Short-Arc orbit improvement for GPS satellites
Over the past four years, different research groups involved in the application of the Global Positioning System (GPS) have investigated the possibility of solving for a combination of dynamical and orbital parameters, along with the station coordinates, in order to obtain geodetic solutions below the 1 –ppm relative accuracy level over large networks. It has been shown, using the GPS carrier phase that this modelling can yield solutions at the 0.1 –ppm level or below. These results have been obtained using orbital arcs modelling varying in length from 1 to 6 days. The scope of this thesis is to develop and demonstrate that a similar procedure over orbital arcs of about 6 to 8 hours can yield results of the same level of accuracy over large networks. We implemented out algorithm in the University of New Brunswick GPS software DIPOP 2.0 to demonstrate some results. First, a numerical integrator was developed in order to generate short-arc a priori trajectories (up to 8 hours) rigorously related to the initial satellite state vectors. A force model including the earth’s gravitational potential up to degree and order 10, the luni-solar gravitational perturbation and a simple solar radiation pressure model have been implemented. Afterwards, Keplerian motion is used, in the final least-squares adjustment, to approximate the partial derivatives with respect to the initial conditions. Our orbit modelling was tested with a subset of the T1 4100 data from the Spring 1985 High Precision Baseline Test (HPBT) campaign (including baselines up to 4000 km). Free-network as well as fiducial network solutions as well as the daily-network solutions are at the 0.1 –ppm relative accuracy levels. Over shorter baselines, the repeatability is at the 0.25 –ppm level. To further assess the quality of the improved orbit, a pure orbit solution was performed in order to produce a set of improved initial conditions. Short-arc orbits are then numerically integrated from these improved state vectors, which in turn are used to solve a long and a shirt baseline vector. The relative accuracy of these solutions is at the same level as the previously stated accuracies. These results really demonstrate that the Keplerian approximation used to compute the partial derivatives with respect the satellite initial state vectors is well justified when short-arc approach is used.