100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Relativity in the Global Positioning System 275It may now be too late to reverse this decision because of the investmentthat many dozens of receiver manufacturers have in their products. However,it does mean that receivers are supposed to incorporate the relativitycorrection; therefore, if appropriate data can be obtained in raw form froma receiver one can measure this effect. Such measurements are discussednext.6. TOPEX/POSEIDON Relativity ExperimentAt present, the frequencies of atomic clocks in replacement satellites arecarefully measured after launch and then adjusted to the frequency thatis required for operation. The largest remaining effect is the eccentricityeffect, Eq. (33). It is intended that GPS receivers correct for this effect, soa receiver that can output data on transmission and reception events canbe used to test whether the relativistic prediction agrees with experiment.The TOPEX satellite carries a six-channel receiver with a very good quartzoscillator to provide the time reference, and is in an orbit of radius 7,714km and period 6745 seconds. The receiver motion is highly dynamic, as itpasses under the GPS constellation eleven times per day. A stringent testof the relativistic prediction can therefore be performed.The local quartz clock, which is a free-running oscillator subject to variousnoise and drift processes, can be in error by a large amount. So thefirst task is to determine the local clock time in terms of GPS time. Forthis purpose the six available channels in the receiver provide considerableredundancy. The trajectories of the TOPEX and GPS satellites were determinedindependently of the on-board clocks, by means of Doppler trackingfrom ≈ 10 2 stations maintained by the Jet Propulsion Laboratory (JPL).Generally, at each time point during the experiment, observations were obtainedfrom six (sometimes five) satellites. There is sufficient redundancyin the measurements to obtain good estimates of the TOPEX clock timeand the rms error in this time due to measurement noise.The rms deviation from the mean of the TOPEX clock time measurementsis plotted in Figure 3 as a function of time. The average rms erroris 29 cm, corresponding to about one ns of propagation delay. Much of thisvariation can be attributed to multipath effects–multiple reflections of thesignals from objects in the neighborhood of the receiver’s antenna.With the local TOPEX clock time determined in terms of GPS time,the eccentricity effect from some GPS satellite clock of interest can bedetermined by using five of the receiver channels to determine the TOPEX