Research Of The Day-boundary Discontinuities In GNSS Carrier Phase Time Transfer

Remote time transfer technology with high-precision is an crucial means for the performance of clock comparison.It is an technical support for establishing the links between local UTC(k)and UTC(Coordinated Universal Time),and it also is the basis of computation of International Atomic Time(TAI).As a typical remote time transfer method,GNSS carrier phase time transfer has been a widely hot topic research for many years due to its high precision and accuracy.The specific means to realize it mainly include undifferenced PPP,single differenced Phase-CV between stations and network solution.Compared to GNSS common view(CV)and Two-Way Satellite Time and Frequency Transfer(TWSTFT),GNSS carrier phase time transfer can not only provide excellent short-term frequency stability,but also has high resolution.As a typical representative and implementation method of GNSS carrier phase time transfer,GPS Precise Point Positioning(PPP)has been formally recommended by the Bureau International des Poids et Mesures(BIPM)for the computation of International Atomic Time(TAI)since 2009,and the accuracy of GPS PPP time transfer can be better than 1ns.At present,more than half of the national time laboratories participating in TAI have established such time links.However,time jumps at the boundary epochs of adjacent batches in station clock estimates result in the discontinuities in GNSS carrier phase time transfer,making it impossible to accurately reflect the performance of the clocks running continuously in real time through GNSS carrier phase time transfer.Moreover,it seriously affects the long-term frequency stability of the clock comparisons,limiting the application of GNSS carrier phase time transfer in high-precision fields,such as in primary frequency standards comparison and time synchronization between VLBI stations.Especially in recent years,with the gradual increase of new GNSS constellations such as Galileo and BDS,and the emergence of MGEX orbit and clock products,the day-boundary discontinuities in GNSS carrier phase time transfer also show new characteristics.Therefore,it is particularly important to research the origins and eliminating methods of the day-boundary discontinuities in GNSS carrier phase time transfer.In this study,the statistical characteristics,origins,effect of day-boundary discontinuiities on time and frequency transfer,and eliminating methods of the day-boundary discontinuities in GNSS carrier phase time transfer have been focused on.The main results and conclusions are stated as follows:(1)The day-boundary discontinuities in PPP station estimates and GNSS precise productsAnalyzing the characteristics of the day-boundary discontinuities in PPP station clock estimates is the basis for studying its origins and eliminating methods.From the statistical results of the day-boundary discontinuities in several PPP station clock estimates,it can be found that the day-boundary discontinuities in PPP station clock estimates are dependent on the stations.For most station clocks,the probability density of the discontinuities obeys the Gaussian distribution,and the level of the day-boundary discontinuities are usually less than 1ns.However,the magnitude of the day-boundary discontinuities in some PPP station clock estimates is even larger than1.5ns.With increasing the length of batch-arcs,the mean and STD of the discontinuities between boundary batches in PPP station clock estimates increase as well,but it is not linearly proportional to the length of batch-arcs.Moreover,it is founded that there are also day-boundary discontinuities in GNSS precise clock products,as like as those discontinuities in PPP station clock estimates.The level of the day-boundary discontinuities in GPS combined clock products provided by IGS is less than 100ps.However,the level of day-boundary discontinuities in individual products provided by IGS analysis centers is even more than 250ps.The level of day-boundary discontinuities in Galileo and BDS-2 clock products provided by individual MGEX ACs are relatively higher.(2)The origins of the day-boundary discontinuitiesIt is generally believed that the day-boundary discontinuities in station clock estimates and time comparisons are mainly caused by the code-pseudorange noise during the analysis of observation data in daily batches,where the absolute clock offset is determined by the average code measurements.However,GNSS precise orbit and clock products,sampling rate of PPP data processing,and length of batch-arcs are very siginificant factors in PPP station clock estimates.Will these factors contribute to the origin of the day-boundary discontinuities?From the results of this research it is found that they are indeed the origins of day-boundary discontinuities in PPP station clock estimates and time comparisons.When the IGS 30s clock products is employed in PPP station clock estimates,the level of the day-boundary discontinuities are less than those in PPP station clock estimates with the 5min clock products employed.Moreover,with decrease of the sampling rate of PPP data processing from 30s to10min,the level of the day-boundary discontinuities in PPP station clock estimates on contrary increases accordingly.As longer batch-arcs employed in PPP station clock estimates,the level of the discontinuities at the boundary of adjacent batches in PPP station clock estimates increases as well,and the level of the day-boundary discontinuities within longer-batch decreases on the contrary.Furthermore,it is demonstrated from the experiments that the influence of discontinuities in the current combined GPS final and rapid clock products on the origin of day-boundary discontinuities in PPP station clock estimates and time comparison are statistically negligible.However,the influence of the day-boundary discontinuities in individual products provided by IGS and MGEX analysis centers on the PPP station clock estimates cannot be ignored,and the discontinuities of GNSS precise products is an important factor that influences the origin of day-boundary discontinuities in PPP station clock estimates and time transfer,especially when the ACs individual products with large discontinuities are employed,which can seriously affect the improvement of the long-term frequency stability.Furthermore,the level of the day-boundary discontinuities in BDS-2 PPP station clock estimates varies with the observations of different BDS-2 constellation satellites.Especially when using the observations of GEO satellites,the level of the day-boundary discontinuities in PPP station clock estimates and time transfer are always higher.(3)The influence of the day-boundary discontinuities on GNSS carrier phase time and frequency transferUsually,it is believed that the day-boundary discontinuities in station clock estimates only affect the results of GNSS carrier phase time transfer but it has no influence on the frequency transfer.From this research it is demonstrated that the day-boundary discontinuities not only affect GNSS carrier phase time transfer also affect on frequency transfer.The day-boundary discontinuities is the main obstacle to restrict short and medium length time links from improvement of time stability so that the performance of station clock comparisons cannot be more accurately reflected.Meanwhile,it is both the day-boundary discontinuities and measurement noise in long time links together affects the stability of time comparisons.When estimating the fractional frequency of two remote reference frequency standards,there are always frequency jumps at the boundary epochs of daily batches,and the uncertainty introduced by the day-boundary discontinuities even make it difficult to accurately estimate the fractional frequency in the total period.The long-term stability of the frequency transfer is also deteriorated.(4)Research of the eliminating methods of the day-boundary discontinuities in GNSS carrier phase time transferThe purpose of remote time transfer is to compare the performance of the real-time running clocks,so the continuity of the station clock estimates is very significant for continuous time transfer.However,the day-boundary discontinuities in the GNSS carrier phase station clock estimates are inherited into time and frequency transfer results,which result in the discontinuities of time comparisons and has become the biggest obstacle preventing the GNSS carrier time transfer from accurately reflecting the performance of clock comparisons.So it is of great significant to research the eliminating methods of the day-boundary discontinuities in GNSS carrier phase time transfer.After studying the methods of shift-overlapping and the longer batches to reduce the day-boundary discontinuities in PPP time transfer,a network solution with sliding-overlapping batch least squares was proposed in this paper,which uses longer batch-arcs in network processing and can sharply eliminate the day-boundary discontinuities in GNSS carrier phase time transfer.From the experiments,it is clearly shown that time transfer accuracy and frequency stability can be significantly improved through the network solution,the time links is more robust as well.It is more suitable for continuous single or combined multi-GNSS carrier phase time transfer,and can accurately reflect the performance of clock stabilities in two different timing laboratories.Additionally,in view of the discontinuities in GPS IPPP time transfer induced by the integer ambiguity resolution during the process of wide-lane and narrow-lane ambiguities fixing,a method of extrapolation with linear interpolation was proposed to accurately estimate the integer circles of ?_NLbetween adjacent batches in time links so that it sucessfully eliminates the discontinuities in the IPPP time transfer resultss.It is clearly illustrated that it can realize continuous GPS IPPP time transfer and can significantly improve the long-term stability of frequency comparisons.