Efficiency of the piecewise constant acceleration modeling - GOCE case study

One of the valuable products of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is a centimeter-accuracy orbit of the GOCE satellite called the precise science orbit (PSO). This orbit, delivered by the European Space Agency (ESA), was the reference for the GOCE orbit modeling using the piecewise constant acceleration approach. Besides initial conditions, the piecewise constant accelerations (i.e. empirical accelerations) were estimated in the radial, along-track and cross-track direction, employing the dedicated package called Torun Orbit Processor (TOP). The TOP software is based on the classical least squares adjustment including the Cowell 8-th order numerical integration for an orbit prediction and the orbit improvement module, taking into account the gravity field model and the background models (BM) describing gravitational and non-gravitational perturbing forces. The positions of GOCE satellite on the reduced-dynamic PSO orbit were treated as observations in the orbit improvement process. A measure of the fit of estimated arcs and their accuracy was the RMS of the residuals between the estimated orbits and the corresponding reference ones. Different variants of the orbit estimation were obtained for the shorter  arcs (22.5, 45, 90 and 180 minutes)  and for the longer 1-day arcs. The solution variants were determined for different numbers of the estimated piecewise constant accelerations. Moreover, these numbers were different for the radial, along-track and cross-track direction. The obtained solutions depend on a kind of computational mode – with and without the BM models in the GOCE orbit modeling using the estimated piecewise constant accelerations. Additionally, for selected solutions, the distributions of the residuals in the aforementioned directions along the estimated arcs are presented.