The paper addresses a problem of ballistic object tracking with the use of the cinetheodolite electro-optical tracking system. Electro-optical systems are applied for acquiring the trajectory data of missiles, satellites, and rockets used for delivery of satellites to their prevised orbits. Despite the importance of such systems and their applications, in the open literature there are no publications describing tracking algorithms processing data from cinetheodolites. The paper describes a model-based algorithm of estimation of position and parameters of target motion for such a system, developed by the authors. The model of the system, nonlinear both in its description of the target dynamics and the measurement equations, is presented in detail. The proposed algorithm of estimation is also described, and chosen simulation results are included in the paper. Furthermore, a comparison of the proposed estimation algorithm with other possible, but simpler algorithms is presented.