A multiplicative perturbation method for satellite orbit prediction based on symplectic property

Abstract

In order to predict artificial satellite orbit accurately, complex dynamic models need to be considered and numerical integration algorithms are used to solve the problem. Desired effect has been obtained for orbit prediction by various integration algorithms such as Runge-Kutta algorithm and Adams-Cowell algorithm. But the symplectic property of the dynamic problem is not taken into consideration, therefore the inherent characteristics of the system are neglected. In this paper, the multiplictive perturbation method based on symplectic propterty, which adapts to orbit prediction, is proposed. Hamiltonian canonical equation, which describes the motion of the satellite, is divided into two sections, including two-body problem and perturbation section. Analytical solution of two-body problem is used. Perturbation section is solved approximately by interval matrices algorithm. Because state transition matrix of the two-body problem is a symplectic matrix, it is a symplectic structure-preserving process. Perturbation factors, including non-spherical Earth, solar-lunar gravitational force, solar radiation pressure and tidal perturbation, are taken into account. GPS satellites are selected to make numerical simulations. The error of orbit prediction is obtained by reference to precise ephemeris of GPS satellites. The results of the proposed perturbation method are compared with that of Runge-Kutta algorithm and Adams-Cowell algorithm. Results show: 3 d prediction errors of proposed algorithm for PRN01 GPS satellite and PRN02 GPS satellite are 4.56 and 10.10 m, respectively. The accuracy of proposed algorithm coincides with that of Runge-Kutta algorithm and Adams-Cowell algorithm. The computational time of Runge-Kutta algorithm is 237.7% of that of proposed algorithm. The computational time of Adams-Cowell algorithm is 71.3% of that of proposed algorithm. So the efficiency of proposed algorithm is obviously higher than that of Runge-Kutta algorithm and is slightly lower than that of Adams-Cowell algorithm.