GPS Satellite Velocity and Acceleration Determination using the Broadcast Ephemeris

Satellite velocity determination using the broadcast ephemeris is discussed and it is pointed out that the conventional rotation matrix method involves a complicated process of computation. This paper proposes an alternative method using a simple differentiator to derive satellite Earth-Centred-Earth-Fixed (ECEF) velocity from the ECEF satellite positions that are calculated using the standard ICD-GPS-200 algorithm. The proposed algorithm simplifies the velocity transformation procedure, and therefore provides a good alternative. It is demonstrated that ±1 mm/s per axis ECEF satellite velocity is achievable by using the first-order central difference of a Taylor series approximation.

A closed-form formula is also derived for the determination of GPS satellite ECEF acceleration using the broadcast ephemeris. This formula is capable of accuracies better than ±0·1 mm per second squared in each axis. With such a high accuracy of satellite acceleration in real-time, it is possible to detect the line-of-sight range acceleration precisely and as such it is concluded that a GPS receiver can be considered as a precise accelerometer.

The success of the position differential method implies that real-time satellite ECEF velocities can be directly derived through numerical differentiation of the position polynomials. This is desirable for GPS velocity determination applications which require high output rate results in real-time. The derived closed-form formula for GPS satellite ECEF acceleration would benefit those who attempt to use a GPS receiver as an accurate accelerometer in real-time.