B´ ezier Description of Space Trajectories Francesco de Dilectis ∗ , Daniele Mortari † , Texas A&M University, College Station, Texas and Renato Zanetti ‡ NASA Jonhson Space Center, Houston, Texas I. Introduction This study introduces a new method to estimate spacecraft trajectories using non-rational B´ ezier functions to fit a set of measured positions. These implicit functions are defined by a set of control points that, in general, do not belong to the trajectory. The values of the implicit parameters, the control points, and the B´ ezier function degree are estimated by an iterative least-squares process. The main advantage of this approach is that it does not require dynamics and perturbations models, and it provides not only a best fitting of the trajectory, but also associates interpolated points with corresponding times. This approach proves particularly useful either when dynamics and/or perturbations are difficult to model (e.g., solar pressure depending on solar activities and attitude) or when unpredictable events (e.g., pipe leak) make the expected dynamics model inaccurate. To validate the proposed approach, comparison with Iterative Batch Least Squares and Extended Kalman Filter is provided for three segments of a cislunar trajectory. The basic inspiration for this method comes from the observation that Gooding’s initial orbit determination method 3 provides, in general, better performances than most alternative methods. This is because Gooding’s method is based on the Lambert problem, which is a known Two-Point Boundary Value Problem (TPBVP), while most of the other methods fall into the Initial Value Problem (IVP) category. In general, IVP’s are easier to solve than TPBVP’s, but the solutions are usually more sensitive to uncertainties in the data. This is because to solve an IVP all * PhD Graduate Student, 301B Reed McDonald, Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141. E-mail: f.de.dilectis@neo.tamu.edu † Professor, 746C H.R. Bright Bldg, Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, AAS Fellow, AIAA Associate Fellow. E-mail: mortari@tamu.edu ‡ GN&C Autonomous Flight Systems Engineer, Aeroscience and Flight Mechanics Division, EG6, 2101 NASA Parkway. NASA Johnson Space Center, Houston, Texas 77058. AIAA Senior Member. 1 of 12