The Corrected Allan Variance: Stability Analysis of Frequency Measurements with Missing Data

Atomic clocks are essential elements in a variety of applications, such as global navigation satellite systems. Consequently, monitoring their performances is fundamental. The Allan variance is the key statistical tool for the performance characterization of atomic clocks. This paper proves that the Allan variance computed from frequency measurements with missing data is affected by a bias, which can make it dramatically different from the expected behavior in the full data case. Furthermore, it shows how to eliminate (or largely reduce) this bias by correcting the Allan variance. The corrected Allan variance is obtained for some of the most common atomic clock noise components, and it is validated through numerical simulations

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

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

Interference management for moving networks in ultra-dense urban scenarios

The number of users relying on broadband wireless connectivity while riding public transportation vehicles is increasing significantly. One of the promising solutions is to deploy moving base stations on public transportation vehicles to form moving networks (MNs) that serve these vehicular users inside the vehicles. In this study, we investigated the benefits and challenges in deploying MNs in ultra-dense urban scenarios. We identified that the key challenge limiting the performance of MNs in ultra-dense urban scenarios is inter-cell interference, which is exacerbated by the urban canyon effects. To address this challenge, we evaluated different inter-cell interference coordination and multi-antenna interference suppression techniques for MNs. We showed that in using MNs together with effective interference management approaches, the quality of service for users in vehicles can be significantly improved, with negligible impacts on the performance of regular outdoor users

Gibbsian Method for the Self-Optimization of Cellular Networks

In this work, we propose and analyze a class of distributed algorithms performing the joint optimization of radio resources in heterogeneous cellular networks made of a juxtaposition of macro and small cells. Within this context, it is essential to use algorithms able to simultaneously solve the problems of channel selection, user association and power control. In such networks, the unpredictability of the cell and user patterns also requires distributed optimization schemes. The proposed method is inspired from statistical physics and based on the Gibbs sampler. It does not require the concavity/convexity, monotonicity or duality properties common to classical optimization problems. Besides, it supports discrete optimization which is especially useful to practical systems. We show that it can be implemented in a fully distributed way and nevertheless achieves system-wide optimality. We use simulation to compare this solution to today's default operational methods in terms of both throughput and energy consumption. Finally, we address concrete issues for the implementation of this solution and analyze the overhead traffic required within the framework of 3GPP and femtocell standards.Comment: 25 pages, 9 figures, to appear in EURASIP Journal on Wireless Communications and Networking 201

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