High Precision GPS IIR Orbit Prediction using Analytical Non-conservative Force Models

The geodesy research group at University College London has developed a suite of generalised non-conservative force modelling tools. These tools model the response of a satellite to: solar radiation pressure, anisotropic thermal re-radiation, forces due to radiation both reflected and emitted by the Earth (termed albedo/long wave infrared effects), and the force effects due to the transmission of the microwave navigation signals. In addition, the variation in the incident radiation flux as the satellites pass through the penumbra is modelled. The modelling techniques are designed to deal with realistic, complex satellite structures without any geometrical simplification required in the model computation process. The tools can be applied to any satellite. The solar radiation pressure and thermal re-radiation modelling tools have been described in earlier papers. This paper gives a detailed description of the albedo/IR techniques and the signal transmission force effects. The complete suite of tools has been applied to the GPS Block IIR satellite. All these forces are shown to have a significant effect on the satellite trajectory and can be modelled successfully a priori. To assess the force model accuracy the orbits of GPS Block IIR satellites are predicted and then compared to the post-processed precise orbits, which are used as a truth model. The orbit predictor employs an 8th order embedded Runge-Kutta integrator with adaptive step-size control. High order GRACE gravity field coefficients are used, generating the associated Legendre polynomials with a numerically stable recursive formulation. Other effects modelled are general relativistic forces, third body accelerations due to the Sun, the Moon, Mars, Venus, Jupiter and Saturn, as well as tidal variations to the Earth gravity field. International Earth Rotation Service conventions are used to compute frame transformations. Custom models for the various non-conservative effects are included, showing how each one gradually forces the predicted trajectory to converge with the truth model. Results are presented using one month of GPS Block IIR data, predicting 12-hour trajectories for all satellites for which a precise orbit is available. Over twelve hours the RMS difference between the predicted orbits and the precise versions is shown to be 0.18m in height, 0.09m across track and 0.59m along track, without rejecting any data on a statistical basis, and without applying any empirical parameters. Empirical estimation of initial conditions is applied, finally, and results are presented showing the expected convergence with the precise trajectories.