Attitude Estimation of Rocket Upper Stages Based on Two-Station Photometric Observations

For rocket upper stages, single-station photometric attitude inversion often suffers from ring-shaped multiple solutions due to geometric degeneracy and target symmetry. To address this issue, this study proposes a two-station photometric rotation-state analysis method and validates it using synchronized optical observations of a Falcon 9 upper stage (NORAD ID 43563) acquired from Kunming and Lenghu stations. Results show that under single-station observation geometry, candidate spin-axis solutions satisfying the error threshold exhibit a characteristic annular distribution, reflecting the ambiguity induced by object symmetry and observational degeneracy. After introducing two-station constraints, the solution bands derived from the two stations intersect and significantly contract, causing the feasible solution set to concentrate into a more stable dominant region rather than remaining distributed along a ring. To quantitatively characterize the credibility of this dominant region, a two-dimensional probability distribution is constructed over the candidate solutions. The probability density is then weighted and fused by incorporating the fitting error and the initial-phase consistency, thereby enabling the characterization of the spin-axis orientation and its uncertainty. Simulation results with a third station further indicate that, when the additional station forms a non-collinear configuration with the original two stations and provides strong geometric complementarity, the feasible solution space can be further compressed and the uncertainty of the result can be further reduced. The proposed method provides a reproducible technical framework for the multi-station photometric rotational-state analysis of axisymmetric space debris, and also offers a basis for future incorporation of more realistic shape and shadowing mechanisms, as well as for real multi-station coordinated observations.