Determination of intermediate orbit and position of GLONASS satellites based on the generalized problem of two fixed centers

摘要

The mathematical model and algorithms for calculating the position of GLONASS satellites by means of their broadcast ephemeris is presented in the paper. The algorithms are based on the generalized problem of two fixed centers. One of the advantages of the analytical solution obtained from the generalized problem of two fixed centers is the fact that it embraces perturbations of all orders, from the second and also partly from the third zonal harmonics (Aksenov, 1969). GLONASS broadcast ephemeris - provided every 30 minutes - contain satellite position and velocities in the Earth fixed coordinate system PZ-90.02 (ICD, 2008), and acceleration due to luni-solar attraction. The GLONASS Interface Control Document recommends that a fourth order Runge-Kutta integration algorithm shall be applied. In the Department of Geomatics (AGH UST) a computer program has been established for fitting position and velocity of GLONASS satellites using their broadcast ephemeris. Intermediate GLONASS satellite orbits are calculated considering also the second and third zonal harmonics in the gravitational potential of the Earth. In this paper results of the analytical integration of the equation of the motion of the GLONASS satellites compared to the numerical solution are provided.