An approximate second-order nonlinear closed-form solution for three-dimensional relative motion assuming Keplerian dynamics and a circular reference track has been applied to the relative initial orbit determination problem recently with promising results. In that work, several solution strategies have been offered including a nonlinear formulation that solves the original measurement equations without exploiting their polynomial structure and an equivalent linear formulation with equality constraints based on eigen decomposition concepts. Consideration of a new solution strategy based on the intersection of quadratic surfaces in a hexa-dimensional space for the relative initial orbit determination problem is the subject of this paper. The polynomial measurement equation structure in terms of the unknown initial relative position and velocity states is shown to be second-order surfaces in the six-dimensional state space, and their intersection corresponds to the relative orbit determination solution. These equations are then reformulated as a single resultant polynomial equation, which can also be solved with eigen decomposition concepts. Numeric examples are presented to assess the performance of the new solution strategy and to compare against the previously offered solution strategies. The intent of the study is to expose and discuss any significant similarities and/or differences in the relative orbit determination solution techniques.
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