Radiotherapy aims to strike a tumour with high accuracy, but anatomic changes and internal organ motion introduce uncertainties and therefore large margins are conventionally used to compensate for this. The MR-Linac will enable target tracking prior to and during treatment which will make daily adjustments of a treatment plan possible. But a motion tracking of the target requires fast 3D imaging and image processing which are currently not viable with sufficiently low latency. In this project a method to estimate the motion of a target by using a parameterized motion model created prior to treatment and a stream of 2D images acquired during treatment was studied. The motion model had been parameterized by using principal component analysis (PCA). The 2D images were aligned to the corresponding images in the motion model through deformable image registration which resulted in a deformation field. Then new parameters (eigenmode weights) of the motion model were calculated by taking the projection of the deformation field on a vector space spanned by the eigenmodes of the PCA motion model. An estimation of the motion was then created by applying the new weights to the PCA motion model. The results were evaluated by visual comparison and with quantitative metrics such as the Dice similarity coefficient. The method was applied to data from 9 volunteers and the results confirmed that the proposed method can estimate the motion of a target and indicated that it is most suitable for volunteers with large intra-fraction motion. The results also showed that the temporal resolution of the motion model can be increased by using 2D images of lower spatial resolution. The created motion model can be used for many clinical applications like retrospectively calculating the accumulated doses in the tumour and the organs-at-risk and potentially could be used for real-time target tracking.