti-1)

EAL-Hi (ti+1-ti)

· ai , I is the time correction relative to EAL of clock Hi at date ti
i

· Bi

p,I

i

is the frequency of clock Hi, relative to EAL, predicted for the period [ti, t]

Linear model: the frequency is considered constant during the month
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Prediction Analysis ­ Cesium Clock
3-year test period (2006-2008)
30 20 Na no s e c on ds 10 0 -10 -20 -30 0

The difference (prediction-reality) of the EAL-CS Clock with standard deviation (red lines).

5

10

15 Days

20

25

30

Considering 100 Cesium Clocks
The mean value of the difference (prediction-reality) for 100 EAL-CS Clock at 30 days is about 0.2 ns and the standard deviation is about 21 ns
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Prediction Analysis ­ H-maser
3-year test period (2006-2008)
5 0

Nanoseconds

The difference (prediction-reality) of the EAL- H Maser

-5 -10 -15 -20 -25

0

5

10

15

20

25

30

Considering 20 H-masers The mean value of the difference (prediction-reality) after 30 days is about -30 ns and the standard deviation at 30 days is about 40 ns
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Day s

As expected, linear model does not take care of the H-maser frequency drift
10


EAL compared to TT(BIPM)
EAL shows a frequency drift w.r.t. TT
f(EAL)-f(TT(BIPM08))
73

72

4 â 10

-16

/ month

71

70
-14

10 69

68

67

66 1999

2000

2001

2002

2003

2004 Year

2005

2006

2007

2008

2009

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EAL-TT
To show the influence of H-masers on EAL drift we consider TT as an independent reference:
6.85 x 10
-13

Normalized frequency

f(EAL
6.8

without Hmaser

)-f(TT)

f(EAL)-f(TT)

6.75

About 40% of EAL frequency drift is due to the H-masers
53600 53800 54000 MJD 54200 54400 54600 54800

6.7 53400

Frequency drift on f(EAL)-f(TT) is: Frequency drift on f(EAL
without Hmaser

4x10-16/ month
)-f(TT) is: 2.4x10
-16

/ month
12

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New prediction algorithm for the H-masers
The obtained relation for the prediction algorithm:

hi (t ) = ai , I i + Bi
'

p,I

i

1 (t - ti ) + Ci 2

p,I

i -1

1 (ti - ti -1 )(t - ti ) + Ci 2

p,I

i

(t

-t

i

)2

Now the frequency is not constant on the interval!
· ai · is the time correction relative to EAL of clock Hi at date t
i

,I

i

i

Bi

p,I

is the frequency of clock Hi, relative to EAL, predicted for the period [ti, t] is the frequency drift of the clock Hi, relative to EAL, predicted for the period [ti, t] is the frequency drift of the clock Hi, relative to EAL, predicted for the period [ti-1, ti]
13

· Cip ·C

,I

i

ip , I

i -1

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Effect of the new prediction algorithm
The difference (prediction-reality) of the EAL- H maser using two different prediction techniques
5 0
15 10

Nanoseconds

-5 -10 -15 -20 -25

Nanoseconds

5 0 -5 -10 -15 -20 0 5 10 15 20 25 30

0

5

10

15

20

25

30

Day s
Linear Prediction

Day s

Quadratic prediction

Considering 20 (EAL-H-masers)

The mean value of the difference (prediction-reality) after 30 days is about 2 ns and the standard deviation at 30 days is about 45 ns
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Effect of the new prediction algorithm
To show the influence of new prediction algorithm on EAL drift we use TT as independent frequency reference:
6.9 x 10
-13

Normalized frequency

6.85

f(EAL

new predition algorithm

)-f(TT)

6.8

f(EAL)-f(TT)

6.75

6.7

6.65 5.36

5.38

5.4

5.42

5.44

5.46

5.48

5.5 x 10
4

MJD

About 20% of EAL frequency drift is due to the linear prediction used in ALGOS 4x10-16/ month
)-f(TT) is: 3.2x10
-16

Frequency drift on f(EAL)-f(TT) is: Frequency drift on f(EAL

new prediction algorithm

/ month
15

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2
0

1.5
-50

EAL'-EA L

Percentage difference

1

-100 -150 -200 -250 -300 -350 -400

0

-0.5

-1

-1.5 0

5

10

15

20

25

30

35

40

N a n o seco n d s

0.5

Number of the months

53800 53900 54000 54100 54200 54300 54400 54500 54600 54700 54800

MJD

Difference of total weight of H-masers when a linear and a quadratic prediction is used. Weights increase. The drift of EAL increases when the prediction model is quadratic. Four months used for estimating the drift. ·Revise the weighting strategy ·Re-considering the use of clocks in the scale formation (caesiumbased scale for long-term stability + H-masers for improving short term stability)
16

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Primary standards in TAI
Primary Standard IT-CSF1 NICT-CSF1 NIST-F1 NMIJ-F1 PTB-CS1 PTB-CS2 PTB-CSF1 SYRTE-FO1 SYRTE-FO2 SYRTE-FOM SYRTE-JPO Type /selection Fountain Fountain Fountain Fountain Beam /Mag. Beam /Mag. Fountain Fountain Fountain Fountain Beam /Opt. Type B std. Uncertainty (0.5 to 0.7)x10 (0.8 to 1.5)x10 0.3x10 3.9x10 8x10
-15 -15 -15 -15

Operation

Comparison with H maser UTC(NICT) H maser H maser TAI TAI H maser H maser H maser H maser H maser

Number/typical duration of comp. 6 / 10 to 20 d 2 / 10-15 d 5 / 15 to 25 d 7 / 15 to 25 d 10 / 30 d 12 / 30 d 2 / 25 d 8 / 10 to 30 d 9 / 10 to 30 d 6 / 10 to 30 d 12 / 10 to 30 d

Discontinuous Discontinuous Discontinuous Discontinuous Continuous Continuous Discontinuous

-15

12x10

-15

0.9x10

-15 -15

(0.4 to 0.6)x10 (0.4 to 0.6)x10 (0.7 to 0.9)x10 6.3x10
-15

Discontinuous Discontinuous Discontinuous Discontinuous

-15

-15

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f(EAL) respect to PFS
f(EAL)-f(PFS) 72.0

71.4

70.8

NIST-F1 PTBCSF1

70.2
FO2 FOM IT-CSF1
- 14

69.6

69.0

NPLCSF1 NMIJ-F1

10

68.4

FO1 NICT-Cs F1

67.8

67.2

66.6

66.0 1999

2000

2001

2002

2003

2004 Years

2005

2006

2007

2008

2009

2010

By using the PFS we evaluate the systematic variation of EAL
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Uncertainty of Optical Clocks
Optical transitions · have five orders of magnitude higher frequency ; Q = / · allow for higher frequency stability · can be measured with arbitrary acctucacy tanfdarombs Op i r al s by s c ds · allow for higher accuracy as compared to microwave transitions

Primary Cs clocks

F. Rihele, Report to CCLCCTF WG, June 2009

In the future a new definition for the second will be required.
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Conclusions
The effect of the linear prediction algorithm has been studied · on the Cesium clock · on the H-masers it works well it does not work well

The impact of the H-masers on EAL frequency drift has been analyzed. A new mathematical expression for the prediction has been found. It includes the treatment of H-maser frequency drift. More work is needed to adapt the algorithm to the proposed frequency prediction. PFS number and accuracy has increased; the accuracy of TAI is approaching 10-16. The challenge is to be able to compare the optical frequency standards at the level of their performances.
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