Real-time estimation of satellite's two-line elements via positioning data

This paper presents a finite difference based Extended Kalman Filter (EKF) for real-time estimation of two-line elements (TLE) to be used in satellite mission. Three finite difference approximation methods are used to compute the highly nonlinear Jacobian matrix of the simplified perturbation propagator (SGP4). The three methods are the fourth order central-difference, second order forward-difference and second order backward-difference approximations. In addition, a line search weightage has been implemented to ensure the state estimates do not violate the boundary constraint during the Kalman filtering update process, such as negative eccentricity. The TLE estimation's accuracy and average computational time of the proposed finite difference based EKF methods have been compared with other optimization algorithms such as the genetic algorithm (GA), particle swarm optimization (PSO) and interior-point method (IPM). Results have shown that the average TLE estimation error of the proposed approach is at least two magnitudes lower than IPM, PSO and GA. In addition, the proposed method has the lowest computational time, and is at least 12 times faster than PSO and GA.