Comparison of BRDF-Predicted and Observed Light Curves of GEO Satellites

Abstract : Although the amount of light received by sensors on the ground from Resident Space Objects (RSOs) in geostationary orbit (GEO) is small, information can still be extracted in the form of light curves (temporal brightness or apparent magnitude). Previous research has shown promising results in determining RSO characteristics such as shape, size, reflectivity, and attitude by processing simulated light curve data with various estimation algorithms. These simulated light curves have been produced using one of several existing analytic Bidirectional Reflectance Distribution Function (BRDF) models. These BRDF models have generally come from researchers in computer graphics and machine vision and have not been shown to be realistic for telescope observations of RSOs in GEO. While BRDFs have been used for SSA analysis and characterization, there is a lack of research on the validation of BRDFs with regards to real data. In this paper, we compared telescope data provided by the Air Force Research Laboratory (AFRL) with predicted light curves from the Ashikhmin-Premoze BRDF and two additional popular illumination models, Ashikhmin-Shirley and Cook-Torrance. We computed predicted light curves based on two line mean elements (TLEs), shape model, attitude profile, observing ground station location, observation time and BRDF. The predicted light curves were then compared with AFRL telescope data. The selected BRDFS provided accurate apparent magnitude trends and behavior, but uncertainties due to lack of attitude information and deficiencies in our satellite model prevented us from obtaining a better match to the real data. The current findings present a foundation for ample future research.