Research On The Theories And Methods Of Multi-GNSS High Precision Clock Offset Prediction And Time Scale Establishment

Global Navigation Satellite System(GNSS)is a system based on time measurement,and the performance of the spaceborne atomic clock as the on-board time reference for system ranging directly determines the accuracy of navigation and positioning timing,and is also the basis for GNSS system time generation and maintenance,so it is very necessary to evaluate the performance of the spaceborne atomic clocks to master its operation status.International GNSS Monitoring and Assessment System(iGMAS)is an international GNSS monitoring and evaluation system established with China as the leader.For iGMAS system,there is a lack of internal time reference,which affects the stability of high precision products.Therefore,it is important to study effective time scale algorithms for iGMAS time scale(iGMAST)establishment based on GNSS spaceborne atomic clocks.The clock offset prediction method is an important part of the time scale algorithm,and the real-time precise point positioning also relies on the assistance of the high-precision prediction method.Therefore,the study of highprecision clock offset prediction method plays an important role in maintaining the system time synchronization,meeting the demand of high-precision real-time precise point positioning,and time scale solving and steering.At the same time,there are inevitable data anomalies in the clock offset data,and high-quality clock offset data is an important prerequisite for atomic clock performance evaluation,clock offset prediction,and time scale calculation.Based on these,this paper presents a systematic and in-depth study on data pre-processing,spaceborne atomic clock performance analysis,high-precision clock prediction,and the establishment of iGMAST,using the clock offset products from iGMAS.The main results and innovations of the paper are:1.A gross error rejection algorithm that takes into account the frequency drift of the atomic clock is proposed.Firstly,the median of each day’s frequency data extracted with the help of the robust property of the median is used to calculate the approximate value of the frequency drift;then the original frequency data is de-frequency drifted with the help of the approximate value of the frequency drift,and the Median Absolute Deviation(MAD)method is used to roughly locate the gross errors;After that,the weights of these positions in the original frequencies are all set to zero.The final fitted residuals are obtained by weighted least squares fitting again,and the gross errors are accurately located on the residuals and the gross errors are removed and interpolated to make up for them.Experimental results show that the method is effective in removing the gross errors of the clock offset data with strong drift,which makes up for the shortcomings of the traditional MAD method.2.The performance of each type of GNSS satellite spaceborne atomic clocks was compared,analyzed,and ranked in order of performance merit.Based on the precision clock offset products from the iGMAS for one year from September 1,2021 to September 1,2022,a detailed analysis was performed in seven aspects:1000 second stability,10,000 second stability,one-day stability,seven-day stability,accuracy,daily drift,and fitting residual.The results show that PHM(Galileo),PHM(BDS-3),Rb(GPS IIIA),Rb(BDS-3),and Rb(GPS IIF)excel in stability and fitting accuracy,while CS(GPSIIF),CS(GLONASS),PHM(Galileo),and PHM(BDS-3)have excellent and comparable performance in daily drift.CS(GPSIIF),CS(GLONASS),PHM(Galileo),and PHM(BDS-3)performed well and comparably,while CS(GPSIIF),CS(GLONASS)excelled in accuracy.3.An enhanced combinatorial forecasting model of ultra-rapid clock offset combining singular spectrum analysis(SSA),robust estimation and gray model(GM)is proposed.First,SSA is used to obtain the deterministic and uncertain parts of the clock offset sequence,and then a robust quadratic polynomial model with period and a robust gray model are used to forecast the deterministic and uncertain parts of the clock offset sequence,respectively,and finally,the forecast values of both are combined and corrected for the starting point deviation to obtain the final forecast value.Based on the iGMAS clock offset product,the effectiveness of the method is verified.Compared to the ISU-P product,the forecast accuracy of the proposed model is improved by 6.7%,19.5%,31.7%and 42.2%for 3h,6h,12h and 24h,respectively,when modeled using two-day clock offset data with a sampling interval of 15 minutes.4.A clock offset forecasting algorithm that fuses Long Short-Term Memory Network(LSTM)and Least Squares Support Vector Machines(LSSVM)through Back Propagation(BP)neural networks is proposed,which aims to take full advantage of multiple neural network forecasting models to achieve the best forecasting results.First,the data is divided into trained data,validated data and tested data,and then BP neural network is trained using the forecast values of LSTM and LSSVM on the validation set and the corresponding real clock offset values.Finally,the trained LSTM and LSSVM models and the fusion model are used to make clock offset forecasts on the test set.The effectiveness of the algorithm is verified by the clock offset data from GNSS spaceborne atomic clocks.The experimental results show that the fusion algorithm improves about 12%in 1-day forecasting accuracy over the LSSVM model with better forecasting accuracy,and improves about 56%in 5-day forecasting accuracy compared to the LSTM model with better forecasting accuracy.5.An improved Kalman Plus Weight(KPW)time scale algorithm is proposed.The algorithm adds a pseudo-measurement value about the master clock to the measurement equation of KPW;meanwhile,in order to eliminate the influence of the pseudo-reference deviation outliers on the calculation of the pseudo-measurement value,an adaptive algorithm for adaptively adjusting the pseudo-reference deviation outliers is also introduced in the algorithm.The results show that the improved KPW algorithm significantly improves the accuracy and stability of the time scale.Compared with the traditional KPW algorithm,the stability of the time scale calculated by the algorithm improves by about 8%when the time interval is less than 1×104 s,and about 30%when the time interval is greater than 1×106 s.The stability of the time scale calculated by the algorithm improves by about 30%when the time interval is greater than 1×106 s.Compared to the traditional KPW algorithm,the improved KPW algorithm reduces the maximum time deviation by 87ns over 6 months.6.The forecast model in the traditional ALGOS algorithm is improved,and an improved ALGOS algorithm based on an equal-weight combination model is proposed.An improved ALGOS algorithm is obtained by replacing the quadratic polynomial forecast model in the traditional ALGOS algorithm with an equal-weight combination model based on the differential gray model and the quadratic polynomial model.Comparative experimental results based on GNSS spacebome atomic clocks offset data show that the improved ALGOS algorithm achieves an average 15%improvement in result stability compared to the traditional ALGOS algorithm.7.By synthesizing various types of GNSS spaceborne atomic clocks,iGMAST has been built using the optimized KPW algorithm and its performance has been evaluated.First,the KPW algorithm is optimized by adding an exponential filter to attenuate the effect of random changes in weights on the results.Then the free iGMAST is generated by combining the hydrogen,cesium,and rubidium atomic clocks of GNSS satellites using the optimized KPW algorithm and the free iGMAST is steered to Coordinated Univeral Time(UTC)using the steering algorithm.the results show that the short-term stability of the free iGMAST in the time interval range less than 1×105s is improved by about 16%on average based on the optimized KPW algorithm.When the time interval is between 2 and 40 days,the stability of iGMAST is better than that of GPST;while at other time intervals,the stability of iGMAST is comparable to that of GPST.8.A steering algorithm with adaptive attenuation factor based on frequency data is proposed.The algorithm is based on free iGMAST to further improve the time difference accuracy and stability.By comparing the average frequency value of the current modeling data with the set threshold value to adaptively adjust the size of the attenuation factor,the optimal value of the parameter is found experimentally,and the performance of the attenuation factor adaptive steering algorithm is compared with the fixed attenuation factor steering algorithm in terms of time difference accuracy and stability.The results show that the algorithm improves the stability and the time difference accuracy of the results.For time intervals exceeding 1 x 106 s,the stability of the results of the attenuation factor adaptive steering algorithm is improved by 32%on average compared to the constant attenuation factor steering algorithm,while the time difference accuracy improves by 27%.