Girish Narayanan, University of Auckland; Roberto Armellin, University of Auckland; Nicholas Rattenbury, University of Auckland
https://doi.org/10.64861/KFXJ9730
Keywords: light curve inversion, attitude estimation, neural posterior estimation, simulation-based inference, normalizing flows, satellite characterization, uncontrolled spacecraft, solar panel articulation, space domain awareness
Abstract:
Characterization of defunct geostationary (GEO) satellites is increasingly important for collision risk assessment, active debris removal mission design, and anomaly detection in the space domain. Light curves – time-series brightness measurements of reflected sunlight collected by ground-based optical sensors – encode information about a resident space object’s attitude, angular velocity, and physical configuration, and absent a resolved image they are the primary observable from which that state must be recovered. However, light-curve inversion for uncontrolled objects remains an open problem: the inverse problem is highly nonlinear and multi-modal, and the convergence basins of local optimizers are narrow._x000D_
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Established inversion methods – particle swarm optimization, Markov chain Monte Carlo sampling, and sequential filters – conduct a search per light curve: each new observation pays the full cost of that search, typically minutes to hours, and no part of the cost is amortized across observations. These methods also assume the angles of articulated components such as solar panels are known. For a defunct satellite that assumption fails – its panels freeze at an angle recorded in no catalogue – and because the panel angle affects both the brightness signature and, through the inertia tensor, the rotational dynamics themselves, an unknown frozen angle corrupts the inversion through two channels at once._x000D_
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This paper presents a mixed-fidelity inversion method whose central contribution is the application of a neural posterior estimator (NPE) to light-curve attitude inversion, replacing the per-light-curve search with amortized inference. The NPE is a normalizing flow over a learned light-curve embedding, trained offline on approximately five million simulated light curves; it maps an observed light curve to a joint posterior over the unknown state in a single forward pass of approximately 20 milliseconds. The training cost is paid once for the target class, not once per observation. The method is demonstrated in two forms: a known-geometry estimator recovering the initial attitude quaternion and body-frame angular velocity of an uncontrolled satellite, and an articulation-aware extension that additionally recovers a frozen solar-panel angle jointly with the spin state. _x000D_
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Because multiple physically distinct configurations can produce similar brightness time-series, the posterior is treated as a candidate generator rather than a point estimator: candidates are screened with a learned brightness surrogate approximately five orders of magnitude cheaper than full rendering, refined by Levenberg-Marquardt descent carrying the panel angle as a continuous parameter, and confirmed by a full-physics, ray-traced render. Run against observations rendered with a frozen panel offset, an inversion assuming nominal geometry returns no solution: the verification stage rejects every candidate, and the residual at the true attitude remains more than an order of magnitude above the photometric noise floor. A panel offset belowone degree is sufficient._x000D_
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Both estimators are validated on synthetic light curves of a realistic articulated GEO satellite model, evaluated throughout on simulated trajectories that were not used in training the estimator. The known-geometry estimator recovers a light-curve fit consistent with the measurement noise in over 98 percent of scenarios at a noise level of 0.05 magnitudes, with recovery demonstrated up to 0.10 magnitudes; the median search time is 49 seconds per light curve, or approximately 2.5 minutes including the confirming high-fidelity render. The articulation-aware estimator performs blind joint inversion over attitude, angular velocity, and panel angle, succeeding in over 91 percent of scenarios with a median runtime of approximately eight minutes on commodity hardware; the median panel-angle error is 0.04 degrees, and articulation is recovered to sub-degree accuracy even for panel offsets below one degree._x000D_
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The articulation-aware results use noiseless light curves and identical geometry in simulation and inversion; noise-hardening this estimator, following the augmentation already demonstrated for the known-geometry version, is work underway. An unmodelled frozen appendage results in no solution being returned rather than a biased attitude estimate propagating into conjunction assessment, and the recovered panel angle carries characterization value of its own: the frozen configuration of an appendage bears directly on a defunct satellite’s reflective cross-section and on the design of_x000D_
any mission that must later approach it._x000D_
Date of Conference: September 15-18, 2026
Track: Satellite Characterization