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The United States Air Force Academy (USAFA) operates the Falcon Telescope Network (FTN) to support its research program in the utility of satellite optical signatures in Space Situational Awareness. In addition to collecting photometric, spectroscopic, and polarimetric data, the FTN sensors which are equipped with diffraction grating elements also operate as slitless spectrographs. FTN spectroscopic data has been used to demonstrate that it can effectively distinguish different stable geosynchronous satellites (GEO). Because the attitude of the GEO's unarticulated parts (e.g. bus) and the axis of rotation of the articulated parts (e.g., solar panel) are predominantly fixed, the light curves and the time-resolved spectra are expected to be nearly repeatable from night to night. Furthermore, the spectra of GEOs may be effective identifying signatures. To demonstrate the ability to distinguish GEOs using spectroscopic data, we reduce the spectra to vectors of features with smaller dimensionality. That can be accomplished by applying a linear dimensionality-reduction technique, e.g., Principal Component Analysis (PCA) or using a physics-based transformation that consists of smoothing and under-sampling the spectra. The PCA features consists of up to the five most prominent principal components. The physics-based feature vector is the smoothed GEO spectral reflectance sampled at 37 fixed and equally spaced wavelengths. The first approach also generates a visualizable 2-dimensional representation using the first two PCA components, while the second approach preserves as much information as allowed by the effective spectrograph's resolution. Using satellite names or numbers as labels of the classes, we trained a number of classifiers with the GEO's feature vectors. Our analyses showed that multi-GEO classification can achieve accuracy as high as 98%. We also demonstrated that instead of collecting many spectra in the range of solar phase angles as training data, we can synthesize training spectra with a limited number of reference spectra and still achieve satisfactory classification accuracies.
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