| The real-time application area of global navigation satellite system is becoming more and more extensive,and its real-time service performance depends on stable,high-precision real-time satellite orbit and clock difference products.Although the International GNSS Service(IGS)provides the ultra-fast ephemeris of which the orbit prediction part can achieve centimeter-level accuracy,the accuracy of the clock prediction cannot meet the needs of high-precision real-time applications.Therefore,real-time satellite clock estimation is the key to the real-time application of navigation satellite systems.In current real-time satellite clock estimation,satellite clock parameters are usually treated as white noise.However,with the continuous development of navigation satellite systems,the stability of space-borne atomic clocks is improving,and it is difficult to fully display the performance of high-precision atomic clocks based on white noise method.On the other hand,in the actual application scenario,due to the stability of the GNSS tracking station,network data loss or transmission delay,the GNSS real-time data stream is frequently interrupted.In this case,if only the satellite clock is estimated as the white noise parameter,it may cause the solution to re-converge,thereby affecting the quality of service of the real-time system.Obviously,establishing a real-time clock estimation model that matches the performance of GNSS space-borne atomic clocks is not only a requirement for the development of GNSS systems,but also a key to further improving the accuracy and reliability of real-time satellite clock products.In this paper,the time-domain analysis of variance is used to evaluate the performance of space-borne atomic clocks of different systems and different types of satellites in terms of frequency stability and noise type.On this basis,the satellite clock difference,clock speed,clock frequency drift,etc.are comprehensively considered,and the clock noise is modeled using the variogram and Hadamard variance,etc.The model is verified through clock fitting and prediction experiments,which have different arc length(multi-day continuous processing,single-day segmented processing).The results point out that the variogram method is suitable for short-term(single day)clock modeling,while the clock noise model established by Hadamard variance is more suitable for long-term solution.To this end,this paper proposes to combine the two models to establish a clock noise model that takes into account the different characteristics of atomic clocks on multiple time scales.Finally,combined with the analysis of the data stability of the GNSS real-time system,the pseudo-real-time Beidou,GPS,GLONASS,and Galileo multi-system satellite clock estimation is used to verify the advantages and reliability of the model.The main research results of this article are as follows:(1)The analysis of the performance of the GNSS space-borne atomic clock shows that the daily stability of Block IIF Rb clock is7×10-1 5?2×10-14,which is the best among the four kinds of atomic clocks in GPS system.The block IIR/IIR-M Rb clock has the same frequency stability and the daily stability is about9×10-1 5?3×10-14.The clock frequency stability of Block IIF Cs clock is the worst,and the daily stability is5×10-1 4?8×10-14.The clock stability of BDS-2 satellite satellites is2×10-1 4?7×10-14,which is basically the same as the clock stability of Block IIF Cs clock.The GLONASS system has the worst stability among these four systems with the3×10-1 4?1×10-13daily stability.The space-borne atomic clock of the Galileo system has a daily stability of6×10-1 5?3×10-14.It is better than GPS Block IIR-M Rb clock,and slightly worse than Block IIF Rb clock.Space-borne atomic clocks show different types of noise in different smooth time periods,and each smoothing period corresponds to a major type of noise.With the same type of satellite atomic clock,the trend of noise type changes with smooth time is about the same,but the noise type of each satellite is different.(2)The clock fitting and prediction results of the two kinds of atomic clock random noise models show that the fitting accuracy of the atomic clock noise model established by Hadamard variance is higher than that of the variogram method.As the fitting time increases,the fitting accuracy of the atomic clock noise model established by the variogram method is reduced.The prediction accuracy of the atomic clock noise model established by the Hadamard variance method increases with the increase of the time of the clock fitting data,and the prediction accuracy of the atomic clock noise model established by the variation function method decreases with the increase of the time of the clock fitting data.When the data fitting time is short,the variogram method has high prediction accuracy,and when the data fitting time is longer,the Hadamard variance method atomic clock noise model has high prediction accuracy.On this basis,the atomic clock noise model that takes into account both the short-term(single day)and long-term(multi-day)is proposed.This method uses the variogram method to constrain the clock difference parameters between each epoch,while the clock speed and the clock drift parameters are only updated once using the atomic clock noise model established by the Hadamard variance when a new day comes.(3)The experiments simulate the real-time satellite clock estimation in the case of GNSS data interruption.When doing the short-term continuous satellite clock estimation,the atomic clock noise model based on the variogram has higher estimation precision than the white noise method.The STD improvement of the Beidou,GPS,GLONASS and Galileo satellite clocks is about 13.7%,21.1%,14.4%and 33.0%;while the estimation precision of the atomic clock noise model based on the Hadamard variance method is slightly lower than that of the white noise method.When doing the long-term continuous satellite clock estimation,the accuracy of the atomic clock noise model based on the Hadamard variance method is higher.The method proposed in this paper takes into account the advantages of the variogram method and the Hadamard variance method.Through simulated real-time satellite clock estimation,when an interruption occurs,the STD improvement of Bei Dou,GPS,GLONASS,and Galileo satellite clock estimated by the new method is about 51.8%,52.2%,49.0%,and 37.4%compared with the variogram method.Compared with the white noise method,the STD improvement of Beidou,GPS,GLONASS and Galileo satellite clocks is about 34.5%,30.0%,29.4%and 16.7%. |
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