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A new computer vision based method for estimating the position and orientation of a spacecraft (camera) relative to a fixed mark on the space station in three-dimensions is developed. This method represents an extension of our previous work where orientation estimation was not considered; the requirement to maintain the axial axis of the camera pointed at the center of the mark on the space station, inherent in our previous work, is eliminated. A system of eight nonlinear measurement equations with two constraints in the unknown position and orientation parameters is obtained. Either a single stage nonlinear constrained optimization algorithm or a two-stage nonlinear least squares estimation algorithm can be used to obtain position and orientation estimates simultaneously. The development assumes noisy measurements of four feature points of the single mark on the space station.