On real-time high precision velocity determination for standalone GPS users

The NAVSTAR Global Positioning System (GPS) is a satellite-based radionavigation system designed for positioning, velocity determination and timing. The relative movement between a GPS receiver and a GPS satellite causes the received signal frequency to differ from the transmitted frequency due to the Doppler effect. This frequency difference, an observable in GPS measurements, is referred to as the Doppler shift. However, the Doppler shift is biased by the inherent errors in the signal propagation. Since velocities of GPS satellites are known, the velocity of a user can be determined through observing four or more satellites, similar to GPS positioning. When the GPS selective availability (SA) was activated, errors imposed on the ephemeris and satellite clocks significantly affected the accuracy of both GPS positioning and velocity determination. The removal of SA has enabled a significant improvement on the accuracy of both GPS satellite orbits and clocks. As a result, velocity accuracy at sub-centimetre per second level is achievable for standalone GPS users if all the errors associated with the Doppler observables are corrected for properly. This paper overviews the developments in precise velocity determination and investigates all error sources associated with the Doppler measurement. The properties of errors in the Doppler shift are analysed and the methods to eliminate or mitigate these errors are discussed. The relativistic errors such as the orbit eccentricity and the Sagnac effect are derived and formulated in easy forms for correction. Algorithms for modelling the atmosphere delay rates are also presented. It is concluded that real-time velocities in millimetres per second level are achievable if the error correction schemes provided are used.