The velocity of a GPS satellite in an Earth inertial frame is high enough that it will significantly affect the precision of position determination. Haustein (2009) indicated if these effects were neglected, an error of 12 km per day for position determination or 39 μs for time determination would occur. Three primary effects of the relativity on GPS are:

References

Ashby N (1995) "Relativistic Effects in the Global Positioning System."

Haustein, M (2009) "Effects of the Theory of Relativity in the GPS."

O’Keefe, K (2000) "Relativity and GPS,Lead Discussion - Fall 2000."

__Fixed Frequency Offset Effect__- There is a fixed frequency offset in the satellite’s clock rate when observed from Earth. Most of the effect is purposely removed by slightly offsetting the satellite clock in frequency prior to launch (O'Keefe, 2000).__Sagnac delay__- The Sagnac effect arises from the rotation of the Earth during the GPS signal propagation. The Sagnac effect is a correction for adapting the dilation of time caused to a clock carried by a rotating object on non-inertial frames (Ashby, 1995). This relates to the fact that a moving clock tends to be slower than one at rest or moving slower. This results in a frequency offset that may be interpreted as a distance (ICD-GPS-200, 2000).__Periodic Clock Error Effect__- The GPS satellite orbit is not truly circular. The slight eccentricity of each satellite orbit causes an additional periodic clock error that varies with the satellite position in its orbital plane. This correction must be applied to the broadcast time of the signal transmission (Ashby 1995). This additional effect is cancelled on the case of double-differencing, while it would bring a maximum of 23 ns for an eccentricity of 0.01 to single point positioning, an equivalent to 6.9 metres in distance (O'Keefe, 2000).References

Ashby N (1995) "Relativistic Effects in the Global Positioning System."

*Journal of Systems Engineering and Electronics,*Vol. 6, No. 4, pp. 199-237.Haustein, M (2009) "Effects of the Theory of Relativity in the GPS."

*Chemnitz University of Technology.*http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf Accessed: 2013.O’Keefe, K (2000) "Relativity and GPS,Lead Discussion - Fall 2000."

*University of Calgary.*http://people.ucalgary.ca/~kpgokeef/pubs/ENGO625relativity.pdf Accessed: 2013.