Bézier description of space trajectories
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Bézier functions are polynomials capable to describe complicate curves. They can be used with a Least Square approach to describe space trajectories when enough positions data are available. This method is here applied to develop an autonomous positioning technique for a spacecraft equipped with a visible camera observing a close celestial body (e.g., Moon, Earth). The images are processed to obtain the position estimates required. Acquired measurements, weighted accordingly to their accuracies, determine the control points, that are estimated with a Least Square approach. Therefore, this method does not require knowledge of the dynamics and eventual perturbations acting on the system, which are often very complicated to model. Its speed and computational efficiency, make it a good candidate for on-board use. The proposed method has been tested for Keplerian orbits (with various values of eccentricity) and a cislunar trajectory. The accuracy is then compared with a weighted iterative least-square and an Extended Kalman Filter.
author list (cited authors)
De Dilectis, F., Mortari, D., & Zanetti, R.