A Centroiding Algorithm for Point-source Trails

Astrometric measurements are significantly challenged by the relative motion between the point source and the telescope, primarily due to the difficulty in accurately determining the position of the point source at the mid-exposure moment. Especially when the trail is irregular in shape or results from nonuniform relative motion, determining the centroid of such a trail becomes significantly more challenging. To address this issue, a new centroiding algorithm for point-source trails has been developed. This algorithm employs a piecewise linear model to approximate the irregular trajectory of a point source. An estimated intensity distribution of the trail is constructed by integrating the point-spread function with the approximated trajectory. The cost function is defined as the difference between the estimated and observed trail intensity distributions, with an added smoothness constraint term. Optimizing this cost function yields a refined trajectory fit. A coarse-to-fine iterative approach is used to progressively converge on the true trajectory of the point source, ultimately determining both the trail's centroid and the trajectory of the point source. The efficacy of the algorithm is validated using synthetic images. Furthermore, this technique is applied to Cassini Imaging Science Subsystem images of several inner Saturnian satellites, successfully processing 267 astrometric observations. The results demonstrate the effectiveness of the algorithm in real astronomical applications.