Cameras are used as position sensors for camera-based control or metrology, the goal being to estimate the position of some markers or features. When one of these markers has significant displacement over the exposure time, the measurement delivered by image processing cannot be considered as a sample of the actual trajectory as dynamic effects become effective. In this paper, models are proposed that allow to reproduce accurately the measurements provided by a camera. Various cases are considered: with full or partial exposure time; with global shutter mode or rolling shutter mode. An experimental evaluation in the global shutter case shows the accuracies of the models. When the continuous-time trajectory of a device needs to be reconstructed, these accurate models of the camera-based position measurement can be used in order to improve the trajectory provided by the camera. A methodology based on a hybrid Kalman filter is proposed to solve this general issue. An experimental evaluation is provided for the global shutter case, based on real images inspired from the problem of heart motion reconstruction.