Characterization of a 450-km Baseline GPS Carrier-Phase Link using an Optical Fiber Link
Stefan Droste, Christian Grebing, Julia Leute, Sebastian M.F. Raupach, Arthur Matveev, Theodor W. Hänsch, Andreas Bauch, Ronald Holzwarth, Gesine Grosche
aa r X i v : . [ phy s i c s . i n s - d e t ] M a y Characterization of a 450-km Baseline GPSCarrier-Phase Link using an Optical Fiber Link
Stefan Droste , Christian Grebing , Julia Leute , SebastianM.F. Raupach , Arthur Matveev , Theodor W. Hänsch , ,Andreas Bauch , Ronald Holzwarth , and Gesine Grosche Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching,Germany Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig,Germany Menlo Systems GmbH, Am Klopferspitz 19a, 82152 Martinsried, Germany Ludwig-Maximilians Universität, Schellingstrasse 4, 80799 München, GermanE-mail: [email protected]
Abstract.
A GPS carrier-phase frequency transfer link along a baseline of 450 kmhas been established and is characterized by comparing it to a phase-stabilized opticalfiber link of 920 km length, established between the two endpoints, the Max-Planck-Institut für Quantenoptik in Garching and the Physikalisch-Technische Bundesanstaltin Braunschweig. The characterization is accomplished by comparing two activehydrogen masers operated at both institutes. The masers serve as local oscillators andcancel out when the double differences are calculated, such that they do not constitutea limitation for the GPS link characterization. We achieve a frequency instability of × − in 30 s and × − for long averaging times. Frequency comparisonresults obtained via both links show no deviation larger than the statistical uncertaintyof × − . These results can also be interpreted as a successful cross-check of themeasurement uncertainty of a truly remote end fiber link.PACS numbers: 06.20.-f, 06.20.fb, 06.30.Ft, 42.62.Eh Keywords : frequency transfer, global positioning system, optical fiber link, atomic clock
Submitted to:
New J. Phys.
1. Introduction
Various scientific experiments in metrology, radio astronomy or particle acceleratorsrequire the syntonization or synchronization between remotely located sites [1, 2, 3].Also applications like telecommunication and navigation rely on precise synchronizationamong remote frequency sources [4]. To take advantage of the rapid increase inperformance of atomic clocks which have recently been reported to achieve an instability haracterization of a 450-km Baseline GPS Carrier-Phase Link × − [5, 6], novel frequency dissemination techniquescapable of supporting the performance of state-of-the-art clocks are being developed.In recent years, extensive research on the transfer of stable optical frequencies viaoptical fiber links demonstrated excellent performances with residual instabilities ofa few parts in [7, 8, 9]. This method, however, requires a fiber link connectionbetween the remote sites which might be impractical for some geographical regions orcertain applications. Additionally, the establishment of intercontinental optical fiberlinks for frequency dissemination will be challenging.A more traditional way of transmitting time or frequency information is based onexchanging microwave signals between ground stations and satellites. Here, two existingtechniques have to be distinguished. If a geostationary telecommunication satellite isused as a space based repeater station, microwave signals are exchanged between tworemote locations on the earth. In this approach, signals are sent from and received byboth locations simultaneously in order to cancel out most one-way propagation delayeffects. This method is typically referred to as Two-Way Satellite Time and FrequencyTransfer (TWSTFT) and requires complex equipment and costly transponder capacityon the commercial satellites [10, 11, 12]. An alternative method is based on GlobalNavigation Satellite Systems (GNSS) such as the Global Positioning System (GPS) toremotely synchronize frequency standards by simply receiving the signals transmittedfrom the satellites [13]. Because of its simplicity and cost efficiency this method is usedby most metrology institutes and timing laboratories to compare the majority of atomicfrequency standards worldwide.A recent comparison between a TWSTFT and a GPS carrier-phase (CP) link overa baseline of 9,000 km revealed a frequency difference of up to . × − between thetwo methods which exceeded the estimated statistical uncertainty [14]. In our currentstudy, we aim to assess the frequency transfer capabilities of a GPS link based on astate-of-the-art Precise Point Positioning analysis over a baseline of 450 km. We employa 920 km phase-stabilized optical fiber link [15], which serves as a reference link totransfer frequency information between the two endpoints of the GPS link with verylow uncertainty.The consistency of the results achieved independently via satellite transfer and fibertransfer provides an upper limit for the accuracy and instability of each of the transfertechniques.
2. Methods and experimental setup
Nowadays, the comparison of atomic frequency standards, for example hydrogen masers,is straightforward. In the simplest case, an antenna capable of receiving signals that arebroadcasted by the constellation of GPS satellites and a suitable receiver are used toderive the difference between the phase of the incoming signals and the local frequencystandard connected to the receiver [13]. Recording the phase difference between thetransmitted GPS signals and the two frequency standards simultaneously generates two haracterization of a 450-km Baseline GPS Carrier-Phase Link Λ -type, K + K MesstechnikGmbH) synchronized between MPQ and PTB. They are operated with a gate timeof 1 s. The GPS link is established using commercially available GPS receivers. AtMPQ, a GPS receiver (Septentrio PolaRx2e) is used which gets its internal frequencyreference via a 10 MHz signal from the maser operated at MPQ. Data from two differentGPS receivers operated at PTB (both Ashtech Z-XII3T) are used which permits anadditional comparison of the two different receivers among one another. Both receivers haracterization of a 450-km Baseline GPS Carrier-Phase Link Figure 1.
Experimental setup for the characterization of the GPS link between MPQand PTB. Two hydrogen masers are compared via a 920 km fiber link and via a GPSlink simultaneously. At each site, an optical frequency comb is referenced to the localmaser. The fiber link is operated from MPQ and the maser comparison via fiber link isaccomplished by measuring the transfer laser frequency against the optical frequencycombs. The maser comparison via GPS is performed by measuring the maser frequencyagainst the GPS signal. are connected to 10 MHz and 1 PPS signals representing PTB’s reference time scaleUTC(PTB) [18] as they constitute the pivot point for all GPS-based time comparisonsmade worldwide in the context of the realization of Coordinated Universal Time (UTC)by the International Bureau of Weight and Measures (BIPM) [19]. The 10 MHz signalfrom the maser at PTB, connected to the local frequency comb, is thus measured againstthe UTC(PTB) frequency signal with the help of a phase comparator (Timetech PCO10265).During recent years it has become more and more common to build on GPS-basedfrequency comparison techniques that were initially developed for positioning. PrecisePoint Positioning (PPP), for instance, is a technique providing position with a highaccuracy on a global scale with a single isolated (not part of a network) GNSS receiverin post-processing. It uses code and carrier-phase measurements that are collectedin geodetic GPS receivers. Instead of differencing observations made at various sites,PPP builds on the precise satellite orbit, clock products and troposphere parametersgenerated by the International GNSS Service (IGS) [20]. Different software packages for haracterization of a 450-km Baseline GPS Carrier-Phase Link
3. Signal validation and uncertainty contributions
The functionality of the fiber link is verified by calculating the instability of thetransferred frequency at PTB against two stable optical references. If the fiber inducednoise cancellation is deactivated, these heterodyne beat notes show a 1-s instability ofabout × − as shown in figure 2. When the noise cancellation control loop isactive on the other hand, the 1-s instability decreases to about × − so that thismeasure can be used to monitor the operation of the fiber links active stabilization.The 1-s instability of these two beat signals was determined from 30 individual adjacentfrequency measurements. If the 1-s instability exceeds a threshold of × − forboth signals, we discard all of those 30 data points. To detect cycle-slips in the opticalpart of the system which includes the frequency combs, we apply a redundant countingscheme in analogy to previous experiments [15, 7]. All data points for which the tworedundant counted signals disagree by more than a predefined threshold are discardedto prevent them from entering the data analysis. This threshold is adapted to the noiseof the individual signals by calculating the medium absolute deviation (MAD). We finda robust value for the cycle-slip threshold to be 8 × MAD in the sense that varying this haracterization of a 450-km Baseline GPS Carrier-Phase Link Figure 2. σ y (1 s ) is about × − while it increases to ≈ × − if the stabilization is deactivated. Athreshold of × − is introduced to verify a proper fiber link operation. The inletshows σ y (1 s ) over the time of the day, indicating a noise reduction during the night asobserved in a previous study [7]. threshold did not change the amount of detected cycle-slips significantly.Due to the different sampling intervals of the fiber and GPS link data (1 s versus30 s), the combination of both data sets requires some preprocessing of the fiber linkdata. The most intuitive approach is to average 30 1-s fiber-link-data-points to equalizethe sampling intervals. However, one single cycle-slip in the fiber link data would lead toa rejection of the remaining 29 data points within the corresponding GPS data window.However, the instability contribution of the maser comparison over the optical link canbe neglected as long as each 30 s interval contains at least 10 valid data points ofthe optical transfer: The frequency difference between the two active hydrogen masersmeasured over the fiber link shows an instability of ≈ × − in 1 s as no excess noiseis introduced by the fiber link. The frequency difference of the masers measured overthe GPS link, however, has an instability of ≈ × − in 30 s. In the worst case, all10 fiber link data points will be incoherent (i.e. non-contiguous) due to cycle-slips whichresults in an instability of × − / √ ≈ × − . Therefore, the instability ofthe ≥ haracterization of a 450-km Baseline GPS Carrier-Phase Link -19 -18 -17 -16 -15 -14 -13 -12 m od i f i ed A ll an de v i a t i on Measurement Time / s
Ashtech Z-XII3T
Figure 3.
Fractional frequency instability of the difference between IGS time and thehydrogen masers for the receiver at MPQ (filled blue circles) and one of the receivers atPTB (filled orange squares). The common clock very-short-baseline realized betweenthe two setups at PTB (filled black triangles) provides a measure of the noise floor forthis kind of data analysis. Contributions from other components in the system likethe phase comparator (open green triangles), from rf cables (open brown diamonds)and from unstabilized optical fibers (filled red diamonds) are well below the instabilitydetermined from the common clock very-short-baseline configuration. haracterization of a 450-km Baseline GPS Carrier-Phase Link × − isreached after an averaging time of s. The mean frequency difference was measuredto . × − , thereby excluding a significant systematic error.The phase comparator used at PTB may also constitute a limiting factor. It isknown that the device may produce a measurement error that depends on the frequencydifference between the two signals that are being compared. Therefore, UTC(PTB) andmaser signals were compared in two different types of phase comparators simultaneously.From the difference of the two phase comparator outputs we derive an upper limit for thecontributions to the measurement instability and uncertainty. In figure 3 it is shown thatthe contribution of the phase comparator to the frequency instability is below the oneof the common clock at all relevant measurement times. As the relative mean differenceof the two phase comparator results is about × − , a significant uncertaintycontribution can be excluded.In figure 1 a connection between the maser and the frequency comb is sketchedthat actually represents a 185 m long rf cable connecting two buildings. The measuredfrequency instability for a signal transferred through such a cable is shown in figure 3as open diamonds. The contribution from this cable is about one order of magnitudebelow that of the common clock for all measurement times and the mean frequency isdetermined to . × − and does therefore not constitute a significant source oferror.Since optical fibers are sensitive to environmental perturbations, unstabilized fibersections might introduce a significant amount of noise to the signals. The longestunstabilized fiber section in our setup is about 11 m long. The contribution from thisfiber is shown in figure 3 as filled diamonds. With a relative mean of × − , thecontribution from this fiber is negligible.Thus, the investigated components revealed no systematic shifts within thestatistical uncertainty derived from the instability. Figure 3 and the measured meanfrequencies indicate that the dominant source of instability and uncertainty of the masercomparison will be linked to the GPS comparison itself. Increasing the baseline froma few meters to 450 km will add additional noise as the signals from the satellitespass through different atmospheric sections. In the following, we aim to determine the haracterization of a 450-km Baseline GPS Carrier-Phase Link
4. Results
The operation of two frequency transfer links in both the microwave and the opticaldomain simultaneously involves a large amount of scientific equipment. The properoperation of every component has to be verified as well as the connection betweenthe two links and frequency domains. Due to the complexity of the system, we firstconducted a test measurement over the course of a few weeks in January 2014. Theinsights gained in this first campaign are used in an extended measurement campaignwith a duration of approximately four weeks, lasting from 4 April to 4 May 2014. Theresults of the first test measurement are in good agreement with the results of theextended campaign discussed below. We measure the difference of the two masers viathe two links and calculate the frequency instability of these signals which is shown infigure 4.The comparison via the fiber link indicates the difference of the masers practicallywithout any noise contribution from the optical transfer. In contrast to that, the masercomparison via the GPS link is dominated by noise components from the GPS linkitself, at least for short averaging times. For long measurement times the instabilities of -16 -15 -14 -13 -12 m od i f i ed A ll an D e v i a t i on Measurement Time / s
Maser Difference via Fiber Link Maser Difference via GPS Link Double Difference
Figure 4.
Frequency instability of the maser difference measured via the fiber linkand via the GPS link, respectively. The double difference reveals the true GPS linkperformance without any contribution from the masers. haracterization of a 450-km Baseline GPS Carrier-Phase Link × − after 500,000 s.This is close to the value of × − measured in the common clock configuration (seefigure 3) for the same measurement time. The double difference in figure 4 raises thequestion whether we reach a noise floor for measurement times > 200,000 s. If we formone continuous data set by merging the data of the test measurement (in January 2014)and the April campaign, we can calculate instability values for even longer measurementtimes, to further search for such a noise floor in the double difference. We find thefrequency instability actually drops to about × − at 600,000 s.The accuracy of the fiber link has been constrained to a few parts in [15] so thatany deviation between the two comparisons greater than this value can be attributedto the GPS link. Figure 5 shows the frequency deviation between the masers measuredvia the GPS link and via the fiber link. The gaps in the trace result from cycle-slips inthe fiber link data as well as from a malfunction of one of the frequency comb systems.The arithmetic mean of the maser difference measured via the fiber link and via -1.5x10 -12 -1.0x10 -12 -5.0x10 -13 -13 -12 -12 -12 -12
25 30 F r equen cy D e v i a t i on Time / days
Maser Difference via GPS Link Maser Difference via Fiber Link
Figure 5.
Frequency deviation between the two masers at MPQ and PTB measuredover the GPS link and over the fiber link, respectively. The masers show a meanfrequency difference of about . × − with respect to each other. The occasionalgaps in the fiber link data are due to cycle-slips and a malfunction of one of thefrequency comb systems. GPS link data are only shown at intervals when the fiberlink data were available. haracterization of a 450-km Baseline GPS Carrier-Phase Link . × − N/AMaser difference via GPS link . × − N/ADouble difference . × − . × − Table 1.
Results of the maser difference measured via the fiber and via the GPS linktogether with the results of the double difference. The results of the double differenceare calculated from 300 s data as explained in the text. the GPS link are shown in table 1. The results are obtained from a total of 71,375 datapoints where each data point represents a measurement interval of 30 s. We calculatethe double difference by subtracting the two data sets of figure 5 in order to eliminatethe contributions of the masers. The statistical uncertainty ( σ/ √ N where σ is thestandard deviation and N the number of data points) of the double difference givenin table 1 is limited by the GPS link data. We apply a non-weighted average to theGPS link data by combining 10 GPS data points, thus representing a measurementtime of 300 s (see [15, 7] for details). In analogy to the procedure described above, weselect and average a minimum of 100 individual fiber link data points that lay withinthe new 300 s GPS measurement window (thus N = 7137 ). In the resulting doubledifference we can constrain any offset between the two frequency transfer methods to (2 . ± . × − . The overall mean frequency for the joint data set (Januaryand April campaigns) is . × − .It is of interest whether the GPS link frequency transfer shows diurnal variations.We separate our measurement data into day time and night time (cut-off at 6am/6pm).Figure 6 shows the frequency instability of the double difference at day and at night.The difference between the day and night frequency instability is below a factor 1.6 atall measurement times. The mean frequency for day and night data was identical withinthe measurement uncertainty.The difference in height above the earth geoid between MPQ and PTB is about400 m, corresponding to a gravitational redshift of . × − . However, this effectdoes not have to be taken into account as it cancels in the double difference betweenthe two maser comparisons.
5. Discussions
The values stated above are determined by averaging over roughly 600 hours of validdata measured over the period of about one month. When we compare the two masersvia the optical link, see the blue curve in figure 4, the instability is about × − in 30 s. The instability of × − in 30 s observed in the GPS link comparison isclearly limited by the noise of the GPS link transfer. At about s the noise of themasers themselves starts to visibly contribute to the comparison via the GPS link ascan be seen by the splitting of the curves for the GPS link and the double difference in haracterization of a 450-km Baseline GPS Carrier-Phase Link -16 -15 -14 -13 -12 m od i f i ed A ll an de v i a t i on Measurement Time / s
Day time (6:00am-6:00pm) Night time (6:00pm-6:00am)
Figure 6.
Frequency instability of the double difference for the day time from 6:00 amto 6:00 pm and for the night time from 6:00 pm to 6:00 am. which the contributions of the masers drop out. The comparison results of UTC(PTB)and UTC(OP) via a PPP GPS link during 2014 are available at the BIPM ftp server[25] and the results fit very well to the data for the PTB to MPQ link.The experiment presented here is the first point-to-point frequency comparisonbetween two independent frequency sources via an optical fiber of such length. Loopexperiments gave evidence that the frequency transfer accuracy of such a fiber-basedsystem is excellent, nevertheless it is justified from a metrological point of view to lookfor an independent assessment of the performance. Here, the GPS PPP link is the bestaffordable alternative and it provides at least an upper limit for the achieved accuracyof the fiber-based frequency comparison. In the near future, comparisons of opticalfrequency standards with uncertainties below − will surely better serve the purpose.
6. Conclusions
We characterized a GPS CP frequency transfer link by comparing two hydrogen masersthat are separated by a physical distance of 450 km over a GPS link and over a phase-stabilized optical fiber link. A short-term instability of the GPS link of × − in 30 s was observed. The parallel operation of a GPS link and a fiber link allowedus to characterize the GPS transfer on timescales of weeks without the contributionof the local oscillators (hydrogen masers). We demonstrated that a GPS CP linkultimately supports an instability and accuracy of below × − . We exclusively haracterization of a 450-km Baseline GPS Carrier-Phase Link Acknowledgments
We acknowledge financial support by the SFB-1128 geo-Q on "Relativistic Geodesy andGravimetry with Quantum Sensors", and the European Metrology Research Programme(EMRP) under SIB-02 NEAT-FT and SIB-60 Surveying. The EMRP is jointly fundedby the EMRP participating countries within EURAMET and the European Union.We thank the members of Deutsches Forschungsnetz in Berlin, Leipzig, and Erlangen,Germany, as well as Gasline GmbH for a fruitful collaboration. PTB acknowledgesNatural Resources Canada for granting the license of the PPP software package.
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