GPS satellite state vector determination in ECI coordinate system using the civil navigation message

A closed form of an algorithm to determine a Global Positioning System (GPS) satellite's position, velocity and acceleration is proposed, and an Earth Centred Earth Fixed (ECEF) to Earth Centred Inertial (ECI) transformation result using the Civil Navigation (CNAV) message is presented in this paper. To obtain the closed form of the GPS satellite velocity and acceleration determination algorithm using the CNAV, we analytically differentiated the IS-GPS-200F position determination function. The calculated data are transformed from the International Terrestrial Reference Frame (ITRF) to the Geocentric Celestial Reference Frame (GCRF) using an equinox-based transform algorithm that is defined in the IAU-2000 resolution system using the Earth Orientation Parameter (EOP) data. To verify the correctness of the proposed velocity and acceleration determination algorithm, the analytical results are compared to the numerical result. The equinox-based transformation result is compared to simple rotation about the z-axis, which does not use the EOP. The results show that by using the proposed algorithm and the equinox-based transformation together, the user can obtain more accurate navigation data in the ECI frame.