Industrial Automatic Control Systems and Controllers Annotation << Back Numerical Integration Method for Error Estimation of Centroid Coordinates Detection in Star Trackers Emanov D.V. One of the key algorithms in a star tracker, which also introduces significant error, is the centroiding algorithm used on point sources of stars in the image obtained from the sensor. The image of a star on the image sensor plane forms an Airy pattern with negligibly faint rings, covering a certain number of pixels. Typically, for more accurate centroid determination, the size of the Airy pattern is several times larger than the size of a single pixel. Under certain assumptions, it becomes possible to estimate the distribution of accumulated charges in the sensor pixels by integrating the intensity of the Airy pattern. This distribution directly affects the performance of centroiding algorithm, and the case of greatest interest for error estimation is when the center of the Airy pattern lies between pixels. The integral of the Airy pattern intensity is easily computed in polar coordinates; however, in this form, it is inconvenient for working with pixels, which are naturally described in Cartesian coordinates. To estimate the intensity integral over a single pixel which is offset from the center of the Airy disk, a numerical integration method was developed, allowing computation of this integral over a rectangular area in Cartesian coordinates. The method was shown to have linear convergence. Thus, it becomes possible to assess the influence of the Airy disk size and its displacement relative to the pixel grid on the error in determining star centroid coordinates. This, in turn, helps refine the requirements for the optical system and the image sensor of the star tracker. Keywords: Star tracker, astrometry, centroid detection, Airy disks, numerical integration. DOI: 10.25791/asu.6.2025.1593 Pp. 45-49.