Robust Initial Orbit Determination Using Streaks and Admissible Regions

A novel, empirically-validated method for robust initial orbit determination from two or more observations of an object’s angles and angle rates is presented. The method can be applied for all orbital regimes including those where traditional methods, such as Gauss and double-r, fail. It also works for all times-of-flight to produce the corresponding set of feasible orbit solutions using admissible regions. The method uses a cost function that has a unique non-trivial zero at the correct orbit solution for the single revolution case and a set of zeros for the multi-orbit case. Applying admissible regions to both observations allows the state space to be further constrained with a corresponding improvement to the computational efficiency. The proposed method overcomes the shortcomings of many traditional initial orbit determination methods and has been empirically verified to find solutions to cases well-approximated by two-body dynamics. Furthermore, this work includes a comparison of the proposed and existing methods for initial orbit determination to highlight the domains that the various methods excel. While the global optimizer approach of the proposed method sacrifices computation time in comparison to the single iteration of the previously established methods, it consistently converges to the correct solution or set of possible solutions independent of the orbital regime.