The precise orbit of a satellite is determined from the exact position and velocity estimated by the dynamic solution obtained from the motion differential equation of a satellite in the inertial space satisfying the Newton second law and by the data measured by some means such as on-board GPS. Because the dynamic solution is from GCRF and the measurement data is from ITRF, coordinates transformation is needed. Therefore, the uncertainty of the coordinates transformation affects the accuracy of position determination of satellites.
Precise ITRF/GCRF transformation is generally conducted using the earth originate parameter (EOP) provided by international earth rotation service (IERS). EOP data is updated every day. ITRF/GCRF transformation methods using the EOP data are classified into the classical equinox-based method and the modern CIO-based approach.
The latter is simpler in procedure than the former as it needs neither ecliptic nor equinox, and it is considered as a suitable method for improving the calculation speed as it can tabulate data necessary for coordinates transformation.
CIO-based approaches include precise theory method, series method and numerical interpolation method. The method using the series can improve the calculation speed by decreasing the order of the series, but it degrades the accuracy of coordinates transformation. Therefore, necessary data in the astrodynamics calculations are tabulated and interpolated to improve the calculation accuracy and speed.
Cha Pong Il, a section head at the Faculty of Aerospace Engineering, proposed a method for reducing the calculation time in precise ITRF/GCRF transformation and verified its effectiveness through simulation.
The simulation results show that the calculation time by the classical equinox-based method is equal to about 195s, while the time by the precise theory method is about 98s, but the numerical interpolation method maintains its accuracy with the calculation time of less than 1s. It means that the numerical interpolation method decreases calculation load and improves calculation speed significantly.
If further information is needed, you can refer to his paper “A Method for the Reduction of the Calculation Cycle in Precise ITRF/GCRF Transformation using the Numerical Interpolation Technology” in “Proceedings of KUTIC-2025”.