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 multiple-model 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 electro-optical data to infer the unknown state vector composed of the resident space object's inertial-tobody orientation, position, and respective temporal rates. Each hypothesized shape model results in a different observed optical cross-sectional area. The effects of solar radiation pressure may be recovered from accurate angles data alone, if the collected measurements span a sufficiently long period of time, so as to make the nonconservative mismodeling effects noticeable. However, for relatively short arcs of data, this effect is weak, and thus the temporal brightness of the resident space object can be used in conjunction with the angles data to exploit the fused sensitivity to both the resident space object shape model and associated trajectory. Initial simulation results show that the resident space object model and states can be recovered accurately with the proposed approach.