Study On The BDS Satellite Orbit Interpolation And Fitting Method And Precision Analysis Based On The Satellite Ephemeris

Since the completion of the regional navigation task at the end of 2012,China's Beidou Navigation Satellite System,which is independently constructed and developed,has received more and more attention from people and has been widely used in transportation,finance,power,agriculture,forestry,public security,fishery industries,etc.According to the basic principles of satellite positioning,obtaining satellite orbit coordinates is the basis and prerequisite for the completion of user terminal positioning.The satellite coordinates are often obtained via broadcast ephemeris and precise ephemeris.When real-time positioning is proceeding based on broadcast ephemeris,it is often necessary to repeatedly calculate the satellite position and velocity,which will occupy more memory and reduce efficiency.Aiming at this problem,the satellite ephemeris can be fitted as a polynomial of time;the precise ephemeris provides high-precision discrete satellite coordinates,but more intensive satellite positions are often needed in satellite positioning data processing.Therefore,interpolation and fitting method can be used to find satellite coordinates at any time.In this paper,the basic principles,expressions and solution processes of Lagrange interpolation,Newton interpolation,Chebyshev polynomial fitting,least squares polynomial fitting and generalized extended approximation are respectively studied in depth.It is explored that they are specifically applicated in Beidou satellite coordinate interpolation and fitting.The main work and conclusions of the paper are as follows:(1)The satellite orbit fitting method and fitting precision based on Beidou satellite broadcast ephemeris are studied and analyzed.The fitting precision of different orders under the same fitting time interval is studied.The Chebyshev fitting method and the least squares fitting method have basically the same fitting precision in the same fitting order.Using the Chebyshev fitting method,the fitting precision of different time intervals under the same fitting order is studied.The shorter the fitting time interval is,the higher the fitting precision is generally.(2)The interpolation method and interpolation precison of Beidou satellite precise ephemeris are studied and analyzed.The non-sliding interpolation precison analysis under different interpolation orders is performed.The interpolation precision of Lagrange interpolation method is higher than that of Newton interpolation method.Based on slide-type Lagrange interpolation method,the interpolation precision under different interpolation orders is analyzed.The Lagrange interpolation method is used to compare and analyze the non-sliding and sliding interpolation precision of the same interpolation order.The sliding interpolation method has higher interpolation precision.(3)Using the sliding Chebyshev fitting method,the fitting precision of precise ephemeris of Beidou satellites is analyzed.The fitting precision of different orders under the same fitting period is analyzed.The precision of the best fitting order under the different fitting period is compared.With the increase of the fitting period,the fitting precision under the optimal order is improved.(4)Based on the sliding generalized extended approximation method,the precision of precise ephemeris interpolation of the three types of satellites is analyzed.For GEO satellites,the number of unit domain nodes is a positive correlation with interpolation precision;for IGSO and MEO satellites,the precision of interpolation is greater when the number of approximation function terms and the number of extension domain nodes are higher.(5)Based on the Lagrange interpolation method,Chebyshev polynomial fitting method and generalized extended approximation method under the sliding algorithm,using their parameter conditions with the highest interpolation or fitting precision,the interpolation and fitting precision of Beidou satellite precise ephemeris is compared and analyzed.For GEO and IGSO satellites,the interpolation precision of the three methods is basically the same.The sliding Lagrange interpolation method is the best in terms of comprehensive precision and efficiency.For MEO satellites,the precision of sliding generalized extended approximation method is significantly higher than that of the other two algorithms.