A Simplified–Modified Algorithm for Glonass Broadcast Orbits Computation

The orbits of Global Navigation Satellite System (GLONASS) satellites are computed from the broadcast ephemerides using the fourth order of the Runge–Kutta integration method. Usually, the initial conditions used in the integration of the differential equation of satellite motion are the three positions and the three velocities of satellites at the initial time, and the results are the position and velocity at a given time; the luni-solar perturbation is supposed to be constant during the integration interval. The algorithm used is known in the documentation as the simplified algorithm; this algorithm was modified and replaced by the one called in this investigation as the simplified–modified algorithm, where the luni-solar accelerations were taken as variable terms and three linear functions modeling these luni-solar accelerations were added to the simplified algorithm. The ode45 MATLAB solver, based on the fourth and fifth orders of the Runge–Kutta method, was used to solve the differential equations describing the motion of GLONASS satellites in orbit. The data used in this study is the broadcast orbit files of 24 GLONASS satellites between March 1 and 21, 2024. The results obtained showed an improvement of 1.76 m and 0.0027 m/s in the positions and velocities of GLONASS satellites, respectively, when the simplified–modified algorithm was applied, that is, the three luni-solar accelerations were assumed as variable terms.