Mathematical modeling of velocity and accelerations fields of image motion in the optical equipment of the Earth remote sensing satellite

Objectives. The paper considers a satellite with an optoelectronic payload designed to take pictures of the Earth’s surface. The work sets out to develop a mathematical model for determining the dependencies between the state vector of the satellite, the state vector of the point being imaged on the Earth’s surface, and the distribution fields of the velocity vectors and accelerations of the motion of the image along the focal plane of the optoelectronic payload.Methods. The method is based on double differentiation of the photogrammetry equation when applied to a survey of the Earth’s surface from space. For modeling the orbital and angular motion of the satellite, differential equations with numerical integration were used. The motion parameters of the Earth’s surface were calculated based on the Standards of Fundamental Astronomy software library.Results. Differential equations of motion of the image were obtained. Verification of the developed mathematical model was carried out. The motion of the considered satellite was simulated in orbital orientation mode using an image velocity compensation model. The distribution fields of velocity vectors and accelerations of motion of the image of the Earth’s surface were constructed. The residual motion of the field of image following compensation was investigated.Conclusions. The proposed mathematical model can be used both with an optoelectronic payload when modeling shooting modes and estimating image displacements at the design stage of a satellite, as well as at the satellite operation stage when incorporating the presented model in the onboard satellite software. The presented dependencies can also be used to construct an image transformation matrix, both when restoring an image and when obtaining a super-resolution.