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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.

We consider the response of a finite string to white noise and obtain the exact time-dependent spectrum. The complete exact solution is obtained, that is, both the transient and steady-state solution. To define the time-varying spectrum we ensemble average the Wigner distribution. We obtain the exact solution by transforming the differential equation for the string into the phase space differential equation of time and frequency and solve it directly. We also obtain the exact solution by an impulse response method which gives a different form of the solution. Also, we obtain the time-dependent variance of the process at each position. Limiting cases for small and large times are obtained. As a special case we obtain the results of van Lear Jr and Uhlenbeck and Lyon. A numerical example is given and the results plotted.

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.

Recently, the official Italian time scale UTC(IT) has been successfully automatically generated in real-time, with a steering algorithm using Rapid UTC (UTCr) as steering reference [1]. This work aims to present the results of an on-line test of other two steering algorithms: one using the INRIM cesium fountain (ITCsF2) [2], and another one using an ensemble of various commercial clocks, as steering references alternative to UTCr [3].

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.

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.

The harmonic oscillator is a fundamental prototype for all types of resonances, and hence plays a key role in the study of physical systems governed by differential equations. The time-frequency representation of its Green’s function, obtained through the Wigner distribution, reveals the time-varying frequency structure of resonances. Unfortunately, the Wigner distribution of the Green’s function is affected by strong interference terms with a highly oscillatory structure. We characterize these interference terms by evaluating the ambiguity function of the Green’s function. The obtained result shows that, in the ambiguity domain, the interference terms are localized and separate from the resonance component, and hence they can be reduced by a proper filtering.

The frequency of atomic clocks flying on board the satellites of global navigation satellite systems, as can be observed on the ground, shows periodic variations of different origins. One of them is related to the J2 relativistic effect due to the Earth oblateness, whose amplitude is now measurable thanks to stable clocks like Galileo’s passive hydrogen masers. Orbital estimation errors are also translated into periodic frequency variations, whose amplitude changes in time and which are superimposed to the J2 signal. In this work we analyze the data of a Galileo satellite clock by using two different techniques, with a twofold objective: to characterize the most evident periodic variations affecting the apparent clock frequency; to estimate the amplitude of the J2 relativistic effect for a comparison with its theoretical value. This also represents a validation of the J2 correction that should be applied to the space clocks’ data, in order to improve the timekeeping/positioning performance of global navigation satellite systems.

Background: Anisotropy in conduction velocity (CV) is a key substrate abnormality influencing atrial arrhythmias. In skeletal muscle fibers, CV and frequency content of the surface electromyogram signal are directly related. We hypothesized that in human atria the frequency content of the bipolar signal, recorded on the endocardial surface, is directly related to the local CV. Methods: In 15 patients submitted to ablation of supraventricular arrhythmias, incremental pacing was performed through an octapolar catheter inserted into the coronary sinus (CS), alternatively from both extremities in two different sequences: CS bipole 1-2 as the pacing site and CS bipole 7-8 as the detection site in the first, and vice versa in the second. The pacing cycle length (PCL) was stepwise decreased from 600 ms to 500 ms, 400 ms, 300 ms, until 250 ms. Estimation of the CV was performed as the ratio between the distance traveled by the propagating pulse and the propagation time. The frequency distribution of the signal energy was estimated using the fast Fourier transform, and the characteristic frequency (CF) was estimated as the barycenter of the frequency spectrum. Results: A total of 2,496 bipolar signals were analyzed; CV and CF were estimated and compared. The single patient and group data analysis showed a significant direct correlation between CV and CF of the local bipolar signal. Conclusions: Comparing the degree of spectral compression among signals registered in different points of the endocardial cardiac surface in response to decreasing PCL enables to map local differences in CV, a useful arrhythmogenic substrate index.

Atomic clocks are key elements in several applications, such as global navigation satellite systems. Monitoring their behavior is therefore fundamental. Since during an anomaly the frequency spectrum of the signal made by the clock frequency measurements changes with time, we transform this signal into the time-frequency domain by computing the spectrogram. In the time-frequency domain, the spectrogram localizes and separates the anomalies, and it can be hence used to reveal the nonstationary structure of the clock signal, such as, for instance, the presence of time-varying sinusuoidal terms.

The Allan variance is the key measure for stability analysis, a fundamental tool to establish the performances of atomic clocks, which are often critical elements in many applications, such as global navigation satellite systems (GNSS). In some applications, only frequency measurements with numerous missing data are available. Because of missing data, the resulting Allan variance can be dramatically different from the expected stability behavior. We have developed an Allan variance estimator which corrects this divergence. We show the effectiveness of our estimator by applying it to frequency measurements with up to 94.4% of missing data.

DEMETRA, the 'DEMonstrator of Egnss services based on Time Reference Architecture', is an European Project funded by the European Union in the Horizon 2020 program. The main aim of the project was to develop and test a prototype of Time Service Provider based the European Global Navigation Satellite System (GNSS) providing innovative or improved time services based on different technologies and embedded in a modular architecture. The main innovative features are time certification, non-repudiation, integrity, reliability, resilience. The demonstrator has been developed and tested during the years 2015-2016. Nine different time services were developed and tested also in real environment at users premises. The paper reports the results of the experimental campaigns and the main lesson learned also by the trials with potential users.

Rationale Pulmonary vein isolation (PVI) is the method of choice for the treatment of drug-resistant atrial fibrillation (AF). However, arrhythmia recurrences are frequent due to suboptimal lesions formation and pulmonary vein reconnection. Contact force (CF)- and remote magnetic navigation (RMN)-guided catheters are both capable of improving contact and energy transfer to the tissue, possibly improving PVI outcome. Objective The objective of our study was to compare CF- and RMN-guided PVI in patients with paroxysmal AF in terms of surrogate parameters of the dimension and quality of the lesions. Methods and results Between March 2014 and March 2016, 44 patients affected by paroxysmal AF underwent a circumferential PVI procedure, 22 with a CF catheter and 22 with a RMN catheter. Signals were recorded before and after 30 seconds of radiofrequency point-by-point delivery. For each location, signal energy attenuation and impedance drop were evaluated as lesion dimension surrogates and signal fragmentation and shrinkage were estimated as lesion quality surrogates. Statistical analysis shows that CF catheter achieves higher attenuation and impedance drop than RMN-guided catheter, which instead performs better in terms of shrinkage and fragmentation. There were no differences in terms of PVI rate and sinus rhythm maintenance 1 year after the procedure (77.2% in both groups). Conclusions CF-guided catheters produce lesions that are larger but less homogeneous than those produced by RMN-guided catheters in terms of surrogate parameters. These two features could possibly offset each other, resulting in identical acute and long-term outcomes.

We derive a simple relationship between the Wigner distribution of the Green’s function of the Langevin equation and of the harmonic oscillator. This relationship shows that the Wigner distribution of the Green’s function of the harmonic oscillator consists of the sum of two terms obtained by translating the Wigner distribution of the Green’s function of the Langevin equation at the resonant frequencies of the harmonic oscillator, plus an interference term. This result paves the way for a simplification of the time-frequency representation of differential equations, as well as for a better understanding and filtering of interference terms.

The H2020 research project, DEMETRA (DEMonstrator of EGNSS services based on Time Reference Architecture) is funded by the European Union and aims to develop and test several time services based on the European Global Navigation Satellite System (GNSS) and introducing important new features such as certified time stamping, improved accuracy, or integrity, not yet provided by GNSS systems. The demonstrator has been successfully assembled at INRIM premises by the end of February 2016, and it will be tested with two validation test campaigns. The first closed loop test finished in May 2016, the first experimental results to validate the time services performances are here reported. The second test campaign will be conducted in a realistic case at user premises, to test the real advantages and feasibility of the proposed time services.

DEMETRA aims to be a prototype of an European time dissemination service, based on the timing signal of the European Galileo system, adding particular features like - among the others - certification, calibration, or integrity, that could be of interest to a wide range of users belonging to different sectors as traffic control, energy distribution, finance, telecommunication, and scientific institutions. Nine time dissemination services are proposed. The paper will report about the development status and the first experimentation results of the system, showing potentialities and limits of the proposed time dissemination services, aiming to foster the exploitation of the European GNSS for timing applications.

In the rubidium atomic frequency standard (RAFS), an rf-discharge lamp produces the device's atomic signal. As a consequence of the light-shift effect, variations in the lamplight's intensity result in variations in the RAFS' output frequency. While the basic physics of the light-shift is reasonably well understood, its operational implications for GNSS performance are only beginning to be fully appreciated. Here, we summarize results examining decade-long histories of on-orbit GPS RAFS lamplight variations. In addition to a deterministic variation that is well modeled by the sum of an exponential and linear trend, the stochastic variations appear to be of three types: lamplight jumps, repeating lamplight ramps, and non-stationary lamplight noise. Employing an estimated GPS RAFS light-shift coefficient, these variations can be used to infer lamplight-induced RAFS frequency variations.

In the rubidium atomic frequency standard (RAFS), an rf-discharge lamp produces the device's atomic signal. As a consequence of the light-shift effect, variations in the lamplight's intensity result in variations in the RAFS' output frequency. While the basic physics of the light-shift is reasonably well understood, its operational implications for global navigation satellite system (GNSS) performance is only beginning to be fully appreciated. Here, we describe first results examining decade-long histories of on-orbit GPS RAFS lamplight variations and GPS RAFS frequency variations. Our preliminary analyses have focused on one space vehicle's RAFS, and our conclusions are tempered by that present limitation. Nevertheless, our analyses suggest that a RAFS' long-term frequency stability (i.e., τ 106 sec) is likely lower-bounded by the lamp's intensity fluctuations. Moreover, considering the light-shift coefficient for this one particular RAFS over 12 years, we find that the data do not support Camparo's hypothesis regarding RAFS frequency aging and a time-varying light-shift coefficient.

Due 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 f...

The dynamic Allan variance (DAVAR) measures the stability variations of precise clocks and oscillators. When an anomaly occurs, the DAVAR changes with time, its shape depending on the anomaly. In this work, we first discuss our current knowledge about the DAVAR, by focusing on the meaning of dynamic stability. Then, we extend our knowledge by obtaining additional properties of the DAVAR. Furthermore, we visually investigate the DAVAR for the main anomalies of precise clocks and oscillators. Finally, we review a variety of applications based on the DAVAR.

The dynamic Allan variance (DAVAR) is a surface which describes the stability of a high-precision clock with respect to time. When the DAVAR is evaluated from experimental data, its surface shows random fluctuations caused by the estimation process. It is fundamental to assign a statistical significance to these fluctuations, so that they can be differentiated from the variations of the surface caused by clock anomalies. First, we develop confidence surfaces to assign a statistical significance to the random fluctuations of the DAVAR estimator. Then, we introduce detection surfaces to reveal the variations of the surface caused by clock anomalies. We validate the obtained results through numerical simulations.