Reconstructing a three-dimensional (3D) object from a set of its two-dimensional (2D) X-ray projections requires that the source position and image plane orientation in 3D space be obtained with high accuracy. We present a method for estimating the geometrical parameters of an X-ray imaging chain, based on the minimization of the reprojection mean quadratic error measured on reference points of a calibration phantom. This error is explicitly calculated with respect to the geometrical parameters of the conic projection, and a conjugate gradient technique is used for its minimization. By comparison to the classical unconstrained method, better results were obtained in simulation with our method, specially when only a few reference points are available. This method may be adapted to different X-ray systems and may also be extended to the estimation of the geometrical parameters of the imaging chain trajectory in the case of dynamic acquisitions.