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Collinearity equations provide an essential basis for photogrammetry applications in which the observables in the image and object spaces are related within an imaging system. It has been routine practice to determine the exterior orientation parameters in these equations using observed control points. However, due to the nonlinearity of the collinearity equations, an appropriate set of approximate values for the orientation parameters must be previously given in order to initiate the parameter estimation procedure and result in a converged solution. In this letter, a quick algorithm for determining the orientation parameters is proposed based on the newly developed noniterative solutions to linear transformations technique. This algorithm does not require auxiliary attitude information (e.g., from inertial navigation system (INS) measurements or trajectory data), and a direct solution for the orientation parameters can be obtained using a closed-form expression. It is then demonstrated, in a real case study, that the proposed approach is capable of producing a set of orientation parameter estimates with a sufficient level of quality to support rigorous image analyses.