Restore relative spaceship trajectory during approacing to the space station using mathematic model

The paper considers the problem of reconstructing the trajectory of a spacecraft when docked to an orbital station in the associated coordinate system of the orbital station. The trajectory of the spacecraft movement relative to the orbital station is restored by reconstructing the trajectory of the spacecraft and the orbital station in the Greenwich coordinate system using parametric mathematical models. The movement of the orbital station is considered unperturbed, the movement of the spacecraft is corrected using a series of impulses. The paper proposes an original parametric mathematical model of the perturbed motion of a spacecraft, in which the perturbing acceleration of an impulse is specified by a piecewise constant vector function, the impulse values are refined parameters. Refinement of the parameters of mathematical models is carried out according to the data of autonomous navigation systems installed on the spacecraft and orbital station, using the least squares method. The proposed algorithm and the developed software were used to analyze the rendezvous trajectories at seven docks of the Soyuz and Progress spacecraft with the International Space Station, the paper presents the reconstructed trajectories and estimates the error.