Application of Collocation Method to Numerical Integration of Satellite Orbit

We introduced the basic principle and calculation method of collocation,and studied its application in numerical integration of satellite orbits.Experiments were carried out to analyze the impact of different integration steps and method orders on results of numerical integration.Proper integration steps and method orders were also determined(being identical to the default values of Bernese software,for GPS satellite).Moreover,by comparing with the results of combined integrator designed by traditional numerical integration method,some advantages of collocation method were showed as follows:a quite long step can be used;as the polynomial coefficients of each interval are worked out directly,users could get the position and velocity of satellites at any time without interpolating and fitting;due to the above two reasons,under the same precision condition,the computational efficiency of collocation is much higher than that of normal integration methods.