The task of angular orientation and stabilization of a space structure during its assembly in orbit is solved. The structure includes elastic elements that are installed during the assembly process. The elastic elements of the structure have no sensors to obtain information about their deformation parameters. Control algorithms are proposed to ensure the stability of the angular motion of the structure. A nonlinear extended Kalman filter is used to obtain the necessary information. A joint estimation algorithm for the coordinates of the angular motion of the considered mechanical system and the coordinates of the elastic vibration tones, as well as an algorithm for the identification of their unobservable parameters are developed. The results of mathematical modeling of a variant of the mechanical system of a space structure are presented, which confirm the operability and efficiency of the developed algorithms for estimating coordinates and parameters.