Liam Robinson, Purdue University; Carolin Frueh, Purdue University; Daniel Hampf, DiGOS
https://doi.org/10.64861/EYVV9605
Keywords: Light curve, space object characterization, space debris laser ranging, data fusion, inverse problem, shape determination, attitude determination
Abstract:
Many of the more than 50,000 publicly catalogued human-made space objects are uncharacterized, meaning they have one or more properties that are uncertain or unknown. Over 1,000 analyst set objects in the Space-Track catalog are uncharacterized and cannot be associated with a known launch or public mission. Many more objects can be associated with a launch, but are still partially uncharacterized. Knowledge of an object’s shape and attitude profile is necessary to determine its candidacy for active debris removal. This information is also useful for high-fidelity orbit propagation through coupled attitude-shape orbital perturbations like solar radiation pressure. Despite its utility, this information is often difficult to acquire. Optical imagery from ground-based telescopes is spatially unresolved for all but the largest and closest objects due to atmospheric turbulence and the sheer distances involved. Flybys, adaptive optics, and synthetic aperture radar can produce resolved images of a target object, but at high monetary and logistical costs. Alternatively, cheap but unresolved data can inform characterization by partially or entirely solving an inverse problem to identify potential properties of the target that reliably predict the observed measurements.
Light curves, time histories of an object’s brightness as observed by an optical telescope, are commonly used as input data to solve this inverse problem [1-3]. Without prior information, using light curves alone to jointly determine an object’s shape, attitude, and material properties is an inherently ill-posed problem, as infinitely many solutions may fit the observations equally well. Even when all but one of these properties are known, solutions remain non-unique even without measurement noise. Existing machine learning-based inversion methods that seek to determine multiple properties simultaneously, e.g., [4], reduce the dimensionality of the problem by requiring the solution to be one of a discrete set of candidate shapes, with no guarantee of reliability if this assumption is not met.
We present an approach to determine a solution space of likely shapes and attitudes for an uncharacterized space object in low-Earth orbit by fusing light curves with simultaneous space debris laser ranging measurements to lessen many of the ambiguities observed in prior work. Space debris laser ranging residuals approximately relate the range difference from the station to the object’s center of mass or the point of reflection for each detected photon, providing geometric information about the target that is absent in light curves. We do not use a discrete bank of candidate shapes, but instead define parametric models for the major types of space objects, e.g., box-wing satellites or rocket bodies. This choice keeps the dimensionality of the problem low enough to be tractable in combination with the unknown attitude and reflectivity variables.
Our approach proceeds in two stages. The first stage is a global optimization problem to find a collection of paired space object shapes and attitude profiles that predict the laser ranging measurements. For each parametric model class, we search a constrained space of possible shapes by sampling from a low-discrepancy Sobol sequence. For each sampled shape, we propagate a variety of attitude profiles and measure the error between the observed and simulated leading edge of the laser ranging residuals, where the leading edge refers to the detected reflections from the part of the object closest to the observer. The choice to compare only the leading edge ensures that our approach is robust to unknown material properties and does not become biased due to the time-walk effect. Promising shape and attitude combinations are then fit to the light curve by optimizing surface material reflectivities using an evolutionary strategy global optimization method. This delegation of the light curve for determining only material properties ensures that the specific ambiguities traditionally observed when inverting shape or attitude from the light curve are reduced or absent in our method. Guesses that provide adequate fits to both laser ranging and light curve measurements are deemed candidates for the ground truth, yielding a final set of shape, attitude, and material models.
In our past work, we validated the efficacy and reliability of our algorithm against simulated data where the ground truth is available for comparison. This analysis demonstrated that, for high signal-to-noise ratio measurements, our algorithm can often determine the correct shape classification, with the best guesses often falling close to the ground truth in both attitude and shape. While we provide a simulated data case to motivate the efficacy of the algorithm, we focus in this paper on applying the characterization algorithm to low-Earth orbit debris objects in the Space-Track catalog. Using data acquired by the Izana-1 satellite laser ranging station on Tenerife, we compute likely shape and attitude solutions for a set of these objects observed during the spring and summer of 2026. In the future, this method may be used to associate analyst TLE objects with known launches or similar space objects to shed light on the unknown object population and support future space situational awareness operations.
Date of Conference: September 15-18, 2026
Track: Satellite Characterization