Time-frequency analysis of the Galileo satellite clocks: looking for the J2 relativistic effect and other periodic variations

When observed from the ground, the frequency of the atomic clocks flying on the satellites of a Global Navigation Satellite System is referred to as apparent frequency, because it is observed through the on-board signal generation chain, the propagation path, the relativistic effects, the measurement system, and the clock estimation algorithm. As a consequence, the apparent clock frequency is affected by periodic variations of different origins such as, for example, the periodic component of the J2 relativistic effect, due to the oblateness of the earth, and the clock estimation errors induced by the orbital estimation errors. We present a detailed characterization of the periodic variations affecting the apparent frequency of the Galileo clocks, obtained by applying time-frequency analysis and other signal processing techniques on space clock data provided by the European Space Agency. In particular, we analyze one year of data from three Galileo Passive Hydrogen Masers, flying on two different orbital planes. Time-frequency analysis reveals how the spectral components of the apparent frequency change with time. For example, it confirms that the amplitude of the periodic signal due to the orbital estimation errors depends on the angle between the sun and the orbital plane. Moreover, it allows to find a more precise estimate of the amplitude of the J2 effect, in agreement with the prediction of the general theory of relativity, and it shows that such amplitude suddenly decreases when the corresponding relativistic correction is applied to the data, thus validating the analytical formula used for the correction

Robustness tests for an optical time scale

Optical clocks have reached such an impressive accuracy and stability that the future redefinition of the second will be probably based on an optical transition. Consequently, building time scales based on optical clocks has become a key problem. Unfortunately, optical clocks are still laboratory prototypes and are not yet capable of long times of autonomous operation. It is hence critical to understand the impact of this limited optical clock availability on the generated time scale. In this work, after describing a simple and effective optical time scale algorithm, based on the steering of a flywheel oscillator towards the optical clock, we investigate in detail the impact of the limited availability of the optical clock on the performances of the steering algorithm and of the generated time scale through numerical simulations. In particular, we simulate a time scale generated by a hydrogen maser (with a flicker floor of 5.5 x 10(-16)) steered towards an optical clock, by considering six different scenarios for the availability of the latter, spanning from the ideal one, i.e. continuous operation of the optical clock, to the worst one, i.e. non-uniformly distributed frequency measurements with long unavailability periods. The results prove that the steering algorithm is robust and effective despite its very simple implementation, and it is capable of very good performances in all the considered scenarios, provided that the hydrogen maser behaves nominally. Specifically, they show that a time scale with an accuracy of a few hundreds of picoseconds can be easily realized in the ideal scenario, whereas in a more realistic scenario, with one measurement per week only, the time accuracy is nonetheless of a few nanoseconds, competing with the best time scales currently realized worldwide. The performances degradation due to a non-nominal maser behaviour is also discussed

Time–frequency analysis of the Galileo satellite clocks: looking for the J2 relativistic effect and other periodic variations

When observed from the ground, the frequency of the atomic clocks flying on the satellites of a Global Navigation Satellite System is referred to as apparent frequency, because it is observed through the on-board signal generation chain, the propagation path, the relativistic effects, the measurement system, and the clock estimation algorithm. As a consequence, the apparent clock frequency is affected by periodic variations of different origins such as, for example, the periodic component of the J2 relativistic effect, due to the oblateness of the earth, and the clock estimation errors induced by the orbital estimation errors. We present a detailed characterization of the periodic variations affecting the apparent frequency of the Galileo clocks, obtained by applying time–frequency analysis and other signal processing techniques on space clock data provided by the European Space Agency. In particular, we analyze one year of data from three Galileo Passive Hydrogen Masers, flying on two different orbital planes. Time–frequency analysis reveals how the spectral components of the apparent frequency change with time. For example, it confirms that the amplitude of the periodic signal due to the orbital estimation errors depends on the angle between the sun and the orbital plane. Moreover, it allows to find a more precise estimate of the amplitude of the J2 effect, in agreement with the prediction of the general theory of relativity, and it shows that such amplitude suddenly decreases when the corresponding relativistic correction is applied to the data, thus validating the analytical formula used for the correction

Robustness tests for an optical time scale

Optical clocks have reached such an impressive accuracy and stability that the future redefinition of the second will be probably based on an optical transition. Consequently, building time scales based on optical clocks has become a key problem. Unfortunately, optical clocks are still laboratory prototypes and are not yet capable of long times of autonomous operation. It is hence critical to understand the impact of this limited optical clock availability on the generated time scale. In this work, after describing a simple and effective optical time scale algorithm, based on the steering of a flywheel oscillator towards the optical clock, we investigate in detail the impact of the limited availability of the optical clock on the performances of the steering algorithm and of the generated time scale through numerical simulations. In particular, we simulate a time scale generated by a hydrogen maser (with a flicker floor of 5.5 × 10−16) steered towards an optical clock, by considering six different scenarios for the availability of the latter, spanning from the ideal one, i.e. continuous operation of the optical clock, to the worst one, i.e. non-uniformly distributed frequency measurements with long unavailability periods. The results prove that the steering algorithm is robust and effective despite its very simple implementation, and it is capable of very good performances in all the considered scenarios, provided that the hydrogen maser behaves nominally. Specifically, they show that a time scale with an accuracy of a few hundreds of picoseconds can be easily realized in the ideal scenario, whereas in a more realistic scenario, with one measurement per week only, the time accuracy is nonetheless of a few nanoseconds, competing with the best time scales currently realized worldwide. The performances degradation due to a non-nominal maser behaviour is also discussed

The ac stark shift and space-borne rubidium atomic clocks

open7sìDue to its small size, low weight, and low power consumption, the Rb atomic frequency standard (RAFS) is routinely the first choice for atomic timekeeping in space. Consequently, though the device has very good frequency stability (rivaling passive hydrogen masers), there is interest in uncovering the fundamental processes limiting its long-term performance, with the goal of improving the device for future space systems and missions. The ac Stark shift (i. e., light shift) is one of the more likely processes limiting the RAFS' long-term timekeeping ability, yet its manifestation in the RAFS remains poorly understood. In part, this comes from the fact that light-shift induced frequency fluctuations must be quantified in terms of the RAFS' light-shift coefficient and the output variations in the RAFS' rf-discharge lamp, which is a nonlinear inductively-couple plasma (ICP). Here, we analyze the light-shift effect for a family of 10 on-orbit Block-IIR GPS RAFS, examining decade-long records of their on-orbit frequency and rf-discharge lamp fluctuations. We find that the ICP's light intensity variations can take several forms: deterministic aging, jumps, ramps, and non-stationary noise, each of which affects the RAFS' frequency via the light shift. Correlating these light intensity changes with RAFS frequency changes, we estimate the light-shift coefficient, K-LS, for the family of RAFS: K-LS = -(1.9 +/- 0.3) x 10(-12) /%. The 16% family-wide variation in K-LS indicates that while each RAFS may have its own individual K-LS, the variance of K-LS among similarly designed RAFS can be relatively small. Combining K-LS with our estimate of the ICP light intensity's non-stationary noise, we find evidence that random-walk frequency noise in high-quality space-borne RAFS is strongly influenced by the RAFS' rf-discharge lamp via the light shift effect. Published by AIP Publishing.openFormichella, V.; Camparo, J.; Sesia, I.; Signorile, G.; Galleani, L.; Huang, M.; Tavella, P.Formichella, V.; Camparo, J.; Sesia, Ilaria; Signorile, Giovanna; Galleani, L.; Huang, M.; Tavella, Patrizi

Demonstrator of Time Services based on European GNSS signals: the H2020 DEMETRA Project

During 2015-2016, a European Consortium of 15 partners from 8 different countries, developed the DEMETRA (DEMonstrator of EGNSS services based on Time Reference Architecture), a project funded by the European Union in the frame of the Horizon 2020 program. This project aims at developing and experimenting time dissemination services dedicated to specific users like traffic control, energy distribution, finance, telecommunication, and scientific institutions. Nine services have been developed. These services provide time dissemination with accuracy levels from millisecond to the sub-ns, and also additional services like certification, calibration, or integrity. Five of these services are based on the European GNSS. After a development phase (see PTTI 2016 presentation) the full DEMETRA system has been working during six months for demonstration. The paper will report about the experimentation results, showing performances and limits of the proposed time dissemination services, aiming to foster the exploitation of the European GNSS for timing applications

Influence of the ac-Stark shift on GPS atomic clock timekeeping

The ac-Stark shift (or light shift) is a fundamental aspect of the field/atom interaction arising from virtual transitions between atomic states, and as Alfred Kastler noted, it is the real-photon counterpart of the Lamb shift. In the rubidium atomic frequency standards (RAFS) flying on Global Positioning System (GPS) satellites, it plays an important role as one of the major perturbations defining the RAFS' frequency: the rf-discharge lamp in the RAFS creates an atomic signal via optical pumping and simultaneously perturbs the atoms' ground-state hyperfine splitting via the light shift. Though the significance of the light shift has been known for decades, to date there has been no concrete evidence that it limits the performance of the high-quality RAFS flying on GPS satellites. Here, we show that the long-term frequency stability of GPS RAFS is primarily determined by the light shift as a consequence of stochastic jumps in lamplight intensity. Our results suggest three paths forward for improved GPS system timekeeping: (1) reduce the light-shift coefficient of the RAFS by careful control of the lamp's spectrum; (2) operate the lamp under conditions where lamplight jumps are not so pronounced; and (3) employ a light source for optical pumping that does not suffer pronounced light jumps (e.g., a diode laser)

Mitigation of Lamplight-Induced Frequency Variations in Space Rubidium Clocks

Rubidium clocks are currently the most common atomic clocks for space applications, playing a fundamental role in global navigation satellite systems. Their stability is affected by the light-shift effect, turning lamplight variations into frequency variations, e. g. lamplight jumps into frequency jumps. In our previous work, analyzing data from GPS rubidium (Rb) clocks, we uncovered the impact of the lamp on the in-orbit clock's performance. Specifically, the Rb clock's random walk of frequency seems to be driven by a compound Poisson process associated with lamplight intensity jumps. Moreover, large lamplight-induced frequency jumps could affect the validity of the navigation message. Here, we propose an active compensation scheme for lamplight-induced Rb clock frequency variations. We show how this could be implemented as an automated on-board process, and the potential improvements this scheme might yield in timekeeping/navigation performance

Testing the robustness of a time scale algorithm by using simulated optical clock data

Optical clocks have reached an impressive accuracy, surpassing by orders of magnitude that of microwave clocks, so that the optical transitions on which they are based can be considered as ideal candidates for a possible future redefinition of the second. For these reasons, it is fundamental to develop an effective way to generate time scales based on optical clocks. However, optical clocks are still far from matching the robustness, reliability and long times of autonomous operation typical of microwave clocks. Therefore, the usual way to generate a time scale based on an optical clock, is to use it as a frequency steering reference for a master clock [1], typically an Active Hydrogen Maser (AHM). The master clock is usually referred to as a flywheel oscillator, since it allows the generation of the time scale also when the optical clock is unavailable. It is hence important to understand the impact of the unavailability of the optical clock on the performances of the steering algorithm and of the generated time scale. For example, it is fundamental to understand the minimum availability of the optical clock data needed to guarantee a given level of performances. To this aim, we simulated a time scale steered with an optical clock by considering several possible scenarios for the availability of the latter. By modifying the steering algorithm described in [2], we simulated the measurement data of the frequency offset of an AHM with respect to an optical clock, and we used them to steer the AHM for the time scale generation. Then, we tested the algorithm by considering six different scenarios for the availability of the optical clock, spanning from the ideal one (continuous operation of the optical clock), to the worst one (non-uniformly distributed frequency measurements with long unavailability periods). We also considered a realistic scenario where the optical clock is operated for a few hours once a week, with the possibility of a jitter on the day of the week. Finally, we evaluated the performances by considering the phase offset of the steered time scales with respect to UTC, and we compared and discussed the results obtained within the different scenarios. The results prove that the steering algorithm is robust and effective despite its very simple implementation. As expected, the scenarios giving the best and worst performances are the ideal one and those with long unavailability periods, respectively. More interestingly, the realistic scenario, with one measurement per week only, gives results similar to the ideal scenario ones. This is remarkable, as it means that, even with a much smaller effort dedicated to the optical clock, the final performances of the time scale are still close to the optimal case. This project 18SIB05 ROCIT has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. References [1] H. Hachisu, F. Nakagawa, Y. Hanado and T. Ido, “Months-long real-time generation of a time scale based on an optical clock,” Scientific Reports, (2018) 8:4243. [2] L. Galleani, G. Signorile, V. Formichella and I. Sesia, “Generating a real-time time scale making full use of the available frequency standards,” Metrologia 2020, in press

Generating a Real-Time Time Scale With an Ensemble Clock and a Primary Frequency Standard

The robustness and reliability of a reference time scale is becoming more and more crucial in many applications, particularly in global navigation satellite systems (GNSS) and in critical infrastructures with time synchronization needs. This paper proposes two steering algorithms aimed at generating a real-time time scale, the first based on a primary frequency standard (PFS), and the second on an ensemble of clocks. Extensive tests on real data from the Italian National Metrology Institute (INRIM) cesium fountain ITCsF2 and atomic clocks have been carried out. The results show that the PFS algorithm has higher performances, but it requires a cesium fountain, a prototype standard currently available in a few timing laboratories only, whereas the ensemble clock algorithm uses commercially available clocks. A special emphasis is put on the system robustness: data pre-processing and possible combinations of the proposed algorithms have been tested in order to cope with outage periods, while maintaining good performances in terms of stability and accuracy of the resulting time scale. Such algorithms can be used in several applications where a stable time reference is needed, such as for the generation of a local real-time realization of UTC, as well as for any GNSS reference time