Mean Orbital Elements Estimation for Autonomous Satellite Guidance and Orbit Control

Satellite guidance and orbit control often use mean elements as inputs. Whereas traditional missions can use ground-station-based calculation of mean elements, this is not possible in autonomous satellites, which are required to perform onboard estimation of the mean elements. This problem is not trivial, because analytical satellite theories are not robust to modeling errors and cannot easily accommodate thrust. The purpose of this paper is to develop an effective filtering algorithm for onboard estimation of the mean orbital elements in small-eccentricity low Earth orbits. To that end, a semianalytical astrodynamical model that includes zonal/tesseral/sectorial harmonics and drag is formulated to capture the daily, long-periodic, and secular evolution of the mean orbital elements. The mapping from mean to osculating elements is used as a measurement equation by adding the short-periodic terms. This unique formulation is then fed into a spherical-simplex square-root unscented Kalman filter, which serves as the mean-elements estimator. A comprehensive performance evaluation for both controlled and uncontrolled orbits shows the potential applicability of the method and its advantages compared with Brouwer-based approaches.