Accuracy of Numerical Algorithms for Satellite Orbit Propagation and Gravity Field Determination

The orbit determination process, such as that used for the Gravity Recovery and Climate Experiment, known as GRACE, is highly dependent upon the comparison of measured observables with computed values, derived from mathematical models relating the satellites’ numerically integrated state to the observable. Significant errors in the computed state corrupt this comparison and induce errors in the least-squares estimate of the satellites’ states, as well as the gravity field. Due to the high accuracy of the intersatellite ranging measurements from GRACE, numerical computations must mitigate errors to maintain a similar level of accuracy. One error source is the presence of roundoff errors in the computed intersatellite range-rate when integrating continuous, smoothly varying accelerations with double-precision arithmetic. These errors occur at approximately 8 pm/s root mean square and limit the accuracy of numerically integrating background gravity field models to degrees/orders 260 and 410 for satellite pairs flying at altitudes of 500 and 300 km respectively. In addition, the integration of filtered, transient accelerations, which occur on timescales much smaller than the integration step size, induce errors at an approximately 10 nm/s in range-rate, becoming a limitation as more advanced intersatellite measurement techniques approach this level of accuracy.