Abstract:

This paper assesses the existing numerical integration methods including the Runge-Kutta methods, the Adams-Cowell methods, the Gauss-Jackson methods and the extrapolation methods in the computation of the GRACE satellite orbits and state transition matrix. According to the results, we recommend the Gauss-Jackson methods with optimal parameters to integral orbit and also analyze the advantages of the Gauss-Jackson methods relative to the other methods. Then the resistance capacity of the random errors which are included in the satellite initial state for those methods is analyzed, and the numerical results indicate that all methods show the similar little resistance capacity. The integral orbits are more sensitive to the satellite initial state velocity errors (0.1mm/s) than the initial state position errors(10mm). Compared to the errors in the satellite initial state, the perturbation force model errors have a significant impact on the orbit integral precision. Finally, we proposes a modified method which combines the Gauss-Jackson algorithm and the moving-window polynomial interpolation algorithm to overcome the shortage of the large step size of the Gauss-Jackson method. The simulated and actual results show that the modified method can give the satellite position and state transition matrix at any time and has a significant improvement in computing efficiency while possessing high accuracy.

Key words: Orbit integration, Integral precision, Integral efficiency, Error influence