Advanced Satellite-based Frequency Transfer at the 10^{-16} Level
M. Fujieda, S-H. Yang, T. Gotoh, S-W. Hwang, H. Hachisu, H. Kim, Y. K. Lee, R. Tabuchi, T. Ido, W-K. Lee, M-S. Heo, C. Y. Park, D-H. Yu, G. Petit
aa r X i v : . [ ee ss . SP ] O c t Advanced Satellite-based Frequency Transferat the 10 − Level
M. Fujieda, S-H. Yang, T. Gotoh, S-W. Hwang, H. Hachisu, H. Kim, Y. K. Lee,R. Tabuchi, T. Ido, W-K. Lee, M-S. Heo, C. Y. Park, D-H. Yu, and G. Petit ∗†‡
October 10, 2017
Abstract
Advanced satellite-based frequency transfers by TWCP and IPPP have been performed between NICT andKRISS. We confirm that the disagreement between them is less than × − at an averaging time of severaldays. Additionally, an intercontinental frequency ratio measurement of Sr and Yb optical lattice clocks was directlyperformed by TWCP. We achieved an uncertainty at the mid-10 − level after a total measurement time of 12hours. The frequency ratio was consistent with the recently reported values within the uncertainty. Satellite-based time and frequency transfers are in demand for intercontinental links and typically utilize pseudorangemeasurements using a code phase of a signal modulated by a pseudorandom noise (PN) sequence. Increasing the chiprate of the PN sequence improves the measurement precision, although it occupies a wider frequency bandwidth at thesame time. This has limited the measurement precision of two-way satellite time and frequency transfer (TWSTFT)to an insufficient level for the comparison of advanced optical clocks. To improve the precision, the National Instituteof Information and Communications Technology (NICT) has developed a two-way carrier-phase satellite frequencytransfer (TWCP) [1]. It achieves sub-picosecond-level precision, which is three orders of magnitude better than that ofTWSTFT [2]. On the other hand, the precise point positioning (PPP) technique utilizing code and carrier phases hasbeen used by GPS time and frequency transfer (hereafter called GPS transfer) and contributed to the InternationalAtomic Time (TAI) computation [3, 4]. The measurement precision is improved by two orders of magnitude to a fewtens of ps by the application of the carrier phase in the GPS transfer. However, solving the phase ambiguity mayintroduce random errors in GPS transfer results. To overcome this limitation, the integer PPP (IPPP) technique hasbeen developed [5]. It has been applied to GPS transfer and recently demonstrated a 1 × − frequency transferaccuracy [6]. Thus, these advanced satellite-based frequency transfer techniques such as TWCP and IPPP have thepotential to enable optical clock comparisons in a very long baseline. Aiming at the evaluation and comparison oftheir techniques, NICT and the Korea Research Institute of Standards and Science (KRISS) established the TWCPlink in December 2016. In this paper, we describe the frequency transfer techniques in Sec. II and introduce thecomparison between the two techniques in Sec. III. In Sec. IV, the frequency ratio measurement of Sr and Yb opticallattice clocks by TWCP is demonstrated. NICT and KRISS have performed TWCP and GPS transfer on a regular basis. Here, we introduce the TWCP andIPPP techniques briefly. Then their measurement setups at NICT and KRISS are shown.
By two-way signal exchange, the delay terms in the propagation path are almost canceled in TWCP. When wedetermine a pseudorange from the carrier phase of the transmitted signal from an earth station A at an earth stationB, however, we have to remove two terms: the Doppler effects caused by the satellite motion and the phase noise induced ∗ M. Fujieda, T. Gotoh, H. Hachisu, R. Tabuchi, T. Ido are with the National Institute of Information and Communications Technology,Koganei, Tokyo, 184-8795 Japan. e-mail: [email protected]. † S-H. Yang, S-W. Hwang, Y. K. Lee, H. Kim, W. K. Lee, M-S. Heo, C. Y. Park, D-H. Yu are with the Korea Research Institute ofStandards and Science, Daejeon, 305-600 Korea. ‡ G. Petit is with the Bureau International des Poids et Mesures, S`evres F-92312 France.
1y an onboard oscillator in frequency conversion from uplink to downlink frequencies because most of communicationsatellites do not carry an atomic clock. It was shown in [2] that the mathematical cancellation by using four carrierphases of the four signals from A to A, from A to B, from B to A, and from B to B is effective in removing them.Additionally, the ionosphere delay is not canceled either because the uplink and downlink frequencies are different.Therefore, we utilize an ionosphere map and compute the delays using the total electron contents (TECs) over theearth stations. Since the carrier phase is continuously tracked and accumulated in TWCP measurement without anyfixation of phase ambiguity, the result basically keeps the continuity as long as the measurement continues.Figures 1 (a) and (b) show schematics of the earth stations at NICT and KRISS, respectively. We use an arbitrarywaveform generator for the signal generation and an analogue-to-digital (A/D) sampler for carrier-phase detection.The TWCP signal has a frequency bandwidth of 200 kHz. The code phase of 128 k chips per second (cps) is detected,as well as the carrier phase, and it helps the signal tracking. The frequency conversion is carried out by commercialfrequency up- and downconverters from 70 MHz to uplink and downlink frequencies of 14 and 11 GHz, respectively.The reference signals of 10 MHz are provided to the frequency converters to maintain the carrier phase coherence.At NICT, a dedicated earth station is used for the TWCP measurement. On the other hand, at KRISS, the TWCPand conventional TWSTFT measurements share one earth station. The two signals for the TWCP and TWSTFTare combined and divided at 70 MHz by a signal combiner and divider, respectively. Figure 1 (c) shows the receptionspectrum where the same center frequency was used by the TWCP signal and the TWSTFT signal with a bandwidthof 2.5 MHz. We did not observe any interference between them caused by sharing the same frequency bandwidth.We started continuous TWCP measurement alongside TWSTFT in December 2016 using a geostationary satellitenamed Eutelsat 172A. For the ionosphere delay correction between NICT and KRISS, we use a global ionosphere mapproduced by the Center for Orbit Determination in Europe (CODE) [7]. The typical amplitude of the ionospheredelay is about 10 ps.
In IPPP, as in classical PPP, the user’s clock is determined from dual frequency GPS phase measurements usingsatellite clock products generated by analysis of a global network. For IPPP, the satellite products generated by theGRG analysis centre [8] are designed so that the user can determine the phase ambiguities for each satellite passand the two frequencies as integers N1/N2. This is done in a two-step procedure with the CNES GINS software,first determining the widelane ambiguity Nw = N2 - N1 and then determining e.g. N1, see details in [6, 8]. Clockdifferences are then continuous as long as there is no discontinuity in the set of integer ambiguities for all satellitepasses.As shown in [6], the above treatment is performed on a station by station basis, independently for each day, andthe continuity between successive daily batches is then to be established. By design, discontinuities between batchesshould be an integer number of the so-called narrowlane wavelength λ N ( ∼
350 ps) and it is simpler to determine thesediscontinuities when forming the difference of two station clocks, i.e. a time link. Indeed, when the instability of thetwo compared clocks is sufficiently low, the extrapolation noise from batch to batch is much lower than λ N and it iseasy to determine the discontinuities as an integer number of λ N . This extrapolation technique was used for the IPPPsolution between UTC(NICT) and UTC(KRIS) which are both based on H-masers. Note that such discontinuitiesmust also be determined when all satellite ambiguities are reset within a daily batch, e.g. by a short data gap.The GPS receivers used at NICT and KRISS are Septentrio PolaRx 4 and Ashtech Z12T connected to the referencesignals from UTC(NICT) and UTC(KRIS), respectively. We compared the measurement results obtained by PPP, IPPP, and TWCP for two periods: (1) from MJD 57772 toMJD 57784 and (2) from MJD 57851 to MJD 57883. Here, PPP is computed with NRCan PPP software using 15days batch and IGS final products. The TWCP measurements were continuously carried out without any downtime.The measurement rates of PPP, IPPP, and TWCP are 300, 30, and 1 s, respectively. Figure 2 (a) shows the timedifference between UTC(NICT) and UTC(KRIS) for period (2). For better visibility, offset values are inserted. Figure2 (b) shows the double differences of IPPP-TWCP and PPP-TWCP. A time jump can be observed at MJD 57861. Itis clear that the TWCP result causes it because the signal-to-noise ratio at the KRISS station suddenly decreased by8 dB owing to heavy rain, and a phase excursion of 0.2 ns occurred in the TWCP result. Additionally, a small jumpcan be seen at MJD 57856. It was found that the GPS receiver at NICT caused a reset of all ambiguities at thattime. While IPPP found an exact integer number of cycles to go through the reset, PPP could not. Furthermore, thedouble difference of PPP-TWCP indicates a clear gradient, which can also be seen in the result for period (1). Weassume that the gradients show disagreements among the techniques, and they are summarised in Table 1. IPPP andTWCP show consistency at the 10 − level. Figure 3 shows the modified Allan deviation of UTC(NICT)-UTC(KRIS)for period (2). The stabilities longer than 1 day are limited by those of the time scales. The double differences2 a) (b) (c) TWSTFT
Figure 1: Schematics of the earth stations at (a) NICT and (b) KRISS. BPF: band-pass filter, amp.: amplifier, A/D:analogue-to-digital converter. (c) Spectrum of the reception signals for TWCP and TWSTFT.Figure 2: (a) Time difference between UTC(NICT) and UTC(KRIS), (b) double differences of IPPP-TWCP andPPP-TWCP. 3f IPPP-TWCP and PPP-TWCP are free from the limitation. While the curve of IPPP-TWCP is decreasing andreaches 10 − level after 500,000 s, that of PPP-TWCP becomes flat. For period (1), similar stabilities are achievedof 5 . × − at 250,000 s for IPPP-TWCP and 1 . × − at 250,000 s for PPP-TWCP. By the comparisons amongPPP, IPPP, and TWCP, it proved that TWCP, as well as IPPP, has superior long-term stability. Until now, unless thesignal-to-noise ratio decreases suddenly owing to the weather conditions, the measurement has successfully continuedand phase continuity can be preserved in the TWCP results.Figure 4 shows the time differences of UTC(NICT)-UTC(KRIS) free from the time-scale variation, from which itstwo-day moving average is subtracted and then the remainder is averaged over 1 hour. As shown in Figure 4 (a),IPPP and PPP indicate some variations with periods of one day and half a day. Examination of each receiver’s datashows that both receivers have one-day-period components. In Figure 4 (b), the time difference for TWCP is depictedtogether with the outdoor temperature at NICT. Since the diurnal change of outdoor temperature at KRISS is similarto that of NICT, it is not shown. The fluctuation in TWCP is smaller than those of IPPP and PPP. However, TWCPalso shows one-day-period variation with an amplitude of 10 ps order. The ionosphere delays have already beencompensated. The variation sometimes shows a weak inverse correlation with the outdoor temperature, for example,around April 25, 2017. Additionally, the variation around April 20, 2017 seems to have a positive correlation. Werecently moved the outdoor power amplifier and low-noise amplifier into a temperature-stabilized box at the NICTearth station. Further analysis of the effect will be carried out in the near future. NICT and KRISS operate a Sr optical lattice clock [9, 10] and an
Yb optical lattice clock [11]. The frequency ratiowas measured by TWCP through microwave references. The optical clocks were continuously operated for around4 hours per day over 3 days during February 1-3, 2017. We performed two local measurements and one TWCPmeasurement at the same time. The frequencies of optical clocks were measured with reference to the microwavereferences by using an optical frequency comb at each site. The systematic frequency shifts of the optical clockwere corrected including the gravitational redshift. TWCP evaluates the frequency difference between the microwavereferences of both sites. At NICT and KRISS, a hydrogen maser, HM(NICT), and UTC(KRIS) with frequency f HM(NICT) and f UTC(KRIS) , respectively, were used as the microwave references. These signals were provided to theearth stations for TWCP. By obtaining fractional frequencies y Yb and y Sr against each result of previous absolutefrequency measurements f Yb and f Sr [11, 10] on the basis of f UTC(KRIS) and f HM(NICT) , the frequency ratio of the twooptical clock transitions ν Yb /ν Sr is measured as ν Yb ν Sr = y Yb y Sr · f Yb f Sr = f HM(NICT) f Sr / f Sr · f UTC(KRIS) f HM(NICT) · f Yb / f Yb f UTC(KRIS) · f Yb f Sr (1) The data acquisition rates of the two local measurements and one TWCP measurement were 1 point per every second.First, we extracted the data where both optical clocks were simultaneously operated. Figure 5 (a) depicts their Allandeviations measured on Feb. 1. The HM(NICT) signal was transferred by an unfixed coaxial cable to the Sr clock atthis measurement, which caused an unwanted fluctuation and instability at around 100 s. Since the stabilities shownin Figure 5 (a) display similar values around 30 s, we averaged three frequency ratios over 30 s, aligned the timestamps, and then calculated y Yb / y Sr following (1). The computed difference relative to f Yb / f Sr is depicted in Figure 5(b). The Allan deviation was calculated from the lumped data for 3 days as shown in Figure 5 (c) by a red line, wherethe fitting curve of 9 . × − × t − . is also depicted by a blue line. Table 2 summarises the daily mean values.Weighting the daily mean values by the number of 30-s points divided by the square of the daily standard deviation,we concluded the weighted frequency difference of 4 . × − for the 3-day measurement. As for the daily statisticaluncertainty, it was computed using the fitting curve of the Allan deviation for the measurement period. Table 3shows the uncertainty budget. The total statistical uncertainty was determined using the mean of the daily statisticaluncertainties divided by the square root of three: ((9 . + 9 . + 9 . ) / / . × − . In Figure 5 (c), the Allandeviation of f HM(NICT) / f UTC(KRIS) measured by TWCP for 3 days is depicted by the green line, which meets the fittingcurve at 5 × − around 40,000 s. This implies that the total statistical uncertainty was estimated appropriately.The systematic uncertainty for TWCP was 1 × − from the disagreement with IPPP. On the other hand, the Sr andYb lattice clocks have systematic uncertainties of 0 . × − and 1 . × − , respectively. The uncertainties of the4 E-171E-161E-151E-141E-131E+1 1E+2 1E+3 1E+4 1E+5 1E+6
IPPPIPPP-TWCPPPPPPP-TWCPTWCP M od i f i ed A ll an de v i a t i on MJD
Figure 3: Modified Allan deviation of UTC(NICT)-UTC(KRIS) from MJD 57851 to 57883.Table 1: Disagreement between PPP, IPPP and TWCPPeriod Difference Disagreement (10 − )(1) IPPP-TWCP -0.43MJD 57772-57784 PPP-TWCP 3.8(2) IPPP-TWCP -0.66MJD 57851-57883 PPP-TWCP 5.9 -0.2-0.100.10.2 01020304020 22 24 26 28 30 TWCP Temperature at NICT T i m e d i ff e r en c e [ n s ] T e m pe r a t u r e [ deg C ] Day in 2017/04 -0.2-0.100.10.220 22 24 26 28 30
IPPP PPP T i m e d i ff e r en c e [ n s ] Day in 2017/04 (a)(b)
Figure 4: Time difference free from time-scale variation: (a) IPPP and PPP, (b) TWCP and outdoor temperature atNICT. 5igure 5: (a) Allan deviations of two local measurements and one TWCP measurement carried out on Feb. 1. (b)Frequency difference of y Yb / y Sr − for 3 days. (c) Lumped Allan deviation of y Yb / y Sr , its fitting curve and the Allandeviation of f HM(NICT) / f UTC(KRIS) measured from Feb. 1-3. (d) Frequency ratio R reported so far.6ifferential gravitational redshift between both clocks is 0 . × − . We achieved a total uncertainty of 5 . × − .Thus, the consistency of the previous absolute frequencies reported by NICT and KRISS [10, 11] was confirmed by y Yb / y Sr − . ± . × − . We concluded the frequency ratio, R, asR = ν Yb /ν Sr = 1 . , , , , , We evaluated measurement results achieved by the advanced satellite-based frequency techniques of PPP, IPPP, andTWCP in the NICT-KRISS link. While the disagreement of PPP-TWCP remains at the 10 − level, that of IPPP-TWCP reaches the 10 − level at over 5 × s average time.The intercontinental frequency ratio measurement of Sr and Yb optical lattice clocks was directly performed by TWCP.We performed a dead-time-free and simultaneous measurement for about 12 hours and confirmed that the achievedfrequency ratio is consistent with those shown in other reports within a total uncertainty at the mid-10 − level. Inconclusion, not only optical fiber links but also advanced satellite-based frequency links are applicable to optical clockcomparisons. The satellite-based techniques have the potential to realize uncertainty at the 10 − level when opticalclocks are continuously operated for a week or more. Acknowledgement
The authors would like to thank H. Takiguchi now in JAXA for his technical support in PPP. The use of the GINSsoftware from the CNES and of the GPSPPP software from the NRCan is gratefully acknowledged.
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