This paper presents a new method, based on a multiple-model adaptive estimation approach, to determine the most probable shape of a resident space object among a number of candidate shape models while simultaneously recovering the observed resident space object's inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters, each operating under a different hypothesis to determine an estimate of the physical system under consideration. In this work, the shape model of the resident space object constitutes the hypothesis. Estimates of the likelihood of each hypothesis given the available measurements are provided from the multiple-model adaptive estimation approach. The multiplemodel adaptive estimation state estimates are determined using a weighted average of the individual filter estimates, whereas the shape estimate is selected as the shape model with the highest likelihood. Each filter employs the Unscented estimation approach, reducing passively-collected electrooptical data to infer the unknown state vector comprised of the resident