carrier phase two-way satellite frequency transfer (twcp)
TRANSCRIPT
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Carrier Phase Two-Way Satellite Frequency Transfer (TWCP)
Miho Fujieda
National Institute of Information and Communications Technology (NICT)
APMP TCTF workshop 9/19/2014
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- Motivation
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
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Motivation
For intercontinental transfer, frequency link via satellite is still necessary, especially for island country, Japan.
10-18
10-17
10-16
10-15
10-14
10-13
100 101 102 103 104 105
周波
数安
定度
平均化時間 [s]Averaging time [s]
Alla
n d
evia
tion
Our target
Our target: improvement of transfer stability of TWSTFT in the 10-16 level
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Expected precision
Use of carrier phase is one of ways to improve the measurement precision.
Method Precision [ns] Rate/Frequency [MHz]
GPS code 5 1.023
GPS carrier phase 0.05 1575.42
TWSTFT code 0.5 2.5
TWSTFT carrier phase
0.005 ? 11000 ~ 14500
Brief measurement precision
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2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
History
ETS-VIII experiment at NICT2
First experiment by USNO and Timetech1
1 B. Fonville et al., Proc of PTTI meeting 149 (2004). 2 F. Nakagawa et al., Metrologia 50 200-207 (2013). 3 M. Fujieda et al., IEEE TUFFC 59 12 2625 (2012). 4 M. Fujieda et al., Metrologia 51 253-262 (2014).
NMIJ OP
Short-baseline3
Long-baseline4
TWCP: A technique established recently
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ωs ωu ωd
ωu, ωd : uplink, downlink frequencies
ωs : local frequency at satellite
Earth station A Earth station B
Communication satellite
What is problem for TWCP?
Phase jitter: induced by onboard oscillator in down-conversion
USNO’s proposal: Mathematical solution by using four signals (A->A, A->B, B->A, B->B)
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- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
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What tools are necessary for TWCP?
Name Lab
NICT modem (discontinued) NICT
SATRE modem USNO, OP
Arbitrary Waveform Generator (AWG) NICT
*Signal generation (Tx)
Name Lab
SATRE modem USNO, OP
A/D sampler (vssp32) NICT
*Phase/Frequency detection (Rx)
Frequency converters should be locked to an external reference. Other instruments are identical to conventional TWSTFT (code phase).
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Experimental apparatus for TWCP in NICT Setup of earth station
Power amp.
Low-noise amp.
Up converter
Down converter
Arbitrary waveform generator
A/D sampler
10MHz & 1pps
BPF
1.2-m/1.8-m/2.4-m antenna 99% OBW =
200 kHz
200-kHz signal for TWCP
Sampling : every 20 ms 50 points of 20-ms data
Least-square fit
1-sec data
Narrower bandwidth signal (200 kHz) for save satellite-link fee Slower chip rate signal (127.75 kcps) to help signal tracking
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Name Specification
Sampling frequency
40 kHz ~ 64 MHz
Number of A/D bit
1, 2, 4, 8
Number of channels
4
External reference signals
5 or 10 MHz and 1 pps
A/D Sampler for phase detection
Name Specification
Sampling frequency 204.6 MHz
D/A bit 8
Number of channels 2
Waveform memory 512 kB x 2 /CH
Overlay memory 64 kB / CH
External reference signals 10 MHz and 1 pps
Arbitrary waveform generator
Arbitrary waveform generator(Right)
A/D sampler (Left)
A/D sampler and AWG
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- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
![Page 12: Carrier Phase Two-Way Satellite Frequency Transfer (TWCP)](https://reader031.vdocuments.site/reader031/viewer/2022011915/61d7eed0527a912bac2e660c/html5/thumbnails/12.jpg)
Signal from station A at satellite:
Computation of time difference (1)
Sin(ωu’t+ωuτa(t))
= Sin(ωu (1 – va(t)/c)t + ωuτa(t))
Down-converted signal at satellite: Sin((ωu’-ωs)t+ωuτa(t) –ωsτs(t))
Received signal at station B:
v(t)/c ~1e-9 at GEO
Sin((ωu’-ωs)(1-vb(t)/c)t+ωuτa(t) –ωsτs(t)-ωdτb(t))
= Sin(ωdt + Φab(t))
Signal from station A: Sin(ωut+ωuτa(t))
(ωu’-ωs)(1-vb(t)/c)t = (ωu (1 – va(t)/c) -ωs) (1-vb(t)/c)t
= ωdt –ωuva(t)/c・t - ωdvb(t)/c・t + ωu・va(t)/c・vb(t)/c negligible
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c
ρas(t)
Time at station A: τa(t)
Radial velocity: va(t)
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ωs ωu ωd
A B
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
Phase from station A to station B
ωu, ωd : uplink, downlink frequencies
ωs : local frequency at satellite
τa,τs,τb : time difference of local clock
ρas,ρbs : geometric distance between earth station and satellite
c : speed of light
Computation of time difference (2)
I ij: Ionosphere delay with frequency fi at station j [s]
Time difference:
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φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
Phase from station A to station B
Computation of time difference (3)
*Ionosphere delays: given by TEC map *Troposphere delay independent of frequency: canceled out on the way
Iij(t) = c・fi
2
40.3・TECj(t)
TECj(t): Total electron content at position j [1016 electrons/m2]
4 Unknown values: (τa – τb), τs, ρas, ρbs
4 equations
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φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
1. Phase from station A to station B
φba(t)=ωuτb(t)-ωsτs(t)-ωdτa(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIub(t)+ωdIda(t)
2. Phase from station B to station A
φaa(t)=ωuτa(t)-ωsτs(t)-ωdτa(t)-(ωuρas(t)+ωdρas(t))/c +ωuIua(t)+ωdIda(t)
3. Phase from station A to station A
φbb(t)=ωuτb(t)-ωsτs(t)-ωdτb(t)-(ωuρbs(t)+ωdρbs(t))/c +ωuIub(t)+ωdIdb(t)
4. Phase from station B to station B
Computation of time difference (4)
Time difference:
Target
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φab(t)-φba(t)=(ωu+ωd)(τa(t)-τb(t))-(ωu-ωd)(ρas(t)-ρbs(t))/c +ωu(Iua(t) – Iub(t)) - ωd(Ida(t)-Idb(t))
1-2
φaa(t)-φbb(t)=(ωu-ωd)(τa(t)-τb(t))-(ωu+ωd)(ρas(t)-ρbs(t))/c +ωu(Iua(t) – Iub(t)) + ωd(Ida(t)-Idb(t))
3-4
Computation using 4 phase information
Calculation of time difference (5)
ω+
ω+ ω-
ω- x(t)
x(t) y(t)
y(t)
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Time difference between station A and station B with ionosphere delay terms
τa(t)-τb(t) ω+x(t)-ω-y(t)
= ω+
2 –ω-2
x(t) = φab(t) - φba(t)
ω+ = ωu + ωd
y(t) = φaa(t) - φbb(t)
ω- = ωu - ωd
Calculation of time difference (6)
φab(t) ,φba(t), φaa(t), φbb(t) : Observed data
+ ω+
2 –ω-2
2ωuωd
[(IdA(t)-IuA(t))-(IdB(t)-IuB(t))]
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- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
![Page 19: Carrier Phase Two-Way Satellite Frequency Transfer (TWCP)](https://reader031.vdocuments.site/reader031/viewer/2022011915/61d7eed0527a912bac2e660c/html5/thumbnails/19.jpg)
TWCP experiments in various-length baselines
*0 km Domestic, GE23@172°, free from stability of reference clocks *100-km Domestic (Tokyo-Kashima), GE23@172°, H-maser comparison *1000-km Domestic (Tokyo-Okinawa), GE23@172°, H-maser comparison *10000-km International (NICT-PTB), AM2@80°, UTC(k) or H-maser comparison
AM2@80° GE23@172° (now Eutelsat 172A)
NICT PTB
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NICT-PTB TWCP experiment (2013/3 ~ 2013/6)
*Period: 2013/3/7~2013/6/30 *Satellite: AM2 @ 80E *Satellite transponder on-time: 10:05 h ~ 22:59 h in UTC *Elevation angles: 3.7° @PTB 16.0°@NICT
PTB 1.8-m antenna
@PTB
Special thanks to D. Piester, J. Becker, A. Bauch
AWG
AD sampler
Frequency converters
SSPA
LNA
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TWCP stability in various-length baselines
10-16
10-15
10-14
10-13
100
101
102
103
104
105
106
0 km100 km
1000 km10000 km10000 km
Mo
difie
d A
llan
de
via
tio
n
Averaging time [s]
Short-term stability: Independent of baseline length
(2013/3/15)
(2013/3/7~4/1)
Due to H-maser
Due to Air-
conditioner
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Comparison with GPS CP in 10000-km baseline
-552
-550
-548
-546
-544
-542
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
TWcodeGPSCP (300-s avg)TWCP (300-s avg)
Tim
e d
iffe
rence
[n
s]
MJD
-800
-600
-400
-200
0
200
400
600
800
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
GPSCP
TWCP
Fre
qu
ency d
iffe
ren
ce (
x 1
01
5)
MJD
300-s averageFiber transfer system failed.
Wo/ fiber link stabilization
1-s average, 300-s sampling
Phase ambiguity in TWCP: Filled by integral multiple of one period to agree with GPS CP
Result of TWCP: Consistent with GPS CP within the uncertainty of GPS CP
5 days
2 ns
2e-13
5 days
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Comparison with GPS CP in 10000-km baseline
-552
-550
-548
-546
-544
-542
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
TWcodeGPSCP (300-s avg)TWCP (300-s avg)
Tim
e d
iffe
rence
[n
s]
MJD
-800
-600
-400
-200
0
200
400
600
800
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
GPSCP
TWCP
Fre
qu
ency d
iffe
ren
ce (
x 1
01
5)
MJD
300-s averageFiber transfer system failed.
Wo/ fiber link stabilization
1-s average, 300-s sampling
Phase ambiguity in TWCP: Filled by integral multiple of one period to agree with GPS CP
Result of TWCP: Consistent with GPS CP within the uncertainty of GPS CP GPSCP-TWCP:(1.3±0.8)x10-15
standard error
5 days
2 ns
2e-13
5 days
10-16
10-15
10-14
102
103
104
105
106
GPSCPTWCPGPSCP-TWCP
Mo
difie
d A
llan
de
via
tio
n
Averaging time [s]
w/ gap
GPSCP-TWCP: 5e-16 @ 1 day
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- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
![Page 25: Carrier Phase Two-Way Satellite Frequency Transfer (TWCP)](https://reader031.vdocuments.site/reader031/viewer/2022011915/61d7eed0527a912bac2e660c/html5/thumbnails/25.jpg)
1E-17
1E-16
1E-15
1E-14
1E-13
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6
Error sources (1) *Short term
Item Phase jitter [ps]
Frequency converters ~ 0.2
Instability by common-clock meas. Frequency converters updated.
via Eutelsat 172A
old
new
Averaging time [s]
Alla
n d
evia
tio
n
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*Mid ~ Long term
Item Amplitude in time[ps]
Amplitude in Frequency
Compensation methods
Ionosphere ~ 300 ps 10-15~10-14
-Compensation using global ionosphere map -Average over 1 day
Troposphere A few ps < 10-16 -Not necessary at present
Sagnac effect < 20 ps (AM2, NICT-PTB)
< 10-15
-Calculation using orbit information
2nd order of Doppler shift
< 0.1 ps < 10-17 -Not necessary at present
Phase variation in instruments
A few ~ 200 ps < 10-13 -Temperature stabilization -Correction by measurement
Error sources (2)
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Phase variation due to frequency converters
-1
-0.5
0
0.5
1
1.5
7 8 9 10 11 12
GPSCP, 120-sec avgTWCP, 1-sec avg
Tim
e d
iffe
rence
[n
s]
Day in 2012/12
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20
21
22
23
24
25
26
27
28
7 7.05 7.1 7.15 7.2 7.25 7.3 7.35 7.4
Tim
e d
iffe
rence
[n
s]
Indo
or te
mp
era
ture
[de
g C
]
Day in 2012/12
TWCP
Room temp.
10-15
10-14
10-13
100
101
102
103
104
105
106
TWCPGPSCP
MD
EV
Averaging time [s]
3x10-13@1 s
1 day
0.5 ns
0.15 ns / 1.5 ℃
H-maser comparison
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Ionosphere delay correction using TEC map
TEC: Total Electron Contents Some TEC maps -Global ionosphere maps (GIM) ftp://ftp.unibe.ch/aiub/CODE
*Provided by the Center for Orbit Determination in Europe (CODE) *Time resolution: every 2 hours *Position resolution: 2.5°in latitude, 5.0°in longitude
-Japanese local TEC map http://wdc.nict.go.jp/IONO/gps-tec/tecv/
*Provided by NICT *Every 15 min. *2.0°in latitude, 2.0°in longitude
-European TEC map ftp://gnss.oma.be/gnss/products/IONEX/
*Provided by the Royal Observatory of Belgium (ROB) *Every 15 min. *0.5°in latitude, 0.5°in longitude
Iij(t) = c・fi
2
40.3・TECj(t)
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Ionosphere delay effect in NICT-PTB link Ionosphere delay in NICT-PTB link computed using GIM
Elevation angle: 3.7°@PTB ⇒ Significant impact in TWCP
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Ionosphere delay effect in NICT-PTB link Ionosphere delay in NICT-PTB link computed using GIM
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
10 11 12 13 14 15 16
GPS CP - TWCP: UTC(NICT)-UTC(PTB)
GPSCP-TWCPGPSCP-(TWCP w/ionosphere correction)Ionosphere correction
Do
uble
diffe
ren
ce [
ns]
Day in 2013/4
1-hour average
10-16
10-15
103
104
105
106
GPSCP-TWCP
wo/ correctionw/ correction
Mo
difie
d A
llan d
evia
tio
n
Averaging time [s]
The ionosphere effect was visible and the compensation using GIM was effective in NICT-PTB link.
3e-16
4/10~4/19
GPSCP-TWCP
1 day 0.05 ns
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Optical clock comparison in NICT-PTB link
10-16
10-15
10-14
10-13
100
101
102
103
104
2013/6/26
Sr(PTB)-H8Sr(NICT)-H4H4-H8H4-H8 (all data)Sr(PTB)-Sr(NICT)
Alla
n d
evia
tio
n
Averaging time [s]
Final result: Sr(PTB) = Sr(NICT) ± 1.6e-15
TWCP instability was worse than that of common-clock measurement. Due to instrument’s phase variation, imperfect compensation of ionosphere delays?
Further study is necessary.
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Summary
-TWCP is recently confirmed technique. -It has a measurement precision in the 10-13 level. -The precision is independent of the baseline length. -The result is consistent with GPSCP. Future plans for further study about the instability *24-hours measurement in 10000-km order link *Comparison of frequency standards
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Thank you for your kind attention.
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Global ionosphere maps (GIM) ftp://ftp.unibe.ch/aiub/CODE
*Provided by the Center for Orbit Determination in Europe (CODE) *Vertical total electron content (VTEC) *Time resolution: every 2 hours *Position resolution: 2.5°in latitude, 5.0°in longitude *Accuracy: 2~8 TECU [1016 electrons/m2] Ionosphere effect in TWSTFT: 40.3*(TECa-TECb)/c*(1/fu
2-1/fd2)
= 40.3*8 [TECU]/c*(1/fu2-1/fd
2)
~ 30 ps → 30 ps / 2/3600 ~ 4e-15
Ionosphere delay correction using global ionosphere map
VTEC 0,1 VTEC 1,1
VTEC 0,0 VTEC 1,0
VTEC(ti, j)
Time interpolation using VTEC(ti, j) and VTEC(ti+1, j)
Conversion from VTEC to slant TEC, along with signal path slant_TEC ~ VTEC/sinφ φ: elevation angle
φ
Iij(t) = c・fi
2
40.3・TECj(t)