Mitigation of Orbit Integration Errors for Eclipsing Satellites

Abstract

Numerical integration assumes that accelerations at each node are continuous and smooth. However, when satellite enters into shadow, perturbation caused by solar radiation pressure will jump. Therefore, mathematical theory of numerical integrator cannot match the real motion of satellite, which will bring about integration errors. In order to deal with the problem, some experiments are done for different constellations. The result shows that 99 % of error occurs in along-track direction and will accumulate when crossing more shadow boundaries. For different integrators, errors are different. Runge-Kutta4 integrator is sensitive to step size, especially for eclipsing satellites, and is not competent for long arc integration. Adams integrator relies on former steps, needs a fixed step size, and will induce more integration errors when crossing shadow boundaries. Runge-Kutta9 integrator brings less error during eclipsing season than Runge-Kutta4 and Adams integrators, and can change step size flexibly. To mitigate integration errors during eclipses, this contribution introduces an improved method based on Runge-Kutta9 integrator. We use dichotomy to detect the exact epoch of penumbra boundary, change the step size, and restart the integration. Result shows that after boundary detection, accuracy for 1-day arc improves 65.8 %, 2-day arc improves 55.5 %, 3-day arc improves 33.2 %. This method is suitable for both extended filter and least square method.