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.

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The Doppler Effect is the apparent shift in frequency of an electromagnetic signal that is received by an observer moving relative to the source of the signal. The Doppler frequency shift relates directly to the relative speed between the receiver and the transmitter, and has thus been widely used in velocity determination. A GPS receiver-satellite pair is in the Earth's gravity field and GPS signals travel at the speed of light, hence both Einstein's special and general relativity theories apply.This paper establishes the relationship between a Doppler shift and a user's ground velocity by taking both the special and general relativistic effects into consideration. A unified Doppler shift model is developed, which accommodates both the classical Doppler Effect and the relativistic Doppler Effect under special and general relativities. By identifying the relativistic correction terms in the model, a highly accurate GPS Doppler shift observation equation is presented. It is demonstrated that in the GPS "frequency" or "velocity" domain, the relativistic effect from satellite motion changes the receiver-satellite line-of-sight direction, and the measured Doppler shift has correction terms due to the relativistic effects of the receiver potential difference from the geoid, the orbit eccentricity, and the rotation of the Earth.

Abstract. This paper introduces two sport-related projects conducted by the Satellite Positioning and Orientation Research Team (SPORT) at RMIT University -the speed sailing world record challenge and development of a smart GPS rower tracking system. In the first project, both traditional and contemporary surveying technologies are investigated to assist the Macquarie Speed Sailing Team to reliably record and subsequently claim a world speed sailing record. In the second project, an integrated rower tracking system has been developed in collaboration with other research partners and the system has been used prior to and during the Athens Olympic Games. Three Olympic rowing medals were won by Australia. The technology, research procedures and major developments are presented.