Research On Interpolation And Prediction Of GNSS Satellite Clock Correction

Global Navigation Satellite System(GNSS)plays an important role in all aspects of modern society.With the development of the times and the rapid development of science and technology,the construction of navigation satellite system had been accelerating in all countries of the world.GNSS consists of Global Navigation Satellite System and Regional Navigation Satellite System,it has become a research hotspot to gradually transform the traditional navigation and positioning from a single system to multi-system joint positioning.The ranging principle of the navigation satellite system is based on the measurement of time,so the processing of satellite clock difference data has profound significance,and there are many factors that affect the satellite clock difference,different navigation satellite systems installed different satellite clocks,which has different effects on the mathematical methods used when processing the satellite clock difference data of different navigation systems.Based on this background,this paper uses different interpolation methods and prediction models to interpolate and forecast the clock difference products of the Global Positioning System(GPS),the Global Navigation Satellite System(GLONASS),the Beidou Navigation Satellite System(BDS)and the Galileo satellite navigation system(Galileo)in GNSS,compares and analyzes the accuracy in the processing of clock difference data.Some useful conclusions were reached:(1)Introducing the basic principle and solution process of Lagrange interpolation,Chebyshev polynomial fitting and Generalized extended interpolation.in order to avoid the "Runge phenomenon",a sliding algorithm is used to interpolate the precision clock difference data of 5min to 30 s,and compare it with the precision clock difference of 30 s in GNSS,and find that the accuracy meets the requirements.(2)Using these three sliding interpolation methods to perform clock difference interpolation on different satellite systems in GNSS,the accuracy has reached the sub-nanosecond level.The application effects of the three sliding interpolation methods,from high to low,are Galileo,BDS,GPS and GLONASS.Among the three sliding interpolation methods,the sliding Generalized extended interpolation has the highest interpolation accuracy,the sliding Chebyshev polynomial fitting has the second lowest accuracy,and the sliding Lagrangian interpolation method has the lowest accuracy.For the GPS,5 of the 30 satellites using the sliding Chebyshev polynomial fitting have a slightly better interpolation accuracy than the sliding Generalized extended interpolation,the accuracy difference does not exceed0.01ns;For the GLONASS,only one of the 21 satellites using the sliding Chebyshev polynomial fitting have a slightly better interpolation accuracy than the sliding Generalized extended interpolation,the accuracy difference does not exceed 0.002ns;For the BDS,5 ofthe 14 satellites using the sliding Chebyshev polynomial fitting have a slightly better interpolation accuracy than the sliding Generalized extended interpolation,the accuracy difference does not exceed 0.01ns;For the Galileo,4 of the 16 satellites using the sliding Lagrange interpolation have a slightly better interpolation accuracy than the sliding Generalized extended interpolation,the accuracy difference does not exceed 0.01ns;4satellites using the sliding Chebyshev polynomial fitting have a slightly better interpolation accuracy than the sliding Generalized extended interpolation,the accuracy difference does not exceed 0.01ns;8 of the 16 satellites using the sliding Lagrange interpolation and the sliding Lagrange interpolation have almost the same interpolation accuracy.(3)Using the Quadratic polynomial model,the Gray model,and the Quadratic exponential smoothing model to forecast the clock difference data of GPS,GLONASS,BDS,and Galileo in the GNSS,Utilizing the 30 s precision clock difference data at 24 h on April16 th to forecast the clock difference on the next day(24h),the results are compared with the precision clock difference data with the 30 s interval between April 17 th,analyze forecast accuracy,and compare the application effects of these three forecast models in different systems.For the GPS,the average accuracy of the Gray model and the Quadratic exponential smoothing model can reach sub-nanosecond levels,and the Quadratic exponential smoothing model has the highest forecast accuracy,with an average accuracy of 0.7ns;For the GLONASS,the prediction accuracy of these three models is poor.The Gray model has the highest prediction accuracy,with an average accuracy of 1.32ns;For the BDS,the prediction accuracy of these three models is poor.The Quadratic exponential smoothing model has the highest prediction accuracy,with an average accuracy of 2.36ns;For the Galileo,the average accuracy of the Quadratic polynomial model and the Quadratic exponential smoothing model can reach sub-nanosecond level,and the 16 satellites which have data for the day of the Galileo,the prediction accuracy of these two prediction models is within 1ns.The Quadratic polynomial model has the highest prediction accuracy,with an average accuracy of 0.37 ns.For the Quadratic polynomial model,the prediction accuracy from high to low is Galileo,GPS,BDS and GLONASS;For the Gray model,the prediction accuracy from high to low is GPS,GLONASS,Galileo and BDS;For the Quadratic exponential smoothing model,the forecast accuracy from high to low is Galileo,GPS,GLONASS and BDS.