From pure kinematical to reduced kinematical LEO orbit determination

Abstract

The geometrical point-wise satellite positions can be derived by GNSS analysis techniques. The different precise point positioning techniques based on GNSS observations will be designated as geometric orbit determination methods. In the geometrical determined LEO orbit, there is no connection between subsequent absolute positions, and consequently, no information about the velocity or even the acceleration (or in general kinematical information) of the satellite is available. To describe the time dependency of the motion of a satellite, it is necessary to provide a properly constructed function which consistently connects positions, velocities and accelerations. In this investigation, a new approach is presented based on approximation parameters, which have also a clearly defined relation to the dynamical model of the satellite's motion. To realize this, the kinematical orbit is not only a continuous approximation of the orbit as it is observed by GNSS observations; it is also a solution of Newton's equation of motion of the satellite. If the kinematical parameters are determined by a best fitting process based on the observations, then we perform a pure kinematical orbit determination. If constraints based on the dynamical force function model are used then the reduced kinematical orbit of a LEO is realized. In this case, we carry out a reduced kinematical orbit determination of a specific level, depending on the strength of the dynamical restrictions. The various possibilities of the reduced kinematical orbit determination with the corresponding results of CHAMP based on GNSS observations will be presented.