Realtime GPS Orbital Velocity and Acceleration Determination in ECEF System

J. Zhang, K. Zhang, R. Grenfell, R. Deakin

Abstract:	The determination of velocity and acceleration of GPS satellites in the Earth-Centre-Earth-Fixed (ECEF) reference frame is vitally important for many dynamic applications where GPS satellites are used as known moving signal sources in space. However, satellite position, velocity and acceleration (PVA) are represented in terms of orbital parameters broadcast by the GPS satellites in their navigation message known as the broadcast ephemeris, not directly in the ECEF system. The transformation of velocity and acceleration from the orbital plane system to the ECEF system involves a set of coordinate system rotations. However, existing literature on velocity transformation from orbital plane to ECEF is incorrect in claiming that the same rotation matrices as for a position transformation should be applied, while no literature has been found dealing with the acceleration transformation. This paper derives the formulae, which consider the first and second derivatives of the rotation matrix (with respect to time), for transforming GPS velocity and acceleration from the orbital plane to the ECEF coordinate system directly by using the broadcast ephemeris. The new formulae have been numerically tested and analysed by comparison with the precise SP3 ephemeris, and the velocity and acceleration derived by the satellite positions obtained from the broadcast ephemeris respectively. A practical algorithm for ECEF velocity and acceleration determination is then proposed. With the removal of Selective Availability (SA), the proposed methods can be used in real-time applications for velocity and acceleration determination.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	1288 - 1296
Cite this article:	Zhang, J., Zhang, K., Grenfell, R., Deakin, R., "Realtime GPS Orbital Velocity and Acceleration Determination in ECEF System," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 1288-1296.
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