David Vallverdu Cabrera, Airbus Defence and Space GmbH; Jens Utzmann, Airbus Defence and Space GmbH; Roger Förstner, Universität der Bundeswehr München
Keywords: light curve, object characterization, shape caracterization, extended gaussian image, minkowski
Abstract:
Apart from orbital ephemeris, space debris catalogs may contain other object characteristics that are valuable to perform further debris mitigation e.g., characteristics such as attitude, shape and size are necessary for active debris removal.
The Space Situational Awareness (SSA) group of Airbus Defence and Space Germany develops the Special Perturbations Orbit determination and Orbit analysis toolKit (SPOOK), a software framework aimed at maintaining a catalog of space objects with information on their orbital ephemeris. SPOOK can perform all the main activities of the Space Surveillance and Tracking (SST) workflow, including observation planning, optical and radar measurement (including light curves) simulation and acquisition, either via the in-house Airbus Robotic Telescope (ART) or from third parties, tracklet linking, tracklet correlation and orbit determination. With the aim to include further object characteristics into the catalog, this paper describes how this workflow is updated to add systematic object characterization capabilities in SPOOK [1]. In particular, this paper focuses on shape characterization using light curves chains of brightness measurements from observing a single object with an optical telescope, closely spaced in time. To achieve this goal, a new block has been added to SPOOK: shape characterization from light curves.
After a review of the state of the art on object characterization using light curves, the first part of this paper describes the methodology used to estimate the shape of a convex object from its light curve, in a scenario where the attitude state of the object is known, in addition to the observation geometry i.e. the relative position of the observer, the object and the illumination source, usually the Sun. The text briefly discusses the shape inversion algorithm based on the following two-step approach: first, an Extended Gaussian Image (EGI) representing the albedo-area product distribution of the object is estimated form the light curve, geometry and attitude information using non-negative least squares (NNLS); second, the convex polyhedron associated to the EGI is recovered through Minkowski minimization. The paper describes how shape inversion fits into the SPOOK workflow pipeline.
Although these algorithms have been used for the shape inversion of both asteroids and man-made objects [2,3], this paper explores specific modifications that improve the stability and robustness of the process for the case of artificial objects, which have markedly different shape and reflective properties w.r.t. asteroids. In particular, it is shown that, for these objects, the EGI recovery step can converge even when the least squares Gramian is rank-deficient. Additionally, the plain NNLS approach is compared to its regularized variants that could enhance stability against noisy input. Furthermore, regarding the Minkowski minimization step, the paper compares two separate approaches to calculate the Hessian of the volume of a 3D polyhedron relative to its support values (analytically v.s. numerically), and the respective impact to convergence speed.
The second part of this paper discusses the possibilities to expand this shape inversion approach for the cases where 1) the shape is not convex, 2) the attitude is not known and/or 3) the albedo is not constant throughout the surface. It reviews the approaches used for the asteroid use case [2,4], and their potential to be applied on man-made objects.
The last part of the paper shows the results of the shape inversion approach implemented in SPOOK, using simulated light curves from objects with different shapes and observability conditions, including measurement noise. It focuses on demonstrating the effects of the aforementioned improvements to the two-step shape inversion method, and to show that sharp-edge shapes are recoverable even when the Gramian of the EGI recovery step is rank-deficient.
The paper concludes with a summary of the added value of the shape inversion algorithm tailored to the artificial object use case, and with hints and suggestions for further development. It highlights the role of the presented shape inversion as yet another building block of the cataloguing and characterization pipeline of SPOOK.
References:
[1] Rodriguez Fernandez O, Utzmann J, Hugentobler U. SPOOK – A Comprehensive Space Surveillance and Tracking Analysis Tool. In: 7th European Conference for Aeronautics and Aerospace Sciences (EUCASS). 2017.
[2] Kaasalainen M, Torppa J. Optimization methods for asteroid lightcurve inversion. I. Shape determination. Icarus. 2001;153(1):2436.
[3] Fan S, Frueh C. A Direct Light Curve Inversion Scheme in the Presence of Measurement Noise. J Astronaut Sci. 2020;67:74061.
[4] Kaasalainen M, Torppa J, Muinonen K. Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem. Icarus. 2001;153(1):3751.
Date of Conference: September 14-17, 2021
Track: Non-Resolved Object Characterization