Taking into account the lens geometric distortion during accumulation of blurred star images in an astro-inertial attitude sensor

In this work, when calculating the star blur trajectory, geometric distortion in the accumulated images is taken into account in two ways: analytical and numerical. The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. The numerical approach uses a model of reverse distortion correction that converts points of a trajectory calculated in the ideal image plane into the image plane with distortion. This approach makes it possible to preserve the structure of the subpixel accumulation and star detection algorithms previously obtained for an ideal image. An example of allowing for the radial distortion parameters obtained by calibrating a real camera is given.