Time Series Forecasting applies to the Orbit Propagation Problem

Abstract

The orbital motion of an artificial satellite or space debris object is influenced by a variety of external forces, such as the Earth's gravity, which is the principal perturbation affecting the orbit, as well as atmospheric drag, third-body influences, solar radiation pressure, Earth's tidal effects, and, in the case of an artificial satellite, small perturbing forces produced by its propulsion system. Numerical, analytical and semi-analytical techniques are used in order to solve the nonlinear equations of motion of this complex dynamical system. However, this system may be simplified by removing some of the aforementioned external forces in function of the scientific requirements for the mission, for example, in the case of maintenance of an Earth satellite or space debris catalogue. In this work we present a new approach called hybrid perturbation theory, which may combine a numerical, analytical and semianalytical techniques with statistical time series models [1, 2]. This combination allows for an increase in the accuracy of these integration methods for predicting the position and velocity of any artificial satellite or space debris object, as well as modeling higher-order terms and other external forces not considered in the numerical, analytical or semianalytical theory. The aim of this paper is to develop a Hybrid Orbit Propagator based on an analytical theory in order to model the effect produced by the flattening of the Earth so that this technique can be validated. This Hybrid Orbit Propagator incorporates the analytical integration of the Kepler problem as the integration technique, whereas the forecasting technique is the Additive Holt-Winters.