Choice of numerical integration method of differential equations for global navigation satellite systems

Annotation: Comparative analysis of numerical integration methods for GLONASS satellite movement equations is carried out in this paper. Four methods of differential equations numerical integration were compared in accuracy: Runge-Kutta, Adams-Stermer, Adams-Moulton-Cowell and Everhart methods. Problems of GLONASS ephemeris and time supply require especially high accuracy in numerical integration of satellite orbits. It makes such comparison very necessary. Aim of this research is to make a well-reasoned choice of numerical integration method for recovering satellite orbits using trajectory observations carried out by terrestrial base stations. Methods behavior in case of step disturbance in the right part of satellite movement equation is specially considered. Step disturbance takes place in cases, when satellite comes into a shade of Earth and out of it. It is shown, that Everhart method is most effective for aims of numerical integration of satellites movement equations in a GLONASS ephemeris and time supply problem.

Keywords: navigation satellite, orbits calculation, glonass, ephemeris and time supply, numerical integration, everhart method, mathematical movement model, trajectory observations