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

Abstract

Trajectory estimation during atmospheric re entry 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.

Stability of a nonlinear Moving Horizon Estimator with pre-estimation

“…The main advantages of the MHE are that it allows to handle nonlinear systems without linearisation and to incorporate constraints directly during the optimization. The MHE has also been shown to be more robust against poor initialization than the Extended Kalman Filter (EKF) [5], the Unscented Kalman Filter (UKF) and the particle filter [9]. The convergence of the estimation errors of the MHE has been demonstrated in [2] provided that a quadratic arrival cost is adopted and its weight matrix is adequately chosen.…”

Stability analysis and robustness assessment of deterministic and stochastic nonlinear moving horizon estimators

“…To derive an estimation model for the estimators, let us assume that β is constant over a sampling period T s . The following state equation is obtained [11]:…”

“…the Earth gravity constant, and w k is a modeled as a discretetime zero-mean truncated gaussian white noise of covariance matrix Q. This matrix can be parameterized as Q = Q(T s ).q z where the matrix Q(T s ) can be found in [11] and the scalar q z > 0 should account for both discretization error and model errors, from the fact that β is not constant over a sampling period.…”

Moving Horizon Estimation with Pre-Estimation (MHE-PE) for 3D space debris tracking during atmospheric re-entry

“…The estimation errors, nondivergence percentage and computation time of the MHE-PE will be compared to those of the EKF, the UKF and the RPF through Monte Carlo simulations. Compared to previous work [17], a new estimation model using the derivative of the acceleration is proposed in this paper.…”

“…An assumption on its variation has to be made in the estimation model which results in model errors. In the previous work by the authors [17], we showed that, for a simplified 1D space debris tracking during the re-entry, classical estimators such as the Extended Kalman estimator (EKF), the Unscented Kalman estimator (UKF) and the Regularized Particle estimator (RPF) are outperformed by the Moving Horizon Estimator (MHE) in terms of robustness against poor initialization and accuracy. However, the MHE requires very large computation time and its implementation in 3D cases is limited.…”