Initial orbit determination and satellite tracking using optical observations

The objective of this project is to propose a passive method for orbit determination (OD) of GEO objects using observational data as position measurements. The proposed method use position measurements expressed as right ascension and declination angles, therefore no need of on-board sensors within a satellite are need it to track them using the methodology to be presented in this thesis. The OD method was split in 3 main parts. The perturbed model for the orbit propagator, the initial orbit determination (IOD) methodology to compute initial conditions and a filter algorithm for orbit estimation. We selected an orbit propagator based on state vector and a force model solved by a Runge-Kutta 7-8 numerical integrator. The acting forces considered in the perturbed model were the earth gravitational potential model EGM96 (n=m=70), the third body perturbation due to the moon and sun gravitational forces and the exerted force due to the solar radiation pressure. Since the case study of this project is focused on GEO objects, the perturbation because of atmospheric drag was neglected. Based on the constraints of our observational data, an angles-only method was necessary for the for initial orbit determination implementation. The Gauss method and the Gibbs-Herrick method are the best fit for the position and velocity vector respectively, when short separated observations are used. To achieve precise orbit determination, a estimation algorithm using a Extended Kalman Filter (EKF) method was implemented. The observational data was used as the sensing measurements and the orbit propagator as the state predictor. The results suggested that the EKF can be used to the reduced the uncertainty associated with the orbit propagator error and to avoid this uncertainty to accumulate over the time (up to 3km per day for GEO objects). Nevertheless, future works should discuss and study how to improve the estimation implementations when observations that are closely separated are used as the measurements (separated by less than 1 minute)