Precise Point Positioning with integer ambiguity resolution (IPPP) provides significant improvements in time transfer instability over the classical use of floating ambiguities for averaging times longer than one day, allowing frequency comparisons with 1x10-16 accuracy in about 7 day averaging and reaching the low 10-17 range in 20-30 days. Up until now only GPS satellites were used for frequency transfer with IPPP, due to the lack of availability of special satellite products necessary for integer ambiguity fixing in PPP for Galileo. Since November 2018 the GRG analysis center operated by CNES and CLS provides ambiguity-fixed satellite products for Galileo from a global network solution in the frame of the Multi GNSS Experiment of IGS. This allows for the first time to study the time transfer instability of Galileo IPPP and Multi-GNSS (GPS+GAL) IPPP solutions.
The zero-difference ambiguity fixing is performed in two steps; after the fixing of the wide-lane ambiguity NWL using the Melbourne-Wübbena linear combination of phase and code measurements one of the undifferenced ambiguities can be fixed, e.g. N1. Additionally, to ensure a continuous time link over days, integer narrow-lane cycle discontinuities at ambiguity resets and batch-boundaries need to be fixed. Here we make use of the high stability of the reference clocks used for time transfer. The fixing of the integer batch-boundary discontinuities needs to be performed on the link level in a differential mode between two stations due to the day-boundary discontinuities in the reference timescale. Additional corrections have to be applied to account for simultaneous NWL jumps at batch-boundaries and ambiguity resets, which can be detected based on the receiver wide-lane bias that is estimated together with NWL in the first step of the ambiguity fixing.
We compare Galileo only IPPP links to GPS only and Multi-GNSS IPPP links on short common-clock baselines as well as on a longer baseline, where an optical fiber link delivers the ground truth. The time transfer instability of the Galileo only IPPP links is comparable to the GPS only IPPP links, only at short averaging times a slightly higher noise level can be observed, due to the lower number of visible satellites. The Multi-GNSS approach on the other hand improves the short-term instability up to 30% compared to the GPS only solution.

Thanks to the international GNSS service (IGS), which has provided an open-access real-time service (RTS) since 2013, a technique called real-time precise point positioning (RT-PPP) become a hot topic in the time community. Currently, a few scholars have studied RT-PPP time transfer, while the correlation of clock offsets between-epochs have not been considered. In this work, we present a clock offset model, considering the correlation of between-epochs using a priori value; the clock offset is estimated using a constrained between-epoch model rather than a white noise model. This approach is based on two steps. First, a priori noise variance is based on the Allan variance of IGS final clock products. Second, by applying the constrained between-epoch model, RT-PPP time transfer is achieved. Our numerical analyses clarify how our approach performs for RT-PPP time and frequency transfer. Based on five commonly used RTS products and six IGS stations, two conclusions are drawn straightforwardly. Note that the IGS final clock products are regarded as a reference. First, all RT-PPP solutions with the different real-time products are capable of time transfer. The standard deviation (STD) is less than 0.3 ns. Second, the STD values are reduced significantly, ranging from 3.79 to 37.43 %, when applying our approach. Moreover, the largest improvement ratio factor of frequency stability is up to 28, as compared to the solution of the white noise model.

With the inputs of GNSS satellite orbits and clock offsets, the Precise-Point-Positioning (PPP) processing, as a popular positioning technique, models or removes GNSS system errors to achieve an accurate positioning and timing solution for a single ground GNSS receiver. Satellite orbits and clock offsets, generated from a network of ground GNSS stations, significantly affect the precision of ground positioning. On the other hand, the generation of satellite orbits and clock offsets highly depends on ground-station clocks and coordinates. Since the ground stations are static, the performance of ground-station clocks becomes prominent. We investigate the feasibility of a "reverse" PPP processing for the satellite-clock observation, based on GNSS receivers at national timing laboratories. Similar to PPP, our processing shall take all GNSS system errors into account; Different from PPP, our goal is GNSS satellites instead of ground receivers. Thanks to the nearly-ideal reference time provided by a national timing laboratory, a single GNSS receiver can well monitor the clocks on observable GNSS satellites. A network of globally-distributed timing laboratories enables the clock observation on all GNSS satellites at all times. As an initial study, we have taken the following corrections into account -- Sagnac effect, relativistic effect due to orbit eccentricity, tropospheric delay, and ionospheric delay -- and our result for GPS satellite clocks matches the GFZ result within ~ 1 ns on MJD 58244. We plan to include other GPS error sources in the future computation (e.g., earth tides, antenna offsets), and the latest result will be presented at the conference.

The frequency of space qualified atomic clocks flying on board the satellites of a global navigation satellite system (GNSS), as observed on the ground, is referred to as apparent frequency. The apparent frequency is usually affected by periodic variations of different origins. For example, relativistic effects, such as time dilation and gravitational redshift, give rise to large periodic variations which are corrected at the user level, at a certain order of approximation. The implemented relativistic corrections usually neglect the contribution due to the Earth’s oblateness, which is referred to as the J2 relativistic effect. This tiny effect has a periodic component too, which is now expected to be clearly visible thanks to the impressive stability of the Galileo’s passive hydrogen masers. Orbital estimation errors are also translated into periodic frequency variations, whose amplitude changes in time as a function of the angle between the sun and the satellite’s orbital plane, and which are superimposed to the periodic signal due to the J2 effect. In this work, we analyze Galileo space clock data provided by the European Space Agency, with a twofold objective. First, to characterize the most evident periodic variations affecting the apparent clock frequency. Second, to estimate the amplitude of the J2 periodic effect for a comparison with its theoretical value. This second objective represents also a validation of the J2 correction that could be applied to the space clocks’ data to improve the timekeeping and positioning performance of Galileo and the other GNSSs. The analyses presented in this work are based on phase offset data from a set of Galileo’s passive hydrogen masers, spanning a period of some months. After a first and fundamental preprocessing stage, we analyze the available data with different techniques, such as spectral analysis, to identify and characterize the main periodic signals affecting the data, as well as data fitting with a suitable periodic function, to estimate the amplitude of the periodic variations and in particular of the J2 periodic effect. The results show the presence of at least three harmonics of a periodic signal with period equal to the orbital one, such that the second harmonic is superimposed to the J2 signal. Moreover, the estimated amplitude of the J2 signal is compatible with the theoretical one.

Note: besides the chosen one, also the topic "Physics - Test of General Relativity and alternative theories" may be applicable.