Design of the ESA PROBA-3 Alternative SPS algorithm for formation flight applications

The ESA Project for On-Board Autonomy – 3 (PROBA-3) mission is a technological demonstration for precise formation flying of two small spacecraft in a Highly elliptical Earth Orbit. The mission’s main objective is to demonstrate and validate formation flying techniques with high precision, performing formation control, collision avoidance, and rendezvous operations. In addition to the technological goals, PROBA-3 accommodates a scientific payload that takes advantage of the formation flying capabilities derived from the millimetre relative position precision. The Association of Spacecraft for Polarimetric and Imaging Investigation of the Corona of the Sun (ASPIICS) is a coronagraph system distributed over two satellites: the CSC (Coronagraph SpaceCraft) carrying a telescope imaging the corona in visible light, and the OSC (Occulter SpaceCraft) carrying the Sun occulter disk that will produce an artificial eclipse. This configuration creates a 150-meter instrument that shall obtain fundamental scientific measurements to study the solar corona. The onboard metrology system shall ensure precise reciprocal positioning of the two satellites using a closed-loop arrangement to accomplish these tasks. Thus, a metrology chain of increased accuracy shall be used, culminating with the Shadow Positioning Sensors (SPS) subsystem. These shall return the three-dimensional displacement of the penumbra centre with respect to the entrance pupil, taking as input the irradiance measured by four sensors. An algorithm will be used to compute the necessary correction with respect to the nominal position. The main objective of this thesis, developed in collaboration with the Istituto Nazionale di AstroFisica (INAF), is to design and validate an alternative SPS algorithm that shall validate the lateral positioning results coming from the satellite’s algorithm. The flight algorithm is based on a different approach that allows a faster and straightforward calculation of the centre of the umbra position while maintaining an elevated accuracy. However, this method intrinsically leads to a non-axis-symmetric penumbra profile, and unwanted errors could arise. For this reason, ESA proposed an alternative algorithm that avoids the direct determination of the umbra centre coordinates in the pupil plane for the set of SPS used. Instead, the suggested algorithm uses Cardano’s method to determine the radial position of each sensor with respect to the instrument’s pupil centre and, using the known positions, reconstruct the desired umbra centre coordinates in the pupil plane reference system. This procedure is computationally costly with respect to the onboard algorithm. Still, it can achieve a comparable accuracy while guaranteeing an axis-symmetric model for the penumbra profile, and it shall be used to validate the lateral positioning results of the flight algorithm. Furthermore, this work describes the SPS simulator development and validation, where locally generated and real irradiance values are employed, emulating the expected satellite's subsystem functioning. The results from the alternative algorithm are then compared to the ones implemented onboard to determine the main advantages and disadvantages and the areas where one algorithm shall be favoured for validation and calibration procedures.