Robustness analysis of a Moving Horizon Estimator for space debris tracking during atmospheric reentry

Trajectory estimation during atmospheric reentry of ballistic objects such as space debris is a very complex problem due to high variations of their ballistic coefficients. In general, the characteristics of the tracked object are not accurately known and an assumption on the dynamics of the ballistic coefficient has to be made in the estimation model. The designed estimator must hence prove to be robust enough to such model uncertainties, and to bad initialization if no good prior information on the initial position, velocity, and the characteristics of the object is available. Robustness of a Moving Horizon Estimator (MHE) is studied in this paper and compared to several other filters: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Regularized Particle Filter (RPF). The performances of the filters are analysed in terms of convergence percentage, accuracy, robustness to bad initialization, and computation time, via Monte Carlo simulations of trajectories of several space debris. Contrary to the classical tracking problem of supersonic ballistic objects for which RPF has been proven to be efficient in the literature, it is shown that its performance are overcome by MHE for the space debris tracking problem considered in this paper.