In conventional tomography, the interior of an object is reconstructed from tomographic projections such as X-ray or electron microscope images. All the current reconstruction methods assume that projection geometry of the imaging device is either known or solved in advance by using e.g. fiducial or non-fiducial feature points in the images. In this paper, we propose a novel approach where the imaging geometry is solved simultaneously with the volume reconstruction problem while no correspondence information is needed. Our approach is a direct application of Bayesian inversion theory and produces the maximum likelihood or maximum a posteriori estimates for the motion parameters under the selected noise and prior distributions. In this paper, we experiment the approach with synthetic and real data where 1D affine projections are assumed; this is also often a sufficient assumption since the reconstruction problem is frequently performed as a stack of 2D problems for computational reasons. However, the method can be directly extended to the general, projective 3D case which is left for the future research.