Stochastic noise modelling of kinematic orbit positions in the Celestial Mechanics Approach

Abstract

Gravity field models may be derived from kinematic orbit positions of Low Earth Orbiting satellites equipped with onboard GPS (Global Positioning System) receivers. An accurate description of the stochastic behaviour of the kinematic positions plays a key role to calculate high quality gravity field solutions. In the Celestial Mechanics Approach (CMA) kinematic positions are used as pseudo-observations to estimate orbit parameters and gravity field coefficients simultaneously. So far, a simplified stochastic model based on epoch-wise covariance information, which may be efficiently derived in the kinematic point positioning process, has been applied. We extend this model by using the fully populated covariance matrix, covering correlations over 50 min. As white noise is generally assumed for the original GPS carrier phase observations, this purely formal variance propagation cannot describe the full noise characteristics introduced by the original observations. Therefore, we sophisticate our model by deriving empirical covariances from the residuals of an orbit fit of the kinematic positions. We process GRACE (Gravity Recovery And Climate Experiment) GPS data of April 2007 to derive gravity field solutions up to degree and order 70. Two different orbit parametrisations, a purely dynamic orbit and a reduced-dynamic orbit with constrained piecewise constant accelerations, are adopted. The resulting gravity fields are solved on a monthly basis using daily orbital arcs. Extending the stochastic model from utilising epoch-wise covariance information to an empirical model, leads to a – expressed in terms of formal errors – more realistic gravity field solution.