Orbital estimation of spacecraft under unknown low-thrust acceleration (Second report: estimation of osculating orbital elements)

Abstract

As low-thrust propulsion technology becomes increasingly popular, orbital estimation for low-thrust spacecraft may become an area of increasing interest. More frequent use of low-thrust propulsion to place satellites in orbit gives more opportunities for collisions and radio frequency interference as these spacecraft travel slowly through altitude ranges. The purpose of this paper is to develop a method for estimation of the osculating orbital elements for low-thrust spacecraft. To overcome the instability of the estimation problem with low-thrust acceleration, we estimate the mean elements instead of osculating elements. By use of the averaging technique, Hudson and Scheeres proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only a finite number of Fourier coefficients of the thrust acceleration appear because of the orthogonality of the trigonometric function. Based on the nonlinear state equation representation for the extended state variables which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from perturbed observation data of mean orbital elements. Then, the mapping from mean to osculating elements which is derived from the perturbation theory is used to estimate the osculating elements. The proposed method is demonstrated through numerical simulations.