Gps Hdjsf Jfkskfjdlff'Fg'F

J Geod (2006) 80: 104–110 DOI 10.1007/s00190-006-0038-8

O R I G I NA L A RT I C L E

Jason Zhang · Kefei Zhang · Ron Grenfell · Rod Deakin

Short note: On the relativistic Doppler effect for precise velocity determination using GPS

Received: 8 March 2005 / Accepted: 19 February 2006 / Published online: 21 March 2006 © Springer-Verlag 2006

Abstract 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 receiversatellite 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. Keywords GPS velocity determination · Doppler shifts · Doppler effects · Relativistic Doppler effects · Gravitational potential · Satellite orbit

1 Introduction For high-accuracy velocity determination, GPS satellites are taken as known moving signal sources from which a GPS

J. Zhang · K....