Interpolation methods for tracking spacecraft in ultratight formation

. By measuring the centroid of a beam on a detector, one can track the movement of that beam across the detector. By tracking this movement, one can track the object encompassing the detector, for example, a spacecraft. A variety of system-specific performance inhibitors can make this a challenge, requiring a robust calibration method. The goal of this investigation is to model the true beam position of the instrument in terms of the measured beam position. For this, a mathematical model is created that interpolates and corrects the measured beam position using precollected position data—a “calibration model.” The real-world scenario for this investigation is the flight-representative model of the fine lateral and longitudinal sensor (FLLS) instrument, built by Neptec Design Group and Neptec UK for the European Space Agency mission PROBA-3. Performance inhibitors for FLLS are cropping of the beam, imperfect optics, and a varying distance the beam has traveled (up to 250 m). Using bivariate spline interpolation for the FLLS calibration model gives the best performance, achieving a measurement accuracy well within the mission requirement of <300  μm.