## 1 Introduction  
Since the Global Positioning System (GPS) was first utilized for precise time transfer [1], it has increasingly been applied in time frequency dissemination. From initial common-view (CV) and all-in-view (AV) techniques [2, 3], which use only pseudo-range measurements, to the development of carrier-phase (CP) techniques that combine carrier phase observation [4], the accuracy of GPS time transfer has improved significantly. While earlier studies employing CV and AV techniques have recently been re-evaluated, research on GLObal Navigation Satellite System (GLONASS) time transfer has also increasingly been undertaken in those years [5, 6]. Recently, other satellite systems have also been well developed, and this has provided a rich resource of Global Navigation Satellite System (GNSS) signals for time and frequency transfer. The European Union's Galileo satellite system, which was initiated by the European Space Agency (ESA) and the European Commission in 2011 offers one promising E5 signal component with low noise in the centimeter range, and great potential to improve time transfer performance [7, 8]. The BeiDou Navigation Satellite System (BDS) of China has been in continuous service since 27 December 2012, and the application of its time transfer has also been investigated [9, 10]. Given that combining multi-constellation GNSS can increase the number of available satellites for data retrieval, doing so can improve the redundancy of the receiver clock parameter. While multi-GNSS time transfer has been investigated [11; 12; 13], such research has primarily focused on combining GPS and GLONASS. As the GLONASS satellites emit signals on individual frequencies via a frequency division multiple access (FDMA) design, the effect of inter-frequency biases (IFBs) [12] and differential code-phase biases (DCPBs) [14] for GLONASS is limited, allowing for the full exploitation of the combination potential of these satellites for precise time and frequency transfer. With the development of precise multi-GNSS satellite orbit and clock products, all satellites within the network use the same time scale for different GNSS products [15; 16; 17]. This provides the opportunity to combine the three code-division multiple access (CDMA) satellite constellations (i.e., GPS, Galileo and BDS) for precise time and frequency transfer. By increasing the number of available satellites and improving the time dilution of precision, the time transfer solution was determined by combining the three CDMA GNSS constellations, which outperformed single GNSS solutions [18]. However, the quality of orbit and satellite clock products and pseudo-range observation accuracy of Galileo and BDS differ from those of GPS [19], and it is therefore inappropriate to treat them equally as has been done in previous studies [18]. Meanwhile, the pseudo-range observation is an important measurement in time and frequency transfers as it carries temporal information [20; 21]. However, outliers are often found in these observations owing to the environments surrounding the stations [22; 23], which substantially affect time transfer performance. In this study, a robust Helmert variance component estimation (RVCE) was introduced when using combined multi-GNSS for precise time and frequency transfer estimates based on a CP technique. This was employed to allocate the adaptive weight for different GNSSs and to suppress the influence of outliers based on their adjustment residuals. Five GNSS stations equipped with external time and frequency references, and which were capable of tracking three GNSS constellations, formed four time links that were processed. The performance of the CP technique with three GNSS observations using the RVCE approach was assessed in terms of both time transfer noise level as well as time and frequency stability [13]. The structure of this manuscript is organized as follows: Section 2 describes the observation equation of the time and frequency transfer based on multi-GNSS.