Alexander Burton, Purdue University; Carolin Frueh, Purdue University
Keywords: light curve inversion, attitude determination, space debris
Abstract:
The problem of light curve inversion is by no means a new one. When too far away to gain a resolved image, brightness measurements over time hold information on the albedo-shape, including materials, and the attitude of an object. Even in the slightly simpler problem of a known spacecraft, the attitude inversion is plagued by ambiguities and non-convergence errors, combined with the enormous data hunger to reach any result in both traditional methods and machine learning methods (see e.g. Linares et al, Furfaro et al, Frueh et al, Schildknecht et al., Crassidis et al. to just name a few).
The convergence problems are most prominent due to a lack of a sufficiently good first guess and input constraints (Crassidis et al have highlighted that in great detail). Under very tight input constraints, such as a symmetric object spinning about a single axis, good results in terms of spin rate can be reached if data with small enough measurement errors is available. Benson & Scheeres have shown success with estimating two spin rates when one is significantly larger and around the main axis of inertia, where two moments of inertia are the same. However, objects in space tend to have complex tumbling motion patterns and do not always remain sufficiently well spin-stabilized because of dissipating effects such as Eddy currents, even if their initial condition was more stable.
This paper offers a comprehensive attitude estimation solution for any type of torque-free attitude motion with no constraints on the moments of inertia (no symmetry condition), which offers more flexibility. The method is hence suitable for any type of symmetric or non-symmetric, convex or concave space object at any distance as long as a light curve can be collected.
In this method, first so-called pseudo-measurements are generated. These are possible orientations that correspond to a single point in the light curve within the measurement bounds. Fully analytic torque-free expressions for any attitude motion have been used to quickly compute the set of propagated attitudes from initial conditions. In subsequent optimization steps, using swarm optimization methods, the attitudes that fit the measurements closest are computed. For objects with concavities, an approximation of the reflection model is often used for faster calculations, which still gives results very close to the actual light curve response. In the final step, the best-fitting attitudes are subjected to a quasi-Newton method, where the prior step serves to provide the initial conditions, which are, in all tests run so far, easily close enough to ensure convergence.
In the paper, results for simple non-realistic but highly symmetric objects such as a tetrahedron are shown all the way to multi-faceted models with several thousand surface elements to accurately represent objects such as Astra or Envisat satellites.
Date of Conference: September 19-22, 2023
Track: Satellite Characterization