The Allan variance (AVAR) is widely used to measure the stability of experimental time series. Specifically, AVAR is commonly used in space applications such as monitoring the clocks of the global navigation satellite systems (GNSSs). In these applications, the experimental data present some peculiar aspects which are not generally encountered when the measurements are carried out in a laboratory. Space clocks' data can in fact present outliers, jumps, and missing values, which corrupt the clock characterization. Therefore, an efficient preprocessing is fundamental to ensure a proper data analysis and improve the stability estimation performed with the AVAR or other similar variances. In this work, we propose a preprocessing algorithm and its implementation in a robust software code (in MATLAB language) able to deal with time series of experimental data affected by nonstationarities and missing data; our method is properly detecting and removing anomalous behaviors, hence making the subsequent stability analysis more reliable.

An atomic time scale is a method for marking events and the passage of time by using atomic frequency standards. Thanks to the superior performance of atomic clocks based on optical transitions, time scales generated with optical clocks have the potential to be more accurate and stable than those based on microwave clocks. In this work, we demonstrate an experimental optical time scale based on the INRiM Yb optical lattice clock and a hydrogen maser as a flywheel oscillator, showing sub-nanosecond accuracy over months-long periods and nanosecond accuracy over a 1-year period. The obtained results show that optical time scales have competitive performances even when the optical clock has a limited and non-uniformly distributed up-time. Consequently, we are working to include the Yb clock within the ensemble of clocks routinely used for the generation of the Italian time scale. Furthermore, these results represent a crucial step towards the future redefinition of the second of the International System of Units based on an optical transition.

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 article 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.

We present two different approaches to broadcasting information to retrieve the GNSS-to-GNSS time offsets needed by users of multi-GNSS signals. Both approaches rely on the broadcast of a single time offset of each GNSS time versus one common time scale instead of broadcasting the time offsets between each of the constellation pairs. The first common time scale is the average of the GNSS time scales, and the second time scale is the prediction of UTC already broadcast by the different systems. We show that the average GNSS time scale allows the estimation of the GNSS-to-GNSS time offset at the user level with the very low uncertainty of a few nanoseconds when the receivers at both the provider and user levels are fully calibrated. The use of broadcast UTC prediction as a common time scale has a slightly larger uncertainty, which depends on the broadcast UTC prediction quality, which could be improved in the future. This study focuses on the evaluation of two different common time scales, not considering the impact of receiver calibration, at the user and provider levels, which can nevertheless have an important impact on GNSS-to-GNSS time offset estimation.

The H2020 DEMETRA project provides short latency clock monitoring services to the time users using the Atomium precise point positioning (PPP) software developed by the Royal Observatory of Belgium. In this paper, three recent updates of the current Atomium software are introduced: adding Galileo signals in the PPP computation; the option to constrain the receiver clock; PPP with integer ambiguity resolution. The advantages of these updates are demonstrated: Combining the Galileo and global positioning system (GPS) signals for PPP time transfer will further improve the frequency stability inside the computation batch; PPP with receiver clock constraint is not only used to reduce the short-term noise of the clock measurements but can also be used for some specific applications to a keep continuous clock solution in the computation batch or retrieve correct clock measurements from extremely noisy environments; the integer PPP allows a continuous clock solution, and improves the mid-term and long-term stability of the frequency transfer compared to the current PPP frequency transfer techniques.