Estimation of mean orbital elements with unknown low-thrust acceleration

Space Situational Awareness (SSA) has been recognized to be important for the safe space activities including these problems. As low-thrust propulsion technology becomes increasingly popular, SSA for low-thrust spacecraft may become an area of increasing interest. More frequently use of low-thrust propulsion to place satellites in orbit create 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 mean 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 (2009) proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only 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 variable which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from observation data of mean orbital elements. Moreover, the mapping from mean to osculating elements is derived which can be replaced by a measurement equation. Proposed method is demonstrated through numerical simulations