Maria Alessandra De Luca, Politecnico di Milano; Felix Rosebrock, Fraunhofer FHR; Delphine Cerutti-Maori, Fraunhofer FHR; Marco Felice Montaruli, Politecnico di Milano; Pierluigi Di Lizia, Politecnico di Milano; Mauro Massari, Politecnico di Milano
https://doi.org/10.64861/YCFO6464
Keywords: RSO characterization, model-free, rotation period, spin axis estimation, ground-based sensor, radar cross section, radar imaging, data fusion
Abstract:
In recent decades, the growing volume of Resident Space Objects (RSOs) has become a major global concern. The growing density of artificial objects in Earth orbit leads to an elevated probability of on-orbit collisions and increases the risk associated with uncontrolled atmospheric re-entries. Mitigating these risks requires accurate characterization of orbiting objects, not only in terms of orbit determination but also with respect to their spin state. Such information is essential for Space Situational Awareness (SSA), to effectively monitor space traffic and to support emerging activities such as on-orbit servicing and active debris removal. _x000D_
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Regarding spin state characterization, ground-based optical sensors have been extensively employed for this purpose, but their measurements strongly depend on illumination conditions and viewing geometry, and are therefore subject to noise and data gaps. Radar measurements mitigate some of these limitations, as radar does not rely on solar illumination. Measurements of the Radar Cross Section (RCS), Doppler shift, and range can be exploited, as they contain intrinsic information on the object geometry and rotational motion. Nevertheless, they remain influenced by the electromagnetic properties of the RSO surface, signal-to-noise constraints, and geometric observability conditions related to the orientation of the object spin relative to the radar line of sight._x000D_
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Consequently, determining the full attitude state of the observed RSO from ground-based measurements remains inherently difficult. Although different methods in the literature attempt to recover the complete attitude (by generating, for example, simulated measurements and comparing them with observed data), such approaches typically require accurate knowledge of the object shape and surface properties, information that is rarely available in SSA applications. For this reason, this work proposes a model-free framework aimed at estimating only the most relevant attitude-related parameters of rotating RSO using ground-based RCS measurements, without exploiting prior knowledge of target geometry or material characteristics. In particular, the approach focuses on determining two key attitude quantities from the periodic reoccurrence of patterns in an RCS time series: the rotation period and the direction of the spin axis. _x000D_
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The first stage of the presented work focuses on estimating the synodic rotation period, defined as the apparent rotation period relative to the observer, from a sequence of RCS measurements collected during a single radar pass. To this aim, techniques available in the literature, including the Lomb–Scargle Periodogram, the autocorrelation function, and Phase Dispersion Minimization, are implemented, tested, and compared. However, these approaches provide a single representative estimate of the synodic period over the considered observation window and do not capture its temporal variation caused by the continuously changing observation geometry during the radar pass. To account for this behavior, an adaptation of the “Epoch Method”, originally developed for optical observations of asteroids and artificial objects, is here proposed for radar measurements. A time-dependent model of the synodic period of a rotating RSO is derived by exploiting its dependency on both the sidereal rotation period and the relative orientation between the line of sight and the spin axis. The resulting model is embedded into a constrained optimization framework that searches for the spin axis direction and sidereal spin period that best explain the periodicity observed in the RCS measurements. The approach assumes that the object is undergoing principal axis rotation and its rotational state remains constant over the observation interval. Finally, ambiguities in the estimated solution and possible strategies for resolving them through multiple radar observations of the target are discussed._x000D_
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Furthermore, a possible extension of the framework to objects in non-principal axis rotation is presented. In this case, the measurements are characterized by two dominant periodicities: the rotation period and a second period associated with the precession of the spin axis around the angular momentum vector. To capture this behavior, a two-dimensional Fourier series is fitted to the RCS time series. An optimization procedure minimizes the root mean square error between the model and the measurements to estimate the Fourier coefficients and the synodic values of the two characteristic periods. The extension of the synodic–sidereal relationship to this more complex rotational state is also discussed._x000D_
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The proposed methodology is validated on both simulated and real data. In particular, RCS measurements acquired by the Tracking and Imaging Radar (TIRA) sensor, a space observation system which comprises an L-band tracking radar and an imaging radar operating in the Ku band, are analyzed to enable assessment of the method under realistic operational conditions. Finally, a comparative analysis and data fusion study is performed using both L-band tracking RCS data and Ku-band measurements from the TIRA imaging radar. In this latter case, a dedicated imaging-based approach is adopted to characterize the spin rate and the spin axis direction of the observed RSO by analyzing Inverse Synthetic Aperture Radar (ISAR) images of the object. This multi-frequency framework is investigated to assess how combining radar observations at different bands can improve estimation robustness and accuracy, with the goal of achieving more reliable spin state characterization._x000D_
Date of Conference: September 15-18, 2026
Track: Satellite Characterization